bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Experiments in Nuclear Quadrupole Resonance
Authors: Velten James M. , Story Harold S.
Published: August 2005

Some experiments in nuclear quadrupole resonance suitable for the undergraduate laboratory or senior project are described. The Zeeman splitting of resonance lines and the effect of solid phase transitions may be readily observed with simple apparatus.
Physics-Mathematics Building at Kansas State University
Authors: Katz Robert
Published: August 2005

A building of about 134 000-sq ft area, containing research rooms, shops, store rooms, three lecture halls, classroom, and offices, for the Departments of Physics and of Mathematics has been completed at Kansas State University. Details concerning the construction, the provision of laboratory facilities, and special features of the building are given, as are floor plans and statements of costs involved.
Velocity of Sound in Air Using Schlieren Techniques
Authors: Spenceley Brian J. , Dakin Peter , Scott Kenneth F. N.
Published: August 2005

An undergraduate experiment is described in which Schlieren photographs are made of the sound waves produced by an electric spark. Electronic control of the time lapse between initiation of the sound pulse and the xenon flash tube illumination allows observation of the wavefronts at various stages of their progress through air or of their reflection from curved surfaces. A method of determining the velocity of sound in air is described.
Position of a Point in a Rotating Coordinate System
Authors: Silven Saul
Published: August 2005

This paper treats the problem of determining the position of a point with respect to a fixed reference frame when its motion is known in a rotating frame. The problem is solved by means of a linear vector differential equation.
Mixed States in Classical Mechanics
Authors: Rosen Nathan
Published: August 2005

It is pointed out that the nonlinear equation which corresponds to the Schrödinger equation in the classical limit, and which is equivalent to the Hamilton-Jacobi equation, has pure state solutions describing particle ensembles of a certain kind. These pure states may be combined to form mixed states corresponding to ensembles of a more general sort. An example is given in the case of reflection from a potential barrier. The existence of mixtures of states, without the superpositions like those in quantum mechanics, helps one to understand how a classical system can serve as a measuring instrument.
Resource Letter NMR-EPR-1 on Nuclear Magnetic Resonance and Electron Paramagnetic Resonance
Authors: Norberg R. E.
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters; supported by a grant from the National Science Foundation.

This is one of a series of Resource Letters on different topics, intended to guide college physicists to some of the literature and other teaching aids that may help them improve course contents in specified fields of physics. No Resource Letter is meant to be exhaustive and complete; in time there may be more than one letter in some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed. Such communications should be sent to Professor Arnold Arons, Chairman, Resource Letter Committee, Department of Physics, Amherst College, Amherst, Massachusetts.

Notation: The letter E after an item number indicates elementary level, useful principally for freshman liberal arts through sophomore physics courses; the letter I indicates intermediate (junior, senior) level; and the letter A indicates advanced material principally suited for senior, graduate study. An asterisk (*) indicates items particularly recommended for introductory study.

Additional copies: Available from American Institute of Physics, 335 East 45 Street, New York, New York 10017. When ordering request Resource Letter NMR-EPR-1 and enclose a stamped return envelope.
A Simple Treatment of Potential Barrier Penetration
Authors: Cohen Bernard L.
Published: August 2005

It is pointed out that the penetration of a particle through a potential barrier may be understood as a climb over the barrier during one of the energy fluctuations expected from the uncertainty principle, rather than as a “tunneling” under the barrier. A method of obtaining the quantitative result with this model is presented.
Zener-Diode-Regulated Direct-Current Power Supplies
Authors: Cleary J.
Published: August 2005

Direct-current power supplies with Zener-diode-output voltage regulation are considered in relation to their protection against short-circuiting of their output terminals. It is shown that increasing the input voltage and the series resistance for a given output voltage reduces the ratio of the short-circuit current to the normal load current, allowing the design of power supplies which will sustain prolonged shorting of their output terminals. Criteria for the optimum circuit values for protection are considered. Universal curves of the powers and currents in each part of the circuit are given as functions of the ratio of input to output voltage. The results are generally applicable to Zener diode and glow-discharge-regulator power supplies. The treatment is presented in some detail to emphasize the value of mathematical analysis of apparently simple problems. Brief results are given of measurements on a power supply employing the principles outlined.
Some Thoughts on Radiation Pressure
Authors: Tea Peter L.
Published: August 2005

The relationship between radiation pressure and radiant energy density is examined from the standpoint of photon energy and photon momentum, utilizing geometric optics.
Time Reversal in Heat Conduction
Authors: Masket A. V.
Published: August 2005

The mathematical consequences of assuming heat conduction (or diffusion of particles) in the same sense as the temperature (or concentration) gradient rather than in the opposite sense leads to time reversal in the partial differential equation and the possibility of computing a prior state of temperature from one known in the present. In spite of the similarity in mathematical form for the partial differential equation and solutions, a fundamental physical and mathematical distinction exists in this converse problem with respect to the initial condition permitted for the problem. All temperature distributions assumed as initial conditions fall into three classes with respect to the criterion of how far back in time the time reversal calculation can be carried ideally, but not necessarily in practice. In time reversal, the well-known Green's or Influence Functions become Deinfluence or Concentration or Accumulation Functions as suggested designations with quite different mathematical properties.
Physical Basis for Hund's Rule. II
Authors: Karayianis N.
Published: August 2005

A simple model is proposed that is useful for understanding the role played by the Coulomb interaction in determining the total orbital angular momentum of an atomic ground state. An example is given and some possible shortcomings of the model are discussed.
Three-Dimensional Isotropic Harmonic Oscillator and SU3
Authors: Fradkin D. M.
Published: August 2005

A consideration of the eigenvalue problem for the quantum-mechanical three-dimensional isotropic harmonic oscillator leads to a derivation of a conserved symmetric tensor operator, in addition to the angular momentum vector operator. Upon examining the classical limit, it is found that the symmetric tensor completely specifies the orientation of the elliptical orbit, in a way analogous to the Runge-Lenz vector for the Kepler problem. The tensor operator and the angular momentum vector operator are then related to the infinitesimal operators for the SU3 group.
A Refined-Tube Method for Measuring the Sound Wavelength in Gases
Authors: Hakeem A. S. El
Published: August 2005

A method for measuring the velocity of sound in a gas confined in a tube has been developed. The method is a refinement of the phase-measurement technique described by Lestz. Values of the velocity of sound in nitrogen and argon at one atmosphere and 70°F are presented to show the excellent agreement with the generally accepted values. The results also verify the tube-wall effects predicted by Helmholtz and Kirchhoff.
An Analytical Solution of the Inverted Pendulum
Authors: Phelps F. M. , Hunter J. H.
Published: August 2005

A rigorous solution of the inverted pendulum requires several mathematical techniques which are not in the repetoire of the typical student of classical mechanics at the senior level. However, the problem is tractable by Lagrange's equations and the physics of the situation is sufficiently simple so that it is an excellent example to use to extend the student's analytical abilities. Two unexpected dividends are derived from this problem: (1) the vertically driven case is an example of a time-dependent potential energy function, a rare situation in mechanics; (2) it is a vivid example of a classical system undergoing strong focusing and therefore can be used to introduce a discussion of the strong-focusing synchrotron.
A Scattering-Chamber Experiment for the Modern Physics Laboratory
Authors: Duggan Jerome L.
Published: August 2005

Many Van de Graaff accelerator-type experiments can be performed at modest and even low bombarding energies. In general, for incident particle energies below 150 keV, one is restricted to proton- or deuteron-induced reactions on light target nuclei. This restriction is, of course, due to the Coulomb barrier for most reactions in this energy interval. Several reactions which are feasible with existing equipment found in many universities throughout the United States and foreign countries are discussed. Necessary modifications to existing Cockcroft-Walton-type accelerators are outlined, and the general experimental procedures for reactions of the type C12(p,p) 12C and B11(p,α) 8Be are given.
Einstein's Proposal of the Photon Concept—a Translation of the Annalen der Physik Paper of 1905
Authors: Arons A. B. , Peppard M. B.
Published: August 2005

Of the trio of famous papers that Albert Einstein sent to the Annalen der Physik in 1905 only the paper proposing the photon concept has been unavailable in English translation. The American Journal of Physics is publishing the following translation in recognition of the sixtieth anniversary of the appearance of the original work. Physics teachers may take particular interest in the following aspects: (1) Einstein's keen awareness of the heuristic character of his new conception. (2) His demonstration from thermodynamic and statistical considerations that electromagnetic radiation might be conceived as consisting of finite numbers of discrete corpuscles of energy hv. (3) His prediction of the linear relation between the stopping potential of photoelectrons and the frequency of the incident light. This latter aspect of the photoelectric effect was not included among Lenard's early investigations. It remained for Millikan and others to develop the elegant experimental techniques that confirmed Einstein's bold prediction. Readers interested in pursuing the background in greater depth will find it rewarding to refer to the critical analyses by Martin J. Klein in “Einstein's First Paper on Quanta,” in The Natural Philosopher (Blaisdell Publishing Company, New York, 1963), Vol. II, and “Einstein and the Wave-Particle Duality,” in The Natural Philosopher, Vol. III, 1964. We are grateful to Professor Klein for his criticism and advice regarding this translation and for his generosity in making available to us an unpublished translation of his own.
A Further Note on an Extension of Euler's Theorem to Minkowski Space
Authors: Schwartz H. M.
Published: August 2005

This note supplements a previous note on the subject, and presents an alternative treatment, having independent interest, based on the infinitesimal transformations of the Lorentz group.
Error Analysis of Straight Line Plots in the Undergraduate Physics Laboratory
Authors: Safko John L.
Published: August 2005

A rapid error analysis of straight line plots can be performed in undergraduate laboratories by enclosing the data, in a parallelogram two of whose sides are parallel to the “best fit” line as determined by sight. Relatively little mathematical knowledge is needed for this method, so error analysis need not be ignored in elementary laboratories when straight line plots are made.
Curved Space and Gravitation. I
Authors: Brehme Robert W.
Published: August 2005

A connection is made between geodesics on a curved, two-dimensional space-time surface and the trajectories of objects falling freely in straight paths in time-independent gravitational fields. The treatment is presented on an elementary level, and the Einstein theory is not closely followed. Both geodesic motion and classical gravitation cause accelerations of objects which are not influenced by the intrinsic properties of the object. The acceleration for geodesic motionis velocity as well as position dependent, whereas for classical gravitation, the acceleration depends only on position. However, by the appropriate choice of scale, it is possible to approximate the classical trajectory with geodesic motion to any degree of accuracy. Geodesics on the sphere and cone are given as examples.
Refractive Index for Neutrons
Authors: Devaney Joseph J.
Published: August 2005

A simple derivation is presented for the quadratic index of refraction of scalar waves in a nonmagnetic medium.
Basic Concepts of Self-Consistent-Field Theory
Authors: Blinder S. M.
Published: August 2005

According to Hartree's self-consistent-field (SCF) model of the atom, the motion of each electron in the effective field of the N-1 others is governed by a one-particle Schrödinger equation. Self-consistency of the electronic charge distribution with its own electrostatic field leads to a set of coupled integrodifferential equations (Hartree equations) for N one-particle wavefunctions (atomic orbitals). The Hartree equations were subsequently shown to be precisely the conditions for optimization of an approximate wavefunction consisting of a product of atomic orbitals. An improved formalism, due to Slater and to Fock, represents the atomic wavefunction by a determinant built of atomic spin-orbitals and is thereby consistent with the Pauli principle. Application of the variational principle to a Slater determinant leads to a set of N coupled equations (Hartree-Fock equations), quite similar to Hartree's equations but containing, in addition, exchange interactions—an effect having no classical analog. The error inherent in the Hartree-Fock method, known as electron correlation, arises from smoothing-out of interelectronic repulsive interactions into effective Coulomb and exchange potentials. It accounts for roughly a 1% error in the total energy but is magnified in energy differences, which are more directly related to experimental quantities. A significant improvement in computational facility is achieved if the orbital functions are expanded in terms of a finite set of basis functions. The integrodifferential equations are thereby transformed into algebraic equations (Roothaan's equations) for the expansion coefficients. The analytic approach makes it possible to apply the self-consistent-field method to molecular systems. To date, SCF calculations have been carried out, in some form, for all the atoms in the periodic table and for a growing list of diatomic and polyatomic molecules.
Computer Use in the Intermediate Physics Laboratory
Authors: Davis William P.
Published: August 2005

Undergraduate use of a large computer operated in the time-sharing mode is described. Data obtained in three nuclear physics experiments which were done in the laboratory part of the second-year physics course were analyzed with the aid of programs written for this computer.
Note on the Inequivalence of Classical and Quantum Hamiltonians
Authors: Kennedy Frederick J. , Kerner Edward H.
Published: August 2005

By working directly from Newtonian equations of motion and representing acceleration ẍ as [(x,H), H], families of Hamiltonians may be constructed which are functions of the energy and which, while describing the same classical motions, are not connected by canonical transformations. One dimensional examples are given, and the formal rules of quantization executed when H is (energy)12 to show that the quantum motion does not come out right. The reason is that the commutation rule (x,p) = iħ does not have universal standing; quantum theory in employing this rule is apparently requiring not merely that H be a generator of motion, but also that it be a very particular one, viz., the energy when the system is conservative.
Diamagnetic Cylindrical Bar in a Field
Authors: Puri S. P.
Published: August 2005

It is shown that a bar of diamagnetic material suspended freely in a uniform magnetic field aligns itself with the long axis parallel to the field, just as does a bar with positive susceptibility.
Separable Nonlocal Potentials in Quantum Mechanics
Authors: Nichols William H.
Published: August 2005

The chief properties of separable, nonlocal potentials in quantum theory are pointed out and exemplified by solving the Schrödinger equation for the one-dimensional motion of a particle in an attractive separable square well.
Calculation of Magnetic and Electric Fields from Displacement Currents
Authors: Whitmer Robert M.
Published: August 2005

We calculate the magnetic induction from the integral form of the Biot-Savart law, B = μ0/4π∫(J+Ḋ) × rdV/r3. In the quasistatic case, using only the scalar electric potential, we transform the volume integral of Ḋ into an inner and an outer surface integral, both of which vanish except for a contribution from the polarization current in dielectric materials. Hence the induction is calculable from the sum of the conduction- and polarization-current densities alone. This result has no bearing on the calculation of the induction from Ampere's law, where we must use the entire displacement-current density. In the converse problem of an induced electric field there is no magnetic conduction current, and the quasistatic magnetic displacement current arises from a changing electric current in a closed circuit. We express H through the scalar magnetic potential, which is discontinuous on a surface bounded by the electric circuit. We obtain the induced electric field from a volume integral like the Biot-Savart integral above, and as before we transform it into surface integrals. There are two nonvanishing contributions. One is over both sides of the surface which is bounded by the electric circuit; it gives an expression for the electric field which we commonly compute from the vector potential. The second contribution reappears as a volume integral of magnetization currents in magnetic material.
Potential Scattering of a Wave Packet
Authors: Gettys W. Edward
Published: August 2005

A wave-packet formalism is presented for obtaining the differential cross section for the elastic scattering of a single particle by a potential. The method avoids difficulties inherent in the more common formulations such as interference between incident and scattered waves, box normalization, and density of final states. The time sequence of events in the scattering process is pictured in an intuitively appealing manner. The initial form of the wave packet is specified explicitly, and the time development of the wave packet is determined from the time-translation operator. The asymptotic form of the wave packet is investigated after a sufficiently long time lapse, and the cross section is obtained from a calculation of particle flux densities.
Laser Optics Experiments and Demonstrations
Authors: Whiteside Haven
Published: August 2005

Several demonstrations or experiments illustrating the coherence properties of laser light are described. In addition, a summary is given of demonstrations in interference and diffraction which make use of the high intensity of a laser source. These are discussed specifically within the capabilities of a 0.1-mW laser, the size that is most likely to be available for teaching in an average physics department.
Measurement of Reverberation Time
Authors: Aitchison G. J.
Published: August 2005

A simple experiment to measure the reverberation time of a room is described. The relevant theory is outlined, and typical results are given. The experiment is designed for inclusion in a course of practical work for first-year university students in physics.
Simple Doppler-Shift Apparatus Using Microwaves
Authors: Manchester F. D.
Published: August 2005

A simple apparatus using microwaves for demonstrating the Doppler frequency shift resulting from reflection of a wave train from a moving mirror is described.
Fall of Bodies Near the Earth
Authors: Feinberg Gerald
Published: August 2005

The motion of spheres under the combined effect of gravity and a V2 drag force is considered. It is shown that for conditions such as are described by Galileo in Dialogues Concerning Two New Sciences, one should expect a difference upon reaching the ground of several feet in height between a 1-lb sphere and a 100-lb sphere.
A Contribution to Einstein's Unified-Field Theory
Authors: Pizzo J. , Kronsbein J.
Published: August 2005

The term “unified-field theory” is, at first, suggestive of the unification of only the gravitational and electromagnetic fields through a nonsymmetric tensor gik. This impression is incorrect in that the gik are not necessarily restricted to represent the gravitational plus electromagnetic fields alone. It is, however, known that the field equations of gravitation alone (as given in the general theory of relativity) are contained within the unified-field theory of Einstein. In the present article, it is demonstrated that the covariant electrodynamic equations in the presence of a gravitational field are also included in the unified-field theory.
Coherent States and the Forced Quantum Oscillator
Authors: Carruthers P. , Nieto M. M.
Published: August 2005

It is shown that the forced quantum oscillator subject to a transient classical force is easily described in terms of the “coherent states”recently found useful in the description of light from optical masers. The natural role these states play in understanding the notions of the phase of a quantum oscillator and the transition to the classical limit is also explained. Very simple derivations of the state vectors, energy transfer, and various transition probabilities are given.
Dispersion Relation for a Longitudinal Plasma Wave in the Presence of a Magnetic Field
Authors: Arbab Farzam , Rosen Philip
Published: August 2005

A dispersion relation for electron longitudinal waves in a plasma which has an arbitrary magnetic field along the z axis is derived. The electron velocity distribution function is allowed to be quite general.
Note on the Magnetic Pole
Authors: Chen Henry S. C.
Published: August 2005

It is shown that a semiinfinitely long solenoid produces a magnetic field similar to that of a pole, and two such long solenoids interact to give a force acting through the two poles with no torque acting on the solenoid.
The Kepler Problem in Two-Dimensional Momentum Space
Authors: Shibuya Tai-ichi , Wulfman Carl E.
Published: August 2005

Fock studied the hydrogen atom problem in momentum space by projecting the space into a 4-dimensional hyperspherical space. He found that as a consequence of the symmetry of the problem in this space the eigenfunctions are the R4 spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this paper we note that if his method is applied to the 2-dimensional Kepler problem in momentum space, the eigenfunctions are R3 spherical harmonics, Ylm, and the eigenvalues are determined only by the quantum number l. These facts enable one to give a visualizable geometrical discussion of the dynamical degeneracy.
Inexpensive Student Potentiometer
Authors: Smith William C.
Published: August 2005

A simple, inexpensive student potentiometer of moderate accuracy is discussed, along with a somewhat different calibration source. The calibration source is ac operated, and short-circuit proof. Both the potentiometer and the calibration source were made from readily available commercial parts. Stability of the source is adequate for the 0.1% accuracy of the potentiometer. Long-term temperature stability is only moderate, but short-term stability is outstanding.
Orbit Graphing by Iteration: A Simple Laboratory Exercise
Authors: Lavatelli Leo
Published: August 2005

A simple graphical method for integrating the equation of motion of a particle in any field of force is used as a short laboratory exercise in an introductory course in mechanics. No knowledge of calculus nor differential equations is required of the student. Based directly on the vector definitions of average velocity and acceleration, and on central differences, it is capable of reasonable precision with relatively large steps. Using the three numbers, 6560cm3 = r2a(2τ)2, 53.7 cm = x1 = x−1, and 4.5 cm = y1 = −y−1, the student can develop half an elliptical orbit in 10 steps to about 6% accuracy on a 56 by 86-cm paper sheet in about one hour, and he can see for himself the step-by-step progress of a particle in an inverse-square field. The considerations leading to these or similar numbers are discussed briefly.
Philosophical Basis of Bohr's Interpretation of Quantum Mechanics
Authors: Hall Richard J.
Published: August 2005

In an attempt to throw some light on the controversies over the foundations of quantum mechanics, the author presents what he believes to be the philosophical viewpoint (namely, “idealism”) underlying Bohr's interpretation of quantum mechanics and then illustrates this with some typical passages by Bohr. Why the “realist” might find this interpretation unsatisfactory is briefly indicated by some statements by Einstein.
Elementary Rutherford Scattering Simulator
Authors: Wicher E. R.
Published: August 2005

We present a design for a simple Rutherford Scattering Simulator based on elastic collisions of small spheres with a modified parabolic cylinder.
Philip Morrison: Oersted Medalist for 1964
Authors: Parker Vincent E.
Published: August 2005

Remarks made by the Chairman of the Committee on Awards for 1965 during the presentation ceremony of the Oersted Medal to Philip Morrison in recognition of his notable contributions to the teaching of physics.
Potential and Field Diagram for the Earth-Moon System Neglecting the Effect of the Sun
Authors: Scott William T.
Published: August 2005

A potential and field diagram is given for introducing elementary students to these concepts by means of a semirealistic gravitational example. Problems involving rocket and satellite motion can be solved by use of the diagram, and open-ended questions about the sun's influence are raised.
Curved Space and Gravitation. II
Authors: Brehme Robert W.
Published: August 2005

The Euclidean and Einstein geodesics are defined for a two-dimensional space-time surface. Both are shown to approach the same classical law of gravitational acceleration, and to preserve the equivalence principle. However, only the Einstein geodesic allows a local time to be defined in such a way that the local velocity of light is constant. The conical surface is discussed and the connection is made between it and the frame of the uniformly accelerated relativistic rocket. Coordinate transformations are discussed to the extent that it is established that the shape of the two-dimensional surface embedded in a Euclidean three-space depends on the choice of coordinate frame.
Canonical Transformations in Quantum Mechanics
Authors: Levine Arnold D.
Published: August 2005

A review of canonical transformations in quantum mechanics is outlined with a view toward their use in the solution of specific problems. Several typical problems are worked out by the method of canonical transformations to emphasize the utility of this approach. In this way one may obtain an insight into the nature and limitation of the connection that exists between the canonical transformations of classical mechanics and the unitary transformations of quantum mechanics. The purpose of this paper is to achieve certain expository and pedagogical objectives, and no original contribution to the theory is intended.
Analogous Behavior of Elementary Particles and Some Simple Waveguide and Cavity Systems
Authors: Lawson J. D.
Published: August 2005

Instructive parallels may be drawn between the way that electromagnetic cavities and waveguides behave as the frequency is varied, and the behavior of elementary particle reactions as a function of center-of-mass energy. In this paper, we first establish a series of correspondences between the two types of system, relating, for example, mode number to quantum number and cutoff wavelength to Compton wavelength. We then examine in some detail a particular cavity and waveguide system, and find its resonant frequencies and decay modes. Conservation laws are found, and related to the symmetry of the cavity, which is such that “strong,” “intermediate,” and “weak” decay is possible. Parallels with the interactions, scattering, and decay of elementary particles are discussed.
Equivalent Vector Lorentz Transformations
Authors: Gold Louis
Published: August 2005

The vector method for obtaining the Lorentz transformations of special relativity is shown to have several apparent variants. Investigation of these reveals that equivalence prevails whether or not the exact form of related operators is preserved. A simple scheme for analyzing the defining dyadic, vector, and scalar functionals forms the basis of the present study.
Kinematics of Scattering and Decay Processes
Authors: Nyborg Per
Published: August 2005

The kinematics of processes involving four different particles is discussed. The boundaries of the physical region for the various processes are established one at a time, using explicitly energy and momentum conservation. Then follows a joint description of all processes where all four-momenta formally are considered to be ingoing. The description is given explicitly in terms of two independent variables (s,t), in contrast to the usual symmetric (s,t,u) description.
What are Spinors?
Authors: Rindler W.
Published: August 2005

Spinors have in recent years become an important mathematical tool in special and general relativity. After a general review of the status of physical laws, it is shown why spinors are the “basic building bricks” of any Lorentz invariant law. The properties of spinors are briefly discussed and it is shown why it sometimes pays to translate a tensor problem into spinor language, solve it therein, and finally translate back.
Acoustical Interferometer for “Open-Ended” Laboratory Experiments
Authors: Boyer Robert A.
Published: August 2005

An instrument and its utilization are described which provides for study of several aspects of sound waves. Basically the instrument consists of a pair of telescoping plastic tubes. The inner tube has one end closed by a removable plug containing a built-in microphone. A speaker whose diameter conforms to that of the outer tube is driven by an audio oscillator. O-ring seals are used to confine the major portion of the sound energy inside the tubes. Acoustical phenomena observable include: closed and open-tube resonance, longitudinal nature of sound waves and limitations of mechanical resonance of particles such as cork dust, use of Lissajous figures to observe phase variation of wave as a function of distance from source and to locate resonance positions with increased precision, excitation of various modes of vibration and analysis thereof with a frequency counter, and absorption of sound energy.
Uncertainty Principle and Normal Operators—Some Comments
Authors: Brittin Wesley E.
Published: August 2005

It is shown that an appropriate formulation of the uncertainty principle for normal operators leads to the same mathematical expression as that for Hermitian operators. The treatment is valid for mixed states as well as for pure states.
Quadratic Constants of the Motion for the Classical Harmonic Oscillator
Authors: Bragg Lincoln E. , Turner L. R.
Published: August 2005

The four quadratic constants of the motion for the two dimensional classical harmonic oscillator are examined. Although all four are needed for closure under the operation of Poisson bracketing, the values of three determine the trajectories. A physical meaning and a method of measurement are obtained for the fourth COM, P = q1q2+p1p2, which is found to be a difference of energies measured in a rotated coordinate system. The study is simplified for the two dimensional harmonic oscillator by the use of matrix block multiplication and the use of the correspondence between the multiplication of certain matrices and the multiplication of complex numbers; the simplification is even greater when this easy formalism is extended to the n dimensional case. In n dimensions, if Pkj = qkqj+pkpj and Lkj = qkpj−pkqj, then the Pkj+iLkj provide a basis for a space isomorphic to that of n by n hermitian matrices, the generators of the group SUn. As in two dimensions, the Pkj can be identified as partial energies. The n2 linearly independent COM are redundant: 2n−1 determine the orbit uniquely.
Classical Canonical Transformations without the Use of Hamilton's Principle
Authors: Ansbacher F.
Published: August 2005

A canonical transformation leading from a Hamiltonian system Σ to another Σ* is symmetrical in the sense that the transformation from Σ* to Σ is also canonical. By writing the transformation functions in such a way that the symmetry is exhibited explicitly, i.e., that neither Σ nor Σ* is singled out, one is naturally lead to consider an intermediate coordinate system S with 2n independent coordinates, n coordinates from Σ, and n from Σ*. Working from S it is then a straightforward matter to derive all the properties of canonical transformations. It is shown that the arbitrariness of the Lagrangian to within the addition of the total time derivative of an arbitrary function of the coordinates and the time follows from Lagrange's equations of motion. It is therefore also possible to derive the generating functions of canonical transformations without an appeal to Hamilton's principle.
Significance of Some Equations of State Obtained from Shock-Wave Data
Authors: Cowperthwaite M.
Published: August 2005

A single Hugoniot curve determined from shock-wave experiments does not provide enough thermodynamic information to specify an equation of state. The assumptions which, along with shock-wave data, are sufficient to determine a complete equation of state are instructive to a serious student of thermodynamics, because they illustrate the significance of the state variables and the relations among them. This paper considers the specific problem of calculating the state variables of shock-induced states and discusses calculations based on the assumption of either constant Cv or constant Cp from a structural point of view. Methods of calculating the state variables are formulated to show how the assumptions make them possible. The assumption of constant Cv specifies implicitly the functional forms of the (E-p-v) and (p-v-T) equations of state. Similarly, the assumption of constant Cp specifies the functional forms of the (H-p-v) and (p-v-T) equations of state. The experimental Hugoniot curve is used as a boundary condition to determine arbitrary functions in these equations of state and to show how the assumptions and the experimental data lead to a complete thermodynamic description of shock-induced states.
On the Need of Housecleaning in the Teaching of Mechanics
Authors: Armstrong H. L.
Published: August 2005

It is argued that there is much, in the mechanics commonly taught at University, that serves no purpose whatsoever, either practical or intellectual, and that such parts could be thrown out without any real loss to anyone. The three branches into which mechanics might be divided, introductory, intermediate, and advanced, are each considered, as well as experimental work; and things that could be omitted, or places in which the treatment could be simplified, are pointed out.
Diffusion as a Problem of Statistical Path
Authors: Kurşunoǧlu Behram
Published: August 2005

Feynman's space-time path formulation of nonrelativistic quantum mechanics is applied to the problem of classical diffusion.
Spectrographic Analysis with a Small Telescope and Transmission Grating
Authors: Warren Kenneth Lyle , Graedel Thomas E.
Published: August 2005

Details of an experiment are described in which a transmission grating was constructed of wire and used in conjunction with a reflecting telescope to classify several first magnitude stars.
On Physics Project Laboratories
Authors: King John G.
Published: August 2005

The Robert A. Millikan Lecture Award is made annually to a physicist chosen by a special committee of the American Association of Physics Teachers because of his creative and imaginative contributions to the teaching of physics. The lecturer selected is one whom the Association wishes to honor at the Summer Meeting in the same way that it honors the Oersted Medalist at the time of the Annual Meeting. The award is made possible through the annual support of Prentice-Hall, Inc., and the first award was made in 1964. The recipient of this award for 1965 is John G. King, Professor of Physics at the Massachusetts Institute of Technology.
Joseph Henry and the Relations between Teaching and Research
Authors: Weiner Charles
Published: August 2005

America's leading physicist of the midnineteenth century made his major research contributions while employed full time as a science teacher. A study of Joseph Henry's unpublished correspondence and laboratory journals and the lecture notes of his students reveals the background of his career as a physics professor at Princeton in the 1830's and 1840's. These documents display a reciprocal and mutually advantageous structuring of Henry's lectures and research, which expanded the scope and increased the effectiveness of each. This close interconnection between teaching and research was established by Henry at a time when the research function of the college professor had not yet been accepted.
Accidental Degeneracy
Authors: Greenberg David F.
Published: August 2005

A detailed discussion of nongeometric, or “accidental,” degeneracy is presented in the context of Newtonian, relativistic, and quantum mechanics. An analogy with broken symmetries in elementary-particle physics is used to present an elementary discussion of certain recent developments in theoretical high-energy physics.
A Gravitational Paradox
Authors: Lévy-Leblond Jean-Marc , Thurnauer Peter
Published: August 2005

Adapting an argument by Dyson in quantum electrodynamics, we point out that the attractive and long-range character of the gravitational interaction may seem to prevent the universe from being stable against decay into successively lower energy states. A straightforward solution to this paradox is given, based on the essentially nonlinear nature of gravitational theory. This nonlinearity, whose importance is thus clearly demonstrated, is shown to have a a very elementary origin. A simple approximation, incorporating the nonlinear effects in a physically transparent way, quantitatively substantiates our intuitive argument.
Compton Effect and Electron Binding
Authors: Veigele William J. , Tracy Philip T. , Henry E. Michael
Published: August 2005

The usual expressions for the Compton effect are based on the assumptions that the scattering electron is free and stationary. These assumptions are reasonable when the photon energy is large compared to the electron binding energy; however, in many situations this is not the case, and the binding energy and momentum of the electron alter Compton scattering by causing (1) line broadening, (2) a discrete spectrum, (3) a line-shift defect, (4) a decrease in incoherent scattering at low angles, (5) an increase in coherent scattering at low angles, and (6) a change in recoil electron distribution. These effects are described, and differential and average cross sections for carbon are calculated on the Thomas-Fermi model to illustrate them quantitatively.
The Water Flask with Unequal Holes
Authors: Weissman Eric
Published: August 2005

This article discusses the problem of the water flask with several unequal holes in the bottom by considering it as a nonlinear work problem which can, nevertheless, be solved by elementary considerations. It is described as a suitable fluid-mechanics experiment for elementary courses, and it is then solved analytically—first without the calculus and then with the help of the calculus. It is the solution without the calculus which is of particular interest for non physics majors, because of its comparative simplicity and lack of cumbersome equations.
Graphical Aids in the Teaching of Special Relativity
Authors: Kohler Robert H.
Published: August 2005

The kinematics of special relativity is depicted through space-time diagrams, whereby the Lorentz transformation as well as the Galilean can be presented in graphical form rather than analytic. The space-time diagrams are then used to formulate and explain several of the paradoxes of special relativity. The method is a variation of the Minkowski diagram. The reference axes are kept fixed, and the space-time point undergoes an apparent displacement in the plot as the observation frame is changed. The graphical analysis is semiquantitative for some problems and is quantitative for others.
Interaction Energy of a Dielectric in an Electrostatic Field
Authors: Gilinsky Victor , Holliday Dennis
Published: August 2005

A straightforward computation of the interaction field energy of a dielectric in a uniform external electrostatic field appears to yield a result different from that given by a general theorem. It is shown here that the discrepancy can be resolved by considering the uniform field of infinite extent to be the limit of a field of finite extent. A recent paper by Plesset and Venezian is discussed.
On Linear Friction in Lagrange's Equation
Authors: Denman Harry H.
Published: August 2005

A linear frictional force in the equation of motion of a particle is obtained if one modifies the Lagrange equation of motion by the addition of the frictional term, which may be expressed in terms of the Rayleigh dissipative function. It is shown that one can construct Lagrangians in several simple cases so that the Lagrange equation of motion contains such a frictional force without the addition of any terms. This method is also useful in analyzing some aspects of the motion.
Second Quantization as a Graded Hilbert Space Representation
Authors: Kobe Donald H.
Published: August 2005

A review of the second quantization formulation of quantum mechanics is given based on the idea of a graded Hilbert space whose elements are represented by column matrices containing zero, one, two, ···, particle functions. The creation and annihilation operators are defined in terms of intuitive ideas about adding a particle to or removing a particle from the system. The (anti)commutation relations are shown to follow from the (anti)symmetry of the wavefunctions. The field operators which describe the creation or annihilation of a particle at a point are then obtained and their properties discussed. These operators are then used to express general operators in second quantization. Finally, a basis is introduced and the equations of occupation-number space are obtained.
Contemporary Physics I and II
Authors: Dodd Jack G.
Published: August 2005

A freshman-level two-semester one-credit hour introductory course in contemporary physics has been developed which uses a selection of 25 Scientific American offprints as a text. The course was designed to maintain contact with potential department majors during the freshman year but has been widely used by liberal arts at all levels. Emphasis is placed on current research in physics. Some organizational details are discussed and a list of the offprints used is given.
Theoretical and Experimental Determination of the Two-Dimensional Potential Field for a Right-Angled Bend
Authors: Steere Robin C.
Published: August 2005

An analytical solution is obtained by conformal mapping. The solution is used in a digital computer to provide precise numerical solutions. This process represents a saving in time and effort when compared with approximate numerical methods often used. Information on the density of flow lines is presented. The potential field is explored experimentally using a precision sheet of metal foil, and experiment and theory compared. The experimental arrangement could replace the standard water-tank experiment used in many undergraduate laboratories.
Equations of Motion and Coordinate Covariance in General Relativity
Authors: Ging J. L.
Published: August 2005

The geodesic postulate in the form of a variational principle is derived directly from a surface integral relation which is a consequence of the coordinate invariance of the Hamilton action integral for the field equations.
Electron-Acoustic Wave Resonances
Authors: Schmitt H. J.
Published: August 2005

A simple experiment to determine both the electron-density decay rate and the ambipolar diffusion coefficient in an afterglow plasma is presented. The method is based upon the detection of Tonks-Dattner radial column resonances and requires readily available equipment.
Electric Shock-Tube Experiment
Authors: Hood James D.
Published: August 2005

A small-diameter linear shock tube suitable for laboratory demonstration is described in this paper. Necessary construction details are given along with a discussion of the instrumentation required to measure the velocity of the luminous shock front, the flow velocity of the expanding plasma, and the conductance of the plasma.
Role of Intermolecular Attractions in Liquids and Gases
Authors: Thoburn W. C.
Published: August 2005

Certain conventional elementary ideas relating to the role of intermolecular attractions in liquids and gases are examined critically, and an effort is made to bring out a rationally defensible picture of the effects of these forces, without postulating the presence of any permanent, net force fields. A clear statement of the origin of surface tension is presented. The modification of pressure found in a real gas due to intermolecular attractions is shown not to be a boundary phenomenon. The need for a dynamic mechanism to account for this modification is pointed out.
Resource Letter PB-1 on Physics and Biology
Authors: Baker D. James
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters; supported by a grant from the National Science Foundation.

This is one of a series of Resource Letters on different topics, intended to guide college physicists to some of the literature and other teaching aids that may help them improve course contents in specified fields of physics. No Resource Letter is meant to be exhaustive and complete; in time there may be more than one letter on some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed. Please send such communications to Professor Arnold Arons, Chairman, Resource Letter Committee, Department of Physics, Amherst College, Amherst, Massachusetts.

Notation: The letters E, I, and A after an item indicate the level of biological knowledge (Elementary, Intermediate, or Advanced) necessary for comprehension.

Additional copies: Available from American Institute of Physics, 335 East 45 Street, New York, New York, 10017. When ordering, request Resource Letter PB-1 and enclose a stamped return envelope.
Tube Effects on Sound Propagation Through Real Fluids
Authors: Romer I. Carl
Published: August 2005

This paper extends the results of the classical derivation of the Kirchhoff-Helmholtz effects on the propagation of sound through fluids in tubes by replacing the ideal gas equation of state with a general equation p = p(ρ, T).