Wavefunction | Wikipedia audio article
Channel: wikipedia tts
Date: 24/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Wave_function


00:03:26 1 Historical background
00:08:15 1.1 Wave functions and wave equations in modern theories
00:11:32 2 Definition (one spinless particle in one dimension)
00:11:54 2.1 Position-space wave functions
00:16:26 2.2 Momentum-space wave functions
00:22:18 2.3 Relations between position and momentum representations
00:25:19 3 Definitions (other cases)
00:30:15 3.1 One-particle states in 3d position space
00:30:37 3.2 Many-particle states in 3d position space
00:41:08 3.2.1 Probability interpretation
00:51:53 4 Time dependence
00:53:18 5 Non-relativistic examples
00:55:42 5.1 Finite potential barrier
00:57:45 5.2 Quantum harmonic oscillator
00:58:02 5.3 Hydrogen atom
00:59:21 6 Wave functions and function spaces
01:00:11 6.1 Vector space structure
01:01:29 6.2 Representations
01:01:34 6.3 Inner product
01:04:40 6.4 Hilbert space
01:06:32 6.5 Common Hilbert spaces
01:07:25 6.6 Simplified description
01:08:30 7 More on wave functions and abstract state space
01:12:12 8 Ontology
01:15:32 9 See also
01:18:13 10 Remarks
01:22:06 11 Notes
01:23:29 12 References
01:25:17 13 Further reading
01:26:17 14 External links
01:26:35 {−s, −s + 1, ..., s − 1, s}  is the set of allowed spin quantum numbers and Ω
01:27:02 (sy) for the spin quantum number along the y direction and ω
01:29:36 Ontology
01:30:35 See also
01:31:10 Remarks



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SUMMARY
=======
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.  The wave function is a  complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it.  The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi, respectively).
The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables.  Once such a representation is chosen, the wave function can be derived from the quantum state.
For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique.  For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier transform.  Some particles, like electrons and photons, have nonzero spin, and the wave function for such particles includes spin as an intrinsic, discrete degree of freedom; other discrete variables can also be included, such as isospin.  When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g., a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g., z-component of spin) – these values are often displayed in a column matrix (e.g., a 2 × 1 column vector for a non-relativistic electron with spin ​1⁄2).
According to the superposition principle of quantum mechanics, wave functions can be added together and multiplied by complex numbers to form new wave functions and form a Hilbert space.  The inner product between two wave functions is a measure of the overlap between the corresponding physical states, and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products.  The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation.  This explains the name "wave function," and gives rise to wave–particle duality.  However, the wave function in quantum mech ...