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Oh, I need some debates to! Let's discuss Quantum mechanics (QM " also known as quantum physics, or quantum theory) is a branch of physics which deals with physical phenomena at nanoscopic scales where the action is on the order of the Planck constant. It departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales. Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. Quantum mechanics provides a substantially useful framework for many features of the modern periodic table of elements including the behavior of atoms during chemical bonding and has played a significant role in the development of many modern technologies. In advanced topics of quantum mechanics, some of these behaviors are macroscopic (see macroscopic quantum phenomena) and emerge at only extreme (i.e., very low or very high) energies or temperatures (such as in the use of superconducting magnets). For example, the angular momentum of an electron bound to an atom or molecule is quantized. In contrast, the angular momentum of an unbound electron is not quantized. In the context of quantum mechanics, the wave"particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons, and other atomic-scale objects. The mathematical formulations of quantum mechanics are abstract. A mathematical function, the wavefunction, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. Mathematical manipulations of the wavefunction usually involve bra"ket notation which requires an understanding of complex numbers and linear functionals. The wavefunction formulation treats the particle as a quantum harmonic oscillator, and the mathematics is akin to that describing acoustic resonance. Many of the results of quantum mechanics are not easily visualized in terms of classical mechanics. For instance, in a quantum mechanical model the lowest energy state of a system, the ground state, is non-zero as opposed to a more "traditional" ground state with zero kinetic energy (all particles at rest). Instead of a traditional static, unchanging zero energy state, quantum mechanics allows for far more dynamic, chaotic possibilities, according to John Wheeler. The earliest versions of quantum mechanics were formulated in the first decade of the 20th century. About this time, the atomic theory and the corpuscular theory of light (as updated by Einstein)[1] first came to be widely accepted as scientific fact; these latter theories can be viewed as quantum theories of matter and electromagnetic radiation, respectively. Early quantum theory was significantly reformulated in the mid-1920s by Werner Heisenberg, Max Born and Pascual Jordan, (matrix mechanics); Louis de Broglie and Erwin Schr"dinger (wave mechanics); and Wolfgang Pauli and Satyendra Nath Bose (statistics of subatomic particles). Moreover, the Copenhagen interpretation of Niels Bohr became widely accepted. By 1930, quantum mechanics had been further unified and formalized by the work of David Hilbert, Paul Dirac and John von Neumann[2] with a greater emphasis placed on measurement in quantum mechanics, the statistical nature of our knowledge of reality, and philosophical speculation about the role of the observer. Quantum mechanics has since permeated throughout many aspects of 20th-century physics and other disciplines including quantum chemistry, quantum electronics, quantum optics, and quantum information science. Much 19th-century physics has been re-evaluated as the "classical limit" of quantum mechanics and its more advanced developments in terms of quantum field theory, string theory, and speculative quantum gravity theories. The name quantum mechanics derives from the observation that some physical quantities can change only in discrete amounts (Latin quanta), and not in a continuous (cf. analog) way. Contents [hide] 1 History 2 Mathematical formulations 3 Mathematically equivalent formulations of quantum mechanics 4 Interactions with other scientific theories 4.1 Quantum mechanics and classical physics 4.2 Relativity and quantum mechanics 4.3 Attempts at a unified field theory 5 Philosophical implications 6 Applications 7 Examples 7.1 Free particle 7.2 Step potential 7.3 Rectangular potential barrier 7.4 Particle in a box 7.5 Finite potential well 7.6 Harmonic oscillator 8 See also 9 Notes 10 References 11 Further reading 12 External links History[edit] Modern physics Schr"dinger equation History of modern physics Founders[show] Branches[show] Scientists[show] v t e Main article: History of quantum mechanics Scientific inquiry into the wave nature of light began in the 17th and 18th centuries when scientists such as Robert Hooke, Christiaan Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations.[3] In 1803, Thomas Young, an English polymath, performed the famous double-slit experiment that he later described in a paper entitled "On the nature of light and colours". This experiment played a major role in the general acceptance of the wave theory of light. In 1838, with the discovery of cathode rays by Michael Faraday, these studies were followed by the 1859 statement of the black-body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system can be discrete, and the 1900 quantum hypothesis of Max Planck.[4] Planck's hypothesis that energy is radiated and absorbed in discrete "quanta" (or "energy elements") precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation,[5] known as Wien's law in his honor. Ludwig Boltzmann independently arrived at this result by considerations of Maxwell's equations. However, it was valid only at high frequencies, and underestimated the radiance at low frequencies. Later, Max Planck corrected this model using Boltzmann statistical interpretation of thermodynamics and proposed what is now called Planck's law, which led to the development of quantum mechanics. Among the first to study quantum phenomena in nature were Arthur Compton, C.V. Raman, Pieter Zeeman, each of whom has a quantum effect named after him. Robert A. Millikan studied the Photoelectric effect experimentally and Albert Einstein developed a theory for it. At the same time Niels Bohr developed his theory of the atomic structure which was later confirmed by the experiments of Henry Moseley. In 1913, Peter Debye extended Niels Bohr's theory of atomic structure, introducing elliptical orbits, a concept also introduced by Arnold Sommerfeld.[6] This phase is known as Old quantum theory. According to Planck, each energy element, E, is proportional to its frequency, _7;: Max Planck is considered the father of the Quantum Theory where h is Planck's constant. Planck (cautiously) insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the physical reality of the radiation itself.[7] In fact, he considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizeable discovery.[citation needed] However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect in which shining light on certain materials can eject electrons from the material. theoretical framework consists of concepts, together with their definitions, and existing theory/theories that are used for your particular study. The theoretical framework must demonstrate an understanding of theories and concepts that are relevant to the topic of your research paper and that will relate it to the broader fields of knowledge in the class you are taking. The theoretical framework is not s