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Derivation of Schrödinger equation from the laws of classical mechanics, structures in physical vacuum

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It is proven that the Schrödinger equation can be derived from the laws of classical mechanics. Classical approach leads to a result that the time-independent Schrödinger equation extracts from solutions of the Hamilton‐Jacobi equation only those solutions that satisfy the following two conditions: (I) The orbital angular momentum of a particle moving along a closed trajectory is quantized; (II) the motion of a particle that occur in agreement with these solutions satisfies a necessary condition of stability under small perturbation forces. Hence among all the Schrödinger equation's solutions there can be “extra” solutions that despite satisfying the necessary condition, are unstable and, therefore, are not realized in nature. Besides that, the classical approach leads to a conclusion that an electron’s spin in аn atom precesses. A physical model is suggested, in which the motion of an electron in an atom forms structures in the superfluid physical vacuum. If we consider these structures as quasi-particles that have spin, then it can be demonstrated that the natural frequencies of the atom are the frequencies of precession of the quasi-particle’s spin.
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Keywords: Hidden Variables; Precession of Electron’s Spin in an Atom; Quantum Potential; Schrödinger Equation

Document Type: Research Article

Publication date: September 16, 2014

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  • Physics Essays has been established as an international journal dedicated to theoretical and experimental aspects of fundamental problems in Physics and, generally, to the advancement of basic knowledge of Physics. The Journal's mandate is to publish rigorous and methodological examinations of past, current, and advanced concepts, methods and results in physics research. Physics Essays dedicates itself to the publication of stimulating exploratory, and original papers in a variety of physics disciplines, such as spectroscopy, quantum mechanics, particle physics, electromagnetic theory, astrophysics, space physics, mathematical methods in physics, plasma physics, philosophical aspects of physics, chemical physics, and relativity.
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