American Journal of Physics and Applications
Volume 5, Issue 6, November 2017, Pages: 80-83
Received: Aug. 14, 2017;
Accepted: Sep. 6, 2017;
Published: Oct. 11, 2017
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Hua Ma, The College of Science, Air Force University of Engineering, Xi’an, People’s Republic of China
Based on the operator theories and Hamiltonian canonical equation, an operator based quantum dynamics equation is established, which has the same effect as the Hamiltonian equation in describing the state evolution of quantized dynamical systems. As the reasonable verification of this equation, Schrodinger equation can be derived theoretically, and the variational principle properties of quantum mechanics are revealed. This work will help to promote the development of quantum theory and to perfect the axiomatic system of quantum mechanics.
A Method for Deriving Quantum Dynamic Equations from Classical Mechanics, American Journal of Physics and Applications.
Vol. 5, No. 6,
2017, pp. 80-83.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
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C Lanczos, The Variational Principles of Mechanics (University of Toronto Press, Toronto, 1964).
Cassel, Kevin W., Variational Methods with Applications in Science and Engineering (Cambridge University Press, 2013).
Landau LD and Lifshitz EM, Mechanics (Pergamon Press, 3rd ed., pp. 2–4, 1976).
Hand L. N., Finch J. D., Analytical Mechanics (Cambridge University Press, 2008).
Kragh, Helge, Quantum Generations: A History of Physics in the Twentieth Century (Princeton University Press, p. 58, 2002).
Mehra J., Rechenberg H., The historical development of quantum theory (New York: Springer-Verlag, 1982).
Schrödinger E., Physical Review. 28 (6): 1049–1070 (1926).
Griffiths, David J., Introduction to Quantum Mechanics (Prentice Hall, 2nd ed., 2004).
Sakurai J. J., Modern Quantum Mechanics (Massachusetts: Addison-Wesley, p. 68, 1995).
J. Köppe, W. Grecksch, W. Paul, “Derivation and application of quantum Hamilton equations of motion”, Annalen Der Physik, 2016, 529 (3): 1600251.
VG Zelevinsky, “Microscopic derivation of a quantum hamiltonian for adiabatic collective motion”, Nuclear Physics A, 2016, 337 (1): 40-76.
J Zheng-Johansson, “PI Johansson, Inference of Schrödinger Equation from Classical-Mechanics Solution”, Physics, 2006, 17 (3): 240-244.
MA Ajaib, “A Fundamental Form of the Schrodinger Equation”, Foundations of Physics, 2015, 45 (12): 1586-1598.
T. Hey, P. Walters, The New Quantum Universe (Cambridge University Press, 2009).
D. McMahon, Quantum Mechanics Demystified (Mc Graw Hill (USA), 2006).