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2019 | 116 | 209-221
Article title

An Axiomatic Approach to Quantum Mechanics

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EN
Abstracts
EN
We have shown that the Schrödinger wave equation can be explained and derived from fundamental postulates that are based on the conservation of probability, significance of measurements at infinity and nature’s tendency of maintaining a system as unbiased as possible. As a reasonable measure for the local randomness, Fisher information is considered. The presented approach provides an axiomatic derivation for the Schrödinger wave equation, avoiding imperfect models borrowed from classical mechanics such as direct application of the energy conservation, statistical mechanics or vibrating string models.
Discipline
Year
Volume
116
Pages
209-221
Physical description
Contributors
  • 178/A, Sri Wimalarama Mawatha, Thalavitiya, Parakaduwa, Sri Lanka
  • Department of Physics, University of Colombo, Colombo 03. Sri Lanka
References
  • [1] Edward Nelson, Derivation of the Schrödinger Equation from Newtonian Mechanics, Phys. Rev. 150, 1079 (1966)
  • [2] B. Roy Frieden, Fisher information as the basis for the Schrödinger wave equation, American Journal of Physics 57, 1004 (1989)
  • [3] Marcel Reginatto, Derivation of the equations of nonrelativistic quantum mechanics using the principle of minimum Fisher information, Phys. Rev. A 58, 1775 (1998)
  • [4] U. Klein, The Statistical Origins of Quantum Mechanics, Physics Research International (2010)
  • [5] Maurice Surdin, Derivation of Schrödinger's equation from stochastic electrodynamics, International Journal of Theoretical Physics (1971)
  • [6] John S. Briggs, Jan M. Rost, On the Derivation of the Time-Dependent Equation of Schrödinger, Foundations of Physics (2001)
  • [7] Millard Baublitz, Derivation of the Schrödinger Equation from a Stochastic Theory, Progress of Theoretical Physics (1988)
  • [8] Philip McCord Morse, Herman Feshbach, Methods of Theoretical Physics, Part I, McGraw-Hill, New York (1953)
  • [9] Einstein, B. Podolsky, and N. Rosen, Can 7Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev. 47, 777, (1935)
  • [10] Roy Frieden, Physics from Fisher Information, a Unification, Cambridge University Press, Cambridge, UK.
  • [11] M. Reginatto, Derivation of the equations of nonrelativistic quantum mechanics using the principle of minimum Fisher information, Physical Review A, vol. 58, no. 3, pp. 1775–1778 (1998)
  • [12] M. J. W. Hall, Quantum properties of classical fisher information, Physical Review A, vol. 62, no. 1, Article ID 012107, 6 pages, (2000)
  • [13] R. A. Fisher, Statistical Methods and Scientific Inference, Oliver and Boyd, Edinburgh, UK, (1956)
  • [14] E. T. Jaynes, Information Theory and Statistical Mechanics, Phys. Rev. 106, 620 (1957)
  • [15] Caticha and D. Bartolomeo, Entropic dynamics: From entropy and information geometry to Hamiltonians and quantum mechanics, AIP Conference Proceedings 1641, 155 (2015).
  • [16] L. Nottale, The Theory of Scale Relativity, International Journal of Modern Physics A, Vol. 07, No. 20, pp. 4899-4936 (1992)
  • [17] Shunlong Luo, Quantum Fisher Information and Uncertainty Relations, Letters in Mathematical Physics 53: 243-251 (2000)
  • [18] A.J.Stam, Some Inequalities Satisfied by the Quantities of Information of Fisher and Shannon, Information and Control 2, 101-112 (1959)
  • [19] Cramér, Harald, Mathematical Methods of Statistics, NJ: Princeton Univ. Press, (1946), ISBN 0-691-08004-6
Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-9eeed184-1205-4d3a-89fd-2d2f8b025e01
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