Abstract
In this paper we derive the Schrödinger equation by comparing quantum statistics with classical statistical mechanics, identifying similarities and differences, and developing an operator functional equation which is solved in a completely algebraic fashion with no appeal to spatial invariances or symmetries.
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References
P. A. M. Dirac,The Principles of Quantum Mechanics (Oxford University Press, London, 1958).
D. J. Foulis and C. H. Randall, “Operational statistics I, basic concepts,”J. Math. Phys. 13, 1667–1675 (1972).
Stanley P. Gudder,Quantum Probability (Academic Press, San Diego, 1988).
M. W. Hirsch and S. Smale,Differential Equations, Dynamical Systems, and Linear Algebra (Academic Press, New York, 1974).
C. A. Hooker,The Logico-Algebraic Approach to Quantum Mechanics, Vol. I: Historical Evolution (Reidel, Dordrecht, 1975).
C. A. Hooker,The Logico-Algebraic Approach to Quantum Mechanics, Vol. II: Contemporary Consolidation (Reidel, Dordrecht, 1979).
J. Jauch,Foundations of Quantum Mechanics (Addison-Wesley, Reading, Massachusetts, 1968).
G. Ludwig,Foundations of Quantum Mechanics, Vol. I and II (Springer, New York, 1983 and 1985).
G. W. Mackey,Mathematical Foundations of Quantum Mechnics (Benjamin, New York, 1963).
C. H. Randall and D. J. Foulis, “Operational statistics II, manuals of operations and their logics,”J. Math. Phys. 14, 1472–1480 (1973).
V. S. Varadarajan,Geometry of Quantum Theory, Vol. I (Van Nostrand, Princeton, 1968).
V. S. Varadarajan,Geometry of Quantum Theory, Vol. II (Van Nostrand, Princeton, 1970).
J. von Neumann,Mathematical Foundations of Quantum Mechanics (Oxford University Press, London, 1958).
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Catlin, D.E. The Schrödinger equation via an operator functional equation. Found Phys 20, 667–690 (1990). https://doi.org/10.1007/BF01889454
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DOI: https://doi.org/10.1007/BF01889454