A Stochastic Variational Treatment of Quantum Mechanics

An earlier development of some results in quantum mechanics from a stochastic variational principle is extended in several directions. An outline is first given of the methods of control theory upon which the development is based, and earlier results are briefly described. Extensions are then given...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical and physical sciences Mathematical and physical sciences, 1995-08, Vol.450 (1939), p.417-437
Main Author: Rosenbrock, Howard Harry
Format: Article
Language:English
Subjects:
Approximation
Control theory
Electric fields
Electromagnetic fields
Lagrangian function
Momentum
Oscillators
Photons
Quantum field theory
Quantum mechanics
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Summary:An earlier development of some results in quantum mechanics from a stochastic variational principle is extended in several directions. An outline is first given of the methods of control theory upon which the development is based, and earlier results are briefly described. Extensions are then given to relativistic systems, to Dirac’s equation, and to elementary quantum field theory. The aim thoughout is to show that results in the standard theory can be obtained in a uniform way from an extended form of Hamilton’s principle, which has the advantage of conciseness and a relatively close relationship to the classical theory. The wave function appears as a modified form of the optimal cost function, and the photon can be identified with a singularity in the electromagnetic field. Interference is explained by optimization of an expected value, the ensemble over which the expectation is taken being dependent upon the information available.
ISSN:1364-5021
0962-8444
1471-2946
2053-9177
DOI:10.1098/rspa.1995.0092