Abstract
Schrödinger's original quantization procedure is revisited in the light of Nelson's stochastic framework of quantum mechanics. It is clarified why Schrödinger's proposal of a variational problem led us to a true description of quantum mechanics.
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References
Schrödinger, E., Ann. Physik 79, 361 (1926).
Yourgrau, W., and Mandelstam, S., Variational Principles in Dynamics and Quantum Theory, Pitman & Sons, London, 1960.
Nelson, E., Dynamical Theories of Brownian Motion, Princeton U.P., Princeton, 1967.
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Nelson, E., ‘Connection between Brownian Motion and Quantum Mechanics’, talk given at the Einstein Symposium in Berlin, March 1979.
As one can see easily in Ref. 3, the vector \(\vec b\) depends on the probability distribution of the process \(\vec x(t,\omega ).\)
Yasue, K., J. Math. Phys. 20, 1861 (1979).
Holland, C.J., Commun. Pure Appl. Math. 30, 755 (1977).
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Yasue, K. Schrödinger's variational method of quantization revisited. Lett Math Phys 4, 143–146 (1980). https://doi.org/10.1007/BF00417507
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DOI: https://doi.org/10.1007/BF00417507
Keywords
- Statistical Physic
- Quantum Mechanic
- Group Theory
- Variational Method
- Variational Problem