A variational principle, wave-particle duality, and the Schr\"{o}dinger
equation
- URL: http://arxiv.org/abs/2206.14601v2
- Date: Mon, 14 Aug 2023 13:41:51 GMT
- Title: A variational principle, wave-particle duality, and the Schr\"{o}dinger
equation
- Authors: N. L. Chuprikov
- Abstract summary: The dynamics of a quantum particle in a one-dimensional configuration space is determined by a variational problem for two functionals.
The true dynamics is described by a wave function for which the variations of these two functionals are equal.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: A principle is proposed according to which the dynamics of a quantum particle
in a one-dimensional configuration space (OCS) is determined by a variational
problem for two functionals: one is based on the mean value of the Hamilton
operator, while the second one is based on the mean value of the total energy
of the particle, which is determined through the phase of the wave function
with help of the generalized Planck-Einstein relation. The first functional
contains information about the corpuscular properties of a quantum particle,
and the second one comprises its wave properties. The true dynamics is
described by a wave function for which the variations of these two functionals
are equal. This variational principle, which can also be viewed as a
mathematical formulation of wave-particle duality, leads to the Schr\"{o}dinger
equation.
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