A variational principle, waveparticle duality, and the Schrödinger equation
Abstract
A principle is proposed according to which the dynamics of a quantum particle in a onedimensional 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 PlanckEinstein 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 waveparticle duality, leads to the Schrödinger equation.
 Publication:

arXiv eprints
 Pub Date:
 June 2022
 arXiv:
 arXiv:2206.14601
 Bibcode:
 2022arXiv220614601C
 Keywords:

 Quantum Physics