The Classical Limit of Quantum Mechanics

• Main Author: Hefley, Velton Wade
• Other Authors: Kobe, Donald Holm
• Format: Others
• Language: English
• Published: North Texas State University 1977
• Subjects: quantum theory; space-time; Schrödinger equation; Newtonian mechanics; Mechanics.; Quantum theory.; Feynman integrals.; Ehrenfest theorem.
• Online Access: https://digital.library.unt.edu/ark:/67531/metadc504591/

The Feynman path integral formulation of quantum mechanics is a path integral representation for a propagator or probability amplitude in going between two points in space-time. The wave function is expressed in terms of an integral equation from which the Schrodinger equation can be derived. On taking the limit h — 0, the method of stationary phase can be applied and Newton's second law of motion is obtained. Also, the condition the phase vanishes leads to the Hamilton - Jacobi equation. The secondary objective of this paper is to study ways of relating quantum mechanics and classical mechanics. The Ehrenfest theorem is applied to a particle in an electromagnetic field. Expressions are found which are the hermitian Lorentz force operator, the hermitian torque operator, and the hermitian power operator.