The proofs in a quantum mechanical d'Alembert Principle

Author

Jordan E. Cahn

Date of Award

12-1991

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Boris A. Kupershmidt

Committee Members

K. C. Reddy, Horace Crater

Abstract

The d' Alembert principle states that if a particle is constrained to a manifold, no work can be done normal to the manifold, however, quantum mechanics forbids the restraint of a particle. The constraint is replaced by an infinite potential and the Schödinger equation can be separated to produce a potential field on the manifold which is a function of the manifold's curvature. This is done for a one-dimensional curve and then for a general manifold. New work is presented as the case of a particle on a circle and the case of a product manifold are investigated.

Recommended Citation

Cahn, Jordan E., "The proofs in a quantum mechanical d'Alembert Principle. " Master's Thesis, University of Tennessee, 1991.
https://trace.tennessee.edu/utk_gradthes/12361