Quantization of Nonholonomic Constraints Using the WKB Approximation

Abstract

The Hamilton-Jacobi theory is used to obtain the Hamilton function for nonholonomic constraints in addition to the equations of motion. The technique of separation of variables and canonical transformation is applied here to solve the HamiltonJacobi partial differential equation for nonholonomic systems. The Hamilton-Jacobi function is then used to construct the wave function and to quantize these systems using the WKB approximation.

Keywords:Nonholonomic constraints; Quantization; WKB approximation.