Abstract:

In this work, the Hamilton-Jacobi method for treating singular Lagrangian systems is extended to the case of time dependent constraints by using the separation of variables technique. The necessary and sufficient conditions for recovery of the Hamilton-Jacobi function are found. The equations of motion are obtained as total differential equations in many variables. Moreover, the quantization of time dependent constrained systems is applied using the WKB approximation. The constraints become conditions on the wave function to be satisfied the semi-classical limit; this is illustrated through two examples.