Quantization of Time Independent Damping Systems Using WKB Approximation

In this work time independent damping systems are studied using Lagrangian and Hamiltonian for time independent damping, which are present through the factor eλq. The Hamilton Jacobi equation is formulated to find the Hamilton Jacobi function S using separation of variables technique. We can form this function in compact form of two parts the first part as a function of coordinate q, and the second part as a function of time t. Finally, we find the ability of these systems to quantize through an illustrative example.