Perturbation WKB approximation: Quartic anharmonic oscillator

A perturbation-WKB method, which combines WKB approximation and stationary-state perturbation theory, is presented and used to deal with the bound-state perturbation problem of quantum system. This method inherits the conciseness of WKB, which turns the calculation of matrix element into the calculation of a definite integral, and is especially suitable to a perturbed system in higher excited state. As an example, the perturbation-WKB method is applied to find the energy of lambda chi(4) anharmonic oscillator. The results calculated are compared with the accurate values and the values obtained from low-order variational perturbation theory.