Numerical Study of Anharmonic Oscillator Using Python Code

In this work, we explore the python code to study the anharmonic oscillator. In obtaining the numerical solution for eigenvalues and eigen-functions, we discretize the spatial coordinates into the finite number of grid points and use the finite difference method. We observe that the effect of anharmonic term in hamiltonian in shifting energy level increases towards higher energy states. We compare eigen functions for ground, first excited and second excited state of the harmonic oscillator with anharmonic oscillator. Further, the corrected wave-functions using first order perturbation theory are compared with wave-functions obtained from the numerical solutions of Schrodinger's equations. Both solutions are found to be consistent to each other for small value of anharmonic term.