Solution of Quantum Anharmonic Oscillator with Quartic Perturbation

Abstract

This study was designed to obtain the energy eigenvalues for a Quantum Anharmonic Oscillator with Quartic Perturbation Potential. Two independent methods, the Dirac operator technique and the Numerov approach in solving Schrodinger equation, were used to solve the second order differential equation obtained from this system. An iterative procedure was carried out using the fourth order Runge-Kutta method on the transformed second order differential equation in line with the Numerov equation. The results showed that the normalized eigenvalues obtained from the Dirac operator technique, when compared with eigenvalues obtained from the use of the Fourth order Runge-Kutta method within the Numerov approach agreed closely when the convergence in the perturbing potential is weak, but the set of results diverges only at high excitation states. For the results from the two approaches to be closely compatible at high excitation states, the choice of Zeta axis was made to satisfy the boundary conditions -1< zeta< +1.

Keywords: QQAHO, Hamiltonian, Perturbation, Dirac Operation Technique, Numerov Approach, Zeta, Runge - Kutta Method and Eigenvalues.