A Computational Method to Explore Linear Harmonic Oscillator

Simple harmonic oscillator is of fundamental importance in physics because it is a model for any system involving oscillations. It is used to describe the motion of atoms in molecules and crystals. The attempts have been made to develop the interactive software to understand the vibrational motion of the atoms in a diatomic molecule about their equilibrium position. In the present work the authors have treated heteronuclear diatomic molecule as a harmonic oscillator. The goal of this present work is to provide a computational exercise to undergraduate students for the evaluation of energy levels [E_n], wave functions ψn(x) and probability density |ψn(x)|² for the various vibrational quantum states (n = 0, 1, 2, 3) of a linear harmonic oscillator. Once the vibrational frequencies are obtained, valuable information regarding vibrational spectrum, anharmonicity and bond strength can be determined for heteronuclear diatomic molecule. The method presented in this paper produces the interactive, visual output of Potential energy curve, Morse curve, energy levels, wave functions, probability density for the allowed quantum state on the screen of computer monitor. The main purpose of this paper is to encourage Physics teachers to think along similar line to suggest several computational methods for Physics Education. Giving students such exercise not only sharpens their computer skill but it will also help them in understanding the Physical concept. This paper throws some light on the role of computational physics in Physics Education and also making physics teaching and learning more interesting and innovative using computer softwares.