Calculation of Quantum Harmonic Oscillator Energies Using Path Integral Monte Carlo
Nowo Riveli

Universitas Padjadjaran

Abstract

Energy eigenvalues up to the second excited state of quantum harmonic oscillator are calculated by means of Path Integral Monte Carlo method. Application of the path integral method in simple problem serve as a demonstration of the principal and numerical technique of this important subject in quantum mechanics. This is particularly important for university students whom familiar only with the Schrodinger equation approach. The importance came from the fact that path integral is the foundation of the more advance theories in molecular to particle physics. In this paper, the explanation of path integral formulation for quantum harmonic oscillator will be given, along with the numerical Monte Carlo procedure to perform the calculation. The energies eigenvalues from the ground state up to the second excited states are obtained, with results that matches the analytic solutions.

Keywords: quantum mechanics, harmonic oscillator, path integral, Monte Carlo

Topic: Physics