Path Integral Simulation of the Harmonic and Anharmonic Oscillators

Abstract

In this work, the Path Integral Formulation of Quantum Mechanics is presented. Aside from providing an elegant and intuitive approach to Quantum Mechanics, this formalism has proven to be very useful in fields such as low-energy Quantum Chromodynamics, where the perturbative method cannot be used. Even though there is great difficulty in its analytic treatment, making the formalism not practical for situations where the analytical solution of Schrödinger's equation is known, the use of numerical methods through computer simulations has proven to be a powerful tool to solve complicated problems. The main focus of this project is the implementation of this method using importance sampling in Monte Carlo integration, through which several physical quantities of interest are computed for the quantum harmonic and anharmonic oscillators