Quantum Mechanics by Numerical Simulation of Path Integral

Abstract

The Quantum Mechanics formulation of Feynman is based on the concept of path integrals, allowing to express the quantum transition between two space-time points without using the bra and ket formalism in the Hilbert space. A particular advantage of this approach is the ability to provide an intuitive representation of the classical limit of Quantum Mechanics. The practical importance of path integral formalism is being a powerful tool to solve quantum problems where the analytic solution of the Schrödinger equation is unknown. For this last type of physical systems, the path integrals can be calculated with the help of numerical integration methods suitable for implementation on a computer. Thus, they provide the development of arbitrarily accurate solutions. This is particularly important for the numerical simulation of strong interactions (QCD) which cannot be solved by a perturbative treatment. This thesis will focus on numerical techniques to calculate path integral on some physical systems of interest.