Semiclassical approach for path integrals in quantum mechanics

Abstract

In this work we have explored the formalism of the path integral in the semiclassical approximation and we have obtained both analytical and numerical results to determine the expected values of quantum observables incorporating thermal fluctuations. The study has been done for the harmonic and anharmonic potentials in one dimension. The obtained results have been compared with those obtained by solving the Schr¨odinger equation and the path integral Monte Carlo method; the similarities and discrepancies have been discussed.