Semiclassical solutions in statistical quantum mechanics: second-order corrections and applications to nuclear matter

Abstract

We consider the Feynman path integral formalism applied to different quantum systems at finite temperature under the semiclassical approximation. To refine previous results, we first develop its second-order correction by implementing the Gel’fand-Yaglom method numerically and apply it to the 1D nonperturbative anharmonic oscillator. Then, we extend the semiclassical approach to a generic two-body potential, V (r), and apply it to the 3D spherical harmonic oscillator and to the nucleon-nucleon interaction to obtain thermodynamical properties of nuclear matter