Asymptotic series in quantum mechanics: anharmonic oscillator

Abstract

This thesis deals with the study of the asymptotic series that one obtains for the ground state energy of the anharmonic oscillator, that is, an harmonic oscillator with a quartic perturbation term in its Hamiltonian. First we study a simplified field theory model as an introductory example, and then we use the path integral formulation and semiclassical methods to obtain analytically the behaviour of the series at large order.