The Transfer Matrix Grid Method for Quantum Partition Functions, Eigenvalues and Eigenfunctions

Abstract

Abstract A method for the calculation of quantum partition functions, and bound eigenvalues and eigen-functions of the Hamiltonian operator is presented. The method is based on the discretization of the transfer matrix that relates the Feynman path integral to the conventional operator formulation of quantum mechanics. Its implementation is very simple, only requiring the diagonalization of the discretized transfer matrix. The method is applied to the harmonic oscillator and Morse potential. The results are in excellent agreement with the exact ones.