A quantum-statistical Monte Carlo method; path integrals with boundary conditions

A new Monte Carlo method for problems in quantum-statistical mechanics is described. The method is based on the use of iterated short-time Green’s functions, for which ’’image’’ approximations are used. It is similar to the use of Feynman or Wiener path integrals but with a modification to take account of hard-core boundary conditions. It is applied to two one-dimensional test problems: that of a single particle in a hard-walled box and that of two hard particles in a hard-walled box. For these test problems, the results are in excellent agreement with exact quantum-mechanical results both at high temperatures (near the classical limit) and at very low temperatures such that essentially only the ground state is occupied. Generalizations to three-dimensional systems, to many-body systems, and to more realistic potentials are discussed briefly.