  In this paper we explore new ways to study the zero temperature limit of
quantum statistical mechanics using Quantum Monte Carlo simulations. We develop
a Quantum Monte Carlo method in which one fixes the ground state energy as a
parameter. The Hamiltonians we consider are of the form $H=H_{0}+\lambda V$
with ground state energy E. For fixed $H_{0}$ and V, one can view E as a
function of $\lambda$ whereas we view $\lambda$ as a function of E. We fix E
and define a path integral Quantum Monte Carlo method in which a path makes no
reference to the times (discrete or continuous) at which transitions occur
between states. For fixed E we can determine $\lambda(E)$ and other ground
state properties of H.
