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Quantum Monte Carlo Motivation

As an example from the nuclear many-body problem, we have Schroedinger's equation as a differential equation

\hat{H}\Psi(\boldsymbol{r}_1,..,\boldsymbol{r}_A,\alpha_1,..,\alpha_A)=E\Psi(\boldsymbol{r}_1,..,\boldsymbol{r}_A,\alpha_1,..,\alpha_A)

where

\boldsymbol{r}_1,..,\boldsymbol{r}_A,

are the coordinates and

\alpha_1,..,\alpha_A,

are sets of relevant quantum numbers such as spin and isospin for a system of A nucleons ( A=N+Z , N being the number of neutrons and Z the number of protons).