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).