Monte Carlo methods are good for evaluating probabilistic integrals. A key feature of quantum mechanics is that we must deal with complex amplitudes rather than real positive probabilities. Intrinsically, Monte Carlo methods are not a "natural" match with quantum problems, and can only be successfully used where the quantum problem can be made to look like some classical problem. For example, the ground state wavefunction of a single particle or Bose system is everywhere positive, and so we can

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... evaluate integrals over this wavefunction by Monte Carlo methods. This is a useful and much used approach. On the other hand excited states of these systems, and the ground state of Fermi systems necessarily have regions of positive and negative wave function. This makes the problem much harder, and dealing with the "sign problem" remains an active research area.