  Some recent results in supersymmetric quantum mechanics are presented. New
semi-classical approximation formulas for Witten's realization of
supersymmetric quantum mechanics are discussed. Implications of the
supersymmetric structure of Pauli's Hamiltonian are also considered. In
particular, the paramagnetisation of a non-interacting electron gas is related
to a modified version of Witten's index. We also show that the supersymmetry in
this system provides a new counter example for the paramagnetic conjecture.
