  I examine quantum mechanical Hamiltonians with partial supersymmetry, and
explore two main applications. First, I analyze a theory with a logarithmic
spectrum, and show how to use partial supersymmetry to reveal the underlying
structure of this theory. This method reveals an intriguing equivalence between
two formulations of this theory, one of which is one-dimensional, and the other
of which is infinite-dimensional. Second, I demonstrate the use of partial
supersymmetry as a tool to obtain the asymptotic energy levels in
non-relativistic quantum mechanics in an exceptionally easy way. In the end, I
discuss possible extensions of this work, including the possible connections
between partial supersymmetry and renormalization group arguments.
