  The recently reported compactified hyperboloidal method has found wide use in
the numerical computation of quasinormal modes, with implications for fields as
diverse as gravitational physics and optics. We extend this intrinsically
relativistic method into the non-relativistic domain, demonstrating its use to
calculate the quasinormal modes of the Schr\"odinger equation and solve related
bound-state problems. We also describe how to further generalize this method,
offering a perspective on the importance of non-relativistic quasinormal modes
for the programme of black hole spectroscopy.
