  The numerical treatment of quantum mechanics in the semi-classical regime is
known to be computationally demanding, due to the highly oscillatory behaviour
of the wave function and its large spatial extension. A recently proposed
representation of quantum mechanics as a residual theory on top of classical
Hamiltonian mechanics transforms a semi-classical wave function into a
slowly-fluctuating, spatially confined residual wave function. This
representation is therefore well-suited for the numerical solution of
semi-classical quantum problems. In this note I outline the formulation of the
theory and demonstrate its applicability to a set of semi-classical scenarios,
including a discussion of limitations. I work out the connection to established
numerical approaches, such as the Gaussian beam approximation and the Gaussian
wave packet transform by Russo and Smereka. A prototypical implementation of
the method has been published as open-source software.
