Quantum Systems: A Mathematical Journey from Few to Many Particles
The Gaussian wave packet transform: Efficient computation of the semi-classical limit of the Schroedinger equation
University of Michigan
An efficient method for simulating the propagation of a
localized solution of the Schroedinger equation near the semiclassical
limit is presented. The method is based on a time dependent
transformation closely related to Gaussian wave packets
and yields a Schroedinger type equation that is very
amenable to numerical solution in the semi-classical limit.
The wavefunction can be reconstructed from the
transformed wavefunction whereas expectation values can easily be
evaluated directly from the transformed wavefunction.
The number of grid points needed per degree of freedom is
small enough that computations in dimensions of up to 4 or 5
are feasible without the use of any basis thinning procedures.
This is joint work with Giovanni Russo.