  We describe a parallel algorithm for solving the time-independent 3d
Schrodinger equation using the finite difference time domain (FDTD) method. We
introduce an optimized parallelization scheme that reduces communication
overhead between computational nodes. We demonstrate that the compute time, t,
scales inversely with the number of computational nodes as t ~ N_nodes^(-0.95
+/- 0.04). This makes it possible to solve the 3d Schrodinger equation on
extremely large spatial lattices using a small computing cluster. In addition,
we present a new method for precisely determining the energy eigenvalues and
wavefunctions of quantum states based on a symmetry constraint on the FDTD
initial condition. Finally, we discuss the usage of multi-resolution techniques
in order to speed up convergence on extremely large lattices.
