  One of the unitary forms of the quantum mechanical time evolution operator is
given by Cayley's approximation. A numerical implementation of the same
involves the replacement of second derivatives in Hamiltonian with the
three-point formula, which leads to a tridiagonal system of linear equations.
In this work, we invoke the highly accurate five-point stencil to discretize
the wave function onto an Implicit-Explicit pentadiagonal Crank-Nicolson
scheme. It is demonstrated that the resultant solutions are significantly more
accurate than the standard ones. We also discuss the resolution of bipartite
wavepacket dynamics and derive conditions under which a product state from the
laboratory perspective remains a product state from the center-of-mass point of
view. This has profound applications for decoupling complicated bipartite
dynamics into two independent single-particle problems.
