  We present a very efficient technique for solving the three-dimensional
time-dependent Schrodinger equation. Our method is applicable to a wide range
of problems where a fullly three-dimensional solution is required, i.e., to
cases where no symmetries exist that reduce the dimensionally of the problem.
Examples include arbitrarily oriented molecules in external fields and atoms
interacting with elliptically polarized light. We demonstrate that even in such
cases, the three-dimensional problem can be decomposed exactly into two
two-dimensional problems at the cost of introducing a trivial rotation
transformation. We supplement the theoretical framework with numerical results
on strong-field ionization of arbitrarily oriented H2+ molecules.
