  Crank-Nicolson (C-N) Method combined with $ B $-spline basis set can be used
in both time-dependent and time-independent calculations of the photoionization
cross sections of atoms and molecules. For time-independent systems, it is
found that C-N method in imaginary-time propagation (ITP) can converge directly
to not only the ground state, but also excited and continuum states by
controlling the time step size. The C-N method can also be directly applied in
time-dependent calculations. Both time-dependent and time-independent
calculations agree very well with previous results. This method can also be
extended to two-electron systems directly.
