The Spatial part of the Time-Independent Schrödinger Equation (TISE) is
the equation becomes a wave equation with a source, or scattering equation.
for solving it, we have to find the Green function such that
The solution is easy ( i will post it later, you can think the Green function is the inverse of the Operator)
the particular solution is
plus the homogeneous solution
but it is odd that the solution contain itself!