On a class of non-separable quantum-mechanical eigenvalue problems. Analytical and technical considerations within the frame of a Born expansion method (Q1322973)

The author extends an idea of Born to non-separable quantum-mechanical eigenvalue problems. By analytical and algebraic considerations in one of the singular points of the problem all regular solutions are constructed and mapped. The numerical results show that the Born expansion method is a viable alternative for computational applications which leads to a reduction of computing efforts, compared to an eigenfunction expansion in a Legendre or Landau basis.