Connection factors in the Schrödinger equation with a polynomial potential (Q2643094)

The authors consider the problem of determination of connection factors for a Schrödinger equation of the form \[ -z^{2}\frac{d^{2}w}{dz^{2}}+g(z)w=0, \] where \(g(z)\) is a real polynomial of odd order with a positive leading coefficient. They suggest a procedure to obtain those factors.