the following ode appears in in the quantum mechanics of stark effect.can you obtain the solution and show it is related to associated laguerre polynomials.
The Stark effect here evidently includes both linear (a x) and quadratic (e x^2) contributions. It is usually treated by perturbation theory. The Stark effect with just the linear contribution can be solved exactly in parabolic coordinates. The quadratic part can then be treated as a perturbation.
is there any way to solve it using frobenius power series method ??