Question

Find the energy of an electron of a hydrogen atom in a stationary state for which the wave function takes the form ψ(r) = A (1 + ar) e^-αr, where A, a, and α are constants.

Answer 1

The Schrodinger equation for the problem in Gaussian units

Equating the coefficients of r², r, and constant term to zero we get

This state is one with n = 2 (2s).