Analytical solutions of the Schrödinger equation for a hydrogen atom in a uniform electric field

We consider the Schrödinger equation for the hydrogen atom in a uniform electric field, searching for solutions of this equation in parabolic coordinates in a separable form. With some restrictions on the parameters, we have found the exact analytical expressions for the continuum wave function component and for the most important Stokes multiplier.

Figure 1

The relative error of the semiclassical representation [25] of the Stokes multiplier $T_{2,3}$.