Supersymmetric factorization yields exact solutions to the molecular Stark effect problem for "stretched" states

TL;DR

This paper uses supersymmetry to find exact solutions for the Stark effect in polar molecules under specific conditions, providing explicit wavefunctions and physical quantities for certain states.

Contribution

It introduces a supersymmetry-based method to exactly solve the Stark effect problem for 'stretched' molecular states, deriving explicit wavefunctions and physical observables.

Findings

Exact wavefunctions for specific molecular states obtained

Analytic expressions for energy and dipole moments derived

Method enables reverse-engineering of interaction parameters

Abstract

By invoking supersymmetry, we found a condition under which the Stark effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable. The exact solvability condition for the interaction parameters involved yields exact wavefunction for the "stretched" states, $|J=m,m>$, and for the $|1,1>$ state in the case of a purely induced-dipole interaction. The analytic expressions for the eigenenergy, the space-fixed dipole moment, the alignment cosine, and the expectation value of the angular momentum allow to readily reverse-engineer the problem of finding the values of the interaction parameters required for creating quantum states with preordained characteristics.