Supersymmetric factorization yields exact solutions to the molecular   Stark effect problem for "stretched" states
  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. 
Mikhail Lemeshko, Mustafa Mustafa, Sabre Kais, Bretislav Friedrich
physics.chem-ph math-ph math.MP physics.atom-ph quant-ph