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

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.

4 pages, 2 figures

References in corpus (6)

• Supersymmetry and Quantum Mechanics
• Calculation of accurate permanent dipole moments of the lowest ${}^{1,3}{\Sigma }^{+}$ states of heteronuclear alkali dimers using extended basis sets
• Calculations of static dipole polarizabilities of alkali dimers. Prospects for alignment of ultracold molecules
• Non-Central Potentials and Spherical Harmonics Using Supersymmetry and Shape Invariance
• Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation
• Directional States of Symmetric-Top Molecules Produced by Combined Static and Radiative Electric Fields

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• Manipulation of Molecules with Electromagnetic Fields
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• Topology of surfaces for molecular Stark energy, alignment and orientation generated by combined permanent and induced electric dipole interactions
• Supersymmetry and eigensurface topology of the spherical quantum pendulum
• Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart
• Symmetric Tops Subject to Combined Electric Fields: Conditional Quasi-Solvability via the Quantum Hamilton-Jacobi Theory
• Directional properties of polar paramagnetic molecules subject to congruent electric, magnetic and optical fields