Supersymmetry and eigensurface topology of the planar quantum pendulum

Abstract

We make use of supersymmetric quantum mechanics (SUSY QM) to find three sets of conditions under which the problem of a planar quantum pendulum becomes analytically solvable. The analytic forms of the pendulum's eigenfuntions make it possible to find analytic expressions for observables of interest, such as the expectation values of the angular momentum squared and of the orientation and alignment cosines as well as of the eigenenergy. Furthermore, we find that the topology of the intersections of the pendulum's eigenenergy surfaces can be characterized by a single integer index whose values correspond to the sets of conditions under which the analytic solutions to the quantum pendulum problem exist.

References in corpus (5)

• Manipulating the torsion of molecules by strong laser pulses
• Directional States of Symmetric-Top Molecules Produced by Combined Static and Radiative Electric Fields
• Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically
• Topology of surfaces for molecular Stark energy, alignment and orientation generated by combined permanent and induced electric dipole interactions
• Supersymmetric factorization yields exact solutions to the molecular Stark effect problem for "stretched" states

Cited by in corpus (7)

• Supersymmetry and eigensurface topology of the spherical quantum pendulum
• Symmetric Tops Subject to Combined Electric Fields: Conditional Quasi-Solvability via the Quantum Hamilton-Jacobi Theory
• Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime
• Directional properties of polar paramagnetic molecules subject to congruent electric, magnetic and optical fields
• Quantum dynamics of a planar rotor driven by suddenly switched combined aligning and orienting interactions
• Quantum dynamics of a polar rotor acted upon by an electric rectangular pulse of variable duration
• Mapping atomic trapping in an optical superlattice onto the libration of a planar rotor in electric fields