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arXiv · 1409.2225

Supersymmetry and eigensurface topology of the spherical quantum pendulum

Burkhard Schmidt·Bretislav Friedrich
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Abstract

We undertook a mutually complementary analytic and computational study of the full-fledged spherical (3D) quantum rotor subject to combined orienting and aligning interactions characterized, respectively, by dimensionless parameters $η$ and $ζ$. By making use of supersymmetric quantum mechanics (SUSY QM), we found two sets of conditions under which the problem of a spherical quantum pendulum becomes analytically solvable. These conditions coincide with the loci $ζ=\frac{η^2}{4k^2}$ of the intersections of the eigenenergy surfaces spanned by the $η$ and $ζ$ parameters. The integer topological index $k$ is independent of the eigenstate and thus of the projection quantum number $m$. These findings have repercussions for rotational spectra and dynamics of molecules subject to combined permanent and induced dipole interactions.

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Burkhard Schmidt, Bretislav Friedrich. 2015-01-14. Supersymmetry and eigensurface topology of the spherical quantum pendulum. https://doi.org/10.1103/physreva.91.022111

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