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Journal Article

Supersymmetry and eigensurface topology of the spherical quantum pendulum


Friedrich,  Bretislav
Molecular Physics, Fritz Haber Institute, Max Planck Society;

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Schmidt, B., & Friedrich, B. (2015). Supersymmetry and eigensurface topology of the spherical quantum pendulum. Physical Review A, 91(2): 022111. doi:10.1103/PhysRevA.91.022111.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0024-C6A8-7
We undertook a mutually complementary analytic and computational study of the full-fledged spherical (three-dimensional) quantum rotor subject to combined orienting and aligning interactions, corresponding to a linear polar and polarizable molecule interacting with an electric field. The orienting and aligning interactions are characterized, respectively, by dimensionless parameters η and ζ. By making use of supersymmetric quantum mechanics, we found two sets of conditions (cases A and B) under which the problem of a spherical quantum pendulum becomes analytically solvable. These conditions coincide with the loci ζ=η2/4k2 of the intersections of the eigenenergy surfaces spanned by the η and ζ parameters. In case A, the topological index k=∓m+1 with m the angular momentum projection quantum number, whereas, in case B, k=1, independent of m. These findings have repercussions for rotational spectra and dynamics of molecules subject to combined permanent and induced dipole interactions.