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=4k2η2 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.Comment: arXiv admin note: text overlap with arXiv:1404.224