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تسجيل مستخدم جديدSupersymmetry and eigensurface topology of the spherical quantum pendulum
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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 $eta$ and $zeta$. 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 $zeta=frac{eta^2}{4k^2}$ of the intersections of the eigenenergy surfaces spanned by the $eta$ and $zeta$ 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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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 pendulums eigenfuntions make it possible to find
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