Supersymmetry and eigensurface topology of the planar quantum pendulum
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 inte...
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2014-06-01
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doaj-954226ed8d79474caf5f6961d78476a42020-11-25T00:59:47ZengFrontiers Media S.A.Frontiers in Physics2296-424X2014-06-01210.3389/fphy.2014.0003793621Supersymmetry and eigensurface topology of the planar quantum pendulumBurkhard eSchmidt0Bretislav eFriedrich1Fritz-Haber-Institut der Max-Planck-GesellschaftFritz-Haber-Institut der Max-Planck-GesellschaftWe 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.http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00037/fullOrientationAlignmentsupersymmetryplanar rotor/pendulumspherical rotor/pendulummolecular Stark effect |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Burkhard eSchmidt Bretislav eFriedrich |
spellingShingle |
Burkhard eSchmidt Bretislav eFriedrich Supersymmetry and eigensurface topology of the planar quantum pendulum Frontiers in Physics Orientation Alignment supersymmetry planar rotor/pendulum spherical rotor/pendulum molecular Stark effect |
author_facet |
Burkhard eSchmidt Bretislav eFriedrich |
author_sort |
Burkhard eSchmidt |
title |
Supersymmetry and eigensurface topology of the planar quantum pendulum |
title_short |
Supersymmetry and eigensurface topology of the planar quantum pendulum |
title_full |
Supersymmetry and eigensurface topology of the planar quantum pendulum |
title_fullStr |
Supersymmetry and eigensurface topology of the planar quantum pendulum |
title_full_unstemmed |
Supersymmetry and eigensurface topology of the planar quantum pendulum |
title_sort |
supersymmetry and eigensurface topology of the planar quantum pendulum |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Physics |
issn |
2296-424X |
publishDate |
2014-06-01 |
description |
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. |
topic |
Orientation Alignment supersymmetry planar rotor/pendulum spherical rotor/pendulum molecular Stark effect |
url |
http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00037/full |
work_keys_str_mv |
AT burkhardeschmidt supersymmetryandeigensurfacetopologyoftheplanarquantumpendulum AT bretislavefriedrich supersymmetryandeigensurfacetopologyoftheplanarquantumpendulum |
_version_ |
1725216126515806208 |