Supersymmetry and Eigensurface Topology of the Planar Quantum Pendulum

Perspective view of the eigensurfaces and their intersection loci.Click here for a PDF allowing for interactive rotation, etc. (55 MB); special thanks to Ulrich Reitebuch from the Mathematical Geometry Processing group lead by Prof. Konrad Polthier

Burkhard Schmidt and Bretislav Friedrich 

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 eigenfunctions 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. 

Front. Physics 2, 37 (2014)

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