Supersymmetry and eigensurface topology of the planar quantum pendulum

Frontiers in Physics

Schmidt, Burkhard²  Friedrich, Bretislav³ 

[1] Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany;Institute for Mathematics, Freie Universität Berlin, Berlin, Germany

关键词: Orientation;    Alignment;    planar rotor/pendulum;    spherical rotor/pendulum;    molecular Stark effect;    supersymmetry;    Mathieu equation;   

DOI  :  10.3389/fphy.2014.00037

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY