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Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory

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Schatz,  Konrad
Molecular Physics, Fritz Haber Institute, Max Planck Society;

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Friedrich,  Bretislav
Molecular Physics, Fritz Haber Institute, Max Planck Society;

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PhysRevA.97.053417.pdf
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Citation

Schatz, K., Friedrich, B., Becker, S., & Schmidt, B. (2018). Symmetric tops in combined electric fields: Conditional quasisolvability via the quantum Hamilton-Jacobi theory. Physical Review A, 97(5): 053417. doi:10.1103/PhysRevA.97.053417.


Cite as: http://hdl.handle.net/21.11116/0000-0001-6D1C-7
Abstract
We make use of the quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasisolvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasisolvability of the time-independent Schrödinger equation as well as the corresponding finite sets of exact analytic solutions. We do so for this prototypical trigonometric system as well as for its anti-isospectral hyperbolic counterpart. An examination of the algebraic and numerical spectra of these two systems reveals mutually closely related patterns. The QHJ approach allows us to retrieve the closed-form solutions for the spherical and planar pendula and the Razavy system that had been obtained in our earlier work via supersymmetric quantum mechanics as well as to find a cornucopia of additional exact analytic solutions.