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

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.

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PhysRevA.97.053417.pdf (Publisher version), 2MB
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PhysRevA.97.053417.pdf
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2018
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 Creators:
Schatz, Konrad1, Author           
Friedrich, Bretislav1, Author           
Becker, Simon2, Author
Schmidt, Burkhard2, Author
Affiliations:
1Molecular Physics, Fritz Haber Institute, Max Planck Society, ou_634545              
2Institute for Mathematics, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany, ou_persistent22              

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 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.

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Language(s): eng - English
 Dates: 2018-02-232018-052018-05-31
 Publication Status: Issued
 Pages: 17
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1103/PhysRevA.97.053417
arXiv: 1802.07939
 Degree: -

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Title: Physical Review A
  Other : Phys. Rev. A
Source Genre: Journal
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Publ. Info: New York, NY : American Physical Society
Pages: - Volume / Issue: 97 (5) Sequence Number: 053417 Start / End Page: - Identifier: ISSN: 1050-2947
CoNE: https://pure.mpg.de/cone/journals/resource/954925225012_2