Conditional Analytic Solvability of the Quantum Pendulum Eigenproblem

Friedrich, Bretislav

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Conditional Analytic Solvability of the Quantum Pendulum Eigenproblem

Friedrich, B. (2018). Conditional Analytic Solvability of the Quantum Pendulum Eigenproblem. Talk presented at 256th ACS National Meeting & Exposition, Nanoscience, Nanotechnology & Beyond, Symposium in Honor of Raphael Levine. Boston, MA, USA. 2018-08.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0002-7AC9-3 Version Permalink: https://hdl.handle.net/21.11116/0000-0003-0A1E-2

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Friedrich, Bretislav¹, Author

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1Molecular Physics, Fritz Haber Institute, Max Planck Society, ou_634545

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Abstract: We made use of supersymmetric quantum mechanics (SUSY QM) to find conditions under which the Stark effect problem for a polar and polarizable molecule subject to collinear electrostatic and nonresonant radiative fields becomes analytically solvable. These conditions coincide with the loci ζ = η2/4k2 of the intersections of the eigenenergy surfaces spanned by the orienting and aligning interaction parameters η and ζ.

In addition, we made use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasi-solvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). The QHJ approach allowed to retrieve the exact closed-form solutions for the spherical and planar pendula and the Razavy double-well system that had been obtained in our earlier work via SUSY QM as well as to find a cornucopia of additional analytic solutions.

The analytic expressions for the characteristics of the strongly oriented and aligned states provide direct access to the values of the interaction parameters required for creating such states in the laboratory. Moreover, the algebraic solutions may serve as benchmarks for numerical analysis and the polynomial Ansatz they suggest could be useful for numerical calculations beyond quasi-solvability, when the topological index is non-integral.

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Language(s): eng - English

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Title: 256th ACS National Meeting & Exposition, Nanoscience, Nanotechnology & Beyond, Symposium in Honor of Raphael Levine

Place of Event: Boston, MA, USA

Start-/End Date: 2018-08

Invited: Yes

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