A new derivation of Judds isolated exact solutions for E ⊗ e and Γ8 ⊗ τ2 Jahn-Teller systems

Reik, H.G.; Ribeiro, Lincoln Almir Amarante; Blunck, M.

doi:10.1016/0038-1098(81)90425-7

Cited by 11 publications

(2 citation statements)

References 12 publications

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“…This is another reason for adoption of χ as a natural parameter-quarters correspond to the newly found states, while half integer values (for which the Bessel function reduce to exponentials) correspond to those of Emary and Bishop. The relation of Juddian states to elementary Bessel functions was also the basis of Reik's approach [16].…”

Section: Third Approachmentioning

confidence: 99%

Level crossings and new exact solutions of the two-photon Rabi model

Maciejewski

Stachowiak

2019

J. Phys. A: Math. Theor.

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An infinite family of exact solutions of the two-photon Rabi model was found by investigating the differential algebraic properties of the Hamiltonian. This family corresponds to energy level crossings not covered by the Juddian class, which is given by elemetary functions. In contrast, the new states are expressible in terms of parabolic cylinder or Bessel functions. We discuss three approaches for discovering this hidden structure: factorization of differential equations, Kimura transformation, and a doubly-infinite, transcendental basis of the Bargmann space.

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Section: Third Approachmentioning

confidence: 99%

Level crossings and new exact solutions of the two-photon Rabi model

Maciejewski

Stachowiak

2019

J. Phys. A: Math. Theor.

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“…Reik et al 12,[36][37][38] simplified the analysis of the Juddian ͑isolated exact͒ solutions for H PJT by observing that, at the Juddian points, a Neumann expansion of the Bargmann space wave function in modified Bessel functions terminates after a finite number of terms. Here, we simply recover the results of Reik et al using the operator approach given above and obtain explicit expressions ͑independent of the realization of the bosonic modes͒ for the Juddian wave functions in the Dirac rather than the Bargmann representation.…”

Section: Juddian Solutionsmentioning

confidence: 99%

Simple accurate coupled cluster results for the linear E⊗e pseudo-Jahn–Teller effect

Bishop

Davidson

Quick

et al. 2000

The Journal of Chemical Physics

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Using the coupled cluster method ͑CCM͒, we present a simple accurate calculation for the energies of the ground-and first excited states of the linear E e Jahn-Teller and pseudo-Jahn-Teller Hamiltonians. From the solution of a single transcendental equation, we obtain results with a maximal error of 1.2%. These results are notably better than previous results obtained both via the CCM and other many-body approximations.

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Isolated exact solutions of Simple Nonadiabatic Model Hamiltonians

Reik

Kaspar

1983

Z. Physik B - Condensed Matter

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A new derivation of Judds isolated exact solutions for E ⊗ e and Γ8 ⊗ τ2 Jahn-Teller systems

Cited by 11 publications

References 12 publications

Level crossings and new exact solutions of the two-photon Rabi model

Level crossings and new exact solutions of the two-photon Rabi model

Simple accurate coupled cluster results for the linear E⊗e pseudo-Jahn–Teller effect

Isolated exact solutions of Simple Nonadiabatic Model Hamiltonians

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