Sensitivity analysis for quantum eigenvalues of bound systems

J. Brickmann; R. D. Levine

doi:10.1016/0009-2614(85)87052-4

Sensitivity analysis for quantum eigenvalues of bound systems

J. Brickmann^*, R. D. Levine

^*Corresponding author for this work

Institute of Chemistry

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The sensitivity of the eigenvalues E_i of a non-integrable Hamiltonian measured by their second differences or second derivatives d²E_i/dλ² with respect to a coupling parameter λ is studied for the regular and the irregular part of the spectrum as well as for the range of isolated avoided crossings. In the regular part the d²E_i/dλ² values are expected to be arranged on branches in a plot versus energy: in the avoided-crossing range there should be a drastic increase, and for the irregular part a decrease and a breakdown of the branching is predicted.

Original language	English
Pages (from-to)	252-256
Number of pages	5
Journal	Chemical Physics Letters
Volume	120
Issue number	3
DOIs	https://doi.org/10.1016/0009-2614(85)87052-4
State	Published - 11 Oct 1985

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AB - The sensitivity of the eigenvalues Ei of a non-integrable Hamiltonian measured by their second differences or second derivatives d2Ei/dλ2 with respect to a coupling parameter λ is studied for the regular and the irregular part of the spectrum as well as for the range of isolated avoided crossings. In the regular part the d2Ei/dλ2 values are expected to be arranged on branches in a plot versus energy: in the avoided-crossing range there should be a drastic increase, and for the irregular part a decrease and a breakdown of the branching is predicted.

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Sensitivity analysis for quantum eigenvalues of bound systems

Abstract

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