Energy-reflection symmetry of Lie-algebraic problems: Where the quasiclassical and weak-coupling expansions meet

M. Shifman, A. Turbiner

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We construct a class of one-dimensional Lie-algebraic problems based on sl(2), where the spectrum in the algebraic sector has a dynamical symmetry E↔ - E. All 2j+l eigenfunctions in the algebraic sector are paired and inside each pair are related to each other by a simple analytic continuation x→ix, except the zero mode appearing if j is integer. At j→∞ the energy of the highest level in the algebraic sector can be calculated by virtue of the quasiclassical expansion, while the energy of the ground state can be calculated as a weak-coupling expansion. Both series coincide identically

Original languageEnglish (US)
Article number1791
Pages (from-to)1791-1798
Number of pages8
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume59
Issue number3
DOIs
StatePublished - Mar 1999

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