Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

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Abstract

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them in the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with nonperiodic boundary conditions. Applications to the Azbel-Hofstadter problem are outlined.

Original languageEnglish
Pages (from-to)762-776
Number of pages15
JournalTheoretical and Mathematical Physics
Volume104
Issue number1
DOIs
Publication statusPublished - Jul 1995
Externally publishedYes

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