Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators

Artemio González-López; Niky Kamran; Peter J. Olver

doi:10.1007/BF02099042

Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators

Artemio González-López, Niky Kamran, Peter J. Olver

School of Mathematics

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123 Scopus citations

Abstract

We completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schrödinger operator on the line. Methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi-exactly solvable Hamiltonians and explicit normalizability conditions in general coordinate systems.

Original language	English (US)
Pages (from-to)	117-146
Number of pages	30
Journal	Communications in Mathematical Physics
Volume	153
Issue number	1
DOIs	https://doi.org/10.1007/BF02099042
State	Published - Apr 1993

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10.1007/BF02099042

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abstract = "We completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schr{\"o}dinger operator on the line. Methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi-exactly solvable Hamiltonians and explicit normalizability conditions in general coordinate systems.",

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AU - Olver, Peter J.

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AB - We completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schrödinger operator on the line. Methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi-exactly solvable Hamiltonians and explicit normalizability conditions in general coordinate systems.

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Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators

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