Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators

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

Research output: Contribution to journalArticlepeer-review

121 Scopus citations


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 languageEnglish (US)
Pages (from-to)117-146
Number of pages30
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Apr 1993


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