A classification of second-order raising operators for Hamiltonians in two variables

Charles P. Boyer, Willard Miller

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We develop a group theoretic method based on results of Winternitz et al. to compute and classify all first- and second-order raising and lowering operators admitted by Hamiltonians of the form H = - (1/2)Δ2 + V (x, y). The key to our results, which generalize to higher dimensions, is a proof that H admits a second-order raising operator only if the Schrödinger equation separates in Cartesian, polar, or elliptic coordinates.

Original languageEnglish (US)
Pages (from-to)1484-1489
Number of pages6
JournalJournal of Mathematical Physics
Volume15
Issue number9
DOIs
StatePublished - 1973

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