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

Charles P. Boyer, Willard Miller

Research output: Contribution to journalArticle

11 Citations (Scopus)

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
StatePublished - Dec 1 1973

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Hamiltonians
Mathematical operators
operators
polar coordinates
Cartesian coordinates
Operator
Cartesian
Higher Dimensions
Classify
First-order
Generalise
Form

Cite this

A classification of second-order raising operators for Hamiltonians in two variables. / Boyer, Charles P.; Miller, Willard.

In: Journal of Mathematical Physics, Vol. 15, No. 9, 01.12.1973, p. 1484-1489.

Research output: Contribution to journalArticle

Boyer, Charles P. ; Miller, Willard. / A classification of second-order raising operators for Hamiltonians in two variables. In: Journal of Mathematical Physics. 1973 ; Vol. 15, No. 9. pp. 1484-1489.
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