### 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 language | English (US) |
---|---|

Pages (from-to) | 1484-1489 |

Number of pages | 6 |

Journal | Journal of Mathematical Physics |

Volume | 15 |

Issue number | 9 |

State | Published - Dec 1 1973 |

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### Cite this

*Journal of Mathematical Physics*,

*15*(9), 1484-1489.

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 15, no. 9, pp. 1484-1489.

}

TY - JOUR

T1 - A classification of second-order raising operators for Hamiltonians in two variables

AU - Boyer, Charles P.

AU - Miller, Willard

PY - 1973/12/1

Y1 - 1973/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36849102796&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849102796&partnerID=8YFLogxK

M3 - Article

VL - 15

SP - 1484

EP - 1489

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

ER -