## 2007.1: A band factorization technique for transition matrix element asymptotics

2007.1:
Emmanuel Perrey-Debain and David Abrahams
(2006)
*A band factorization technique for transition matrix element asymptotics.*
Computer Physics Communications, 175 (5).
pp. 315-322.
ISSN 0010-4655

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DOI: 10.1016/j.cpc.2006.05.003

## Abstract

A new method of evaluating transition matrix elements between wave functions associated with orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. The form of the matrix elements is perfectly suited to very large quantum number calculations by using asymptotic series expansions. In practice, this allows the accurate and fast numerical treatment of transition matrix elements in the quasi-classical limit. Examples include the matrix elements of xp in the harmonic oscillator basis, and connections with the Wigner 3j symbols.

Item Type: | Article |
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Uncontrolled Keywords: | Transition matrix; Quasi-classical approximation; Harmonic oscillator; Orthogonal polynomial |

Subjects: | PACS 2003 > 03 Quantum mechanics, field theories, and special relativity |

MIMS number: | 2007.1 |

Deposited By: | Miss Louise Stait |

Deposited On: | 03 January 2007 |

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