A band factorization technique for transition matrix element asymptotics

Perrey-Debain, Emmanuel and Abrahams, David (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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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
Uncontrolled Keywords:	Transition matrix; Quasi-classical approximation; Harmonic oscillator; Orthogonal polynomial
Subjects:	PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 03 Quantum mechanics, field theories, and special relativity
Depositing User:	Ms Lucy van Russelt
Date Deposited:	03 Jan 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/682

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