Harmonic oscillator tensors. III: Efficient algorithms for evaluating matrix elements of vibrational operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Harmonic oscillator tensors. III: Efficient algorithms for evaluating matrix elements of vibrational operators

Authors:	Pancracio Palting Shan Tao Lai Ying Nan Chiu Jorge Ricardo Letelier

Institution:	(1) Center for Molecular Dynamics and Energy Transfer Department of Chemistry, The Catholic University of America, Washington, DC, 20064, USA;(2) Vitreous State Laboratory and Department of Chemistry, The Catholic University of America, Washington, DC, 20064, USA

Abstract:	Succinct expressions for the matrix elements of various vibrational operators have been derived in the basis of the nondegenerate harmonic oscillator. Among these are the matrix elements of $q^k e^{\lambda q} ,q^k \sin ^l (\mu q),q^k \cos ^l (\mu q),q^k \sinh ^l (\mu q)$ and $q^k \cosh ^l (\mu q)$ , which are found to be dependent upon two quantities and their derivatives. Furthermore, the derivative property of the commutator is used to obtain an explicit expression for the derivatives of an operator in terms of its nested commutator with the conjugate momentum. It may be applied to any of the above cases to obtain the matrix representatives of expressions such as the mixed products $\sin ^l (\mu q)\cos ^{l - m} (\mu q)$ , for example. In addition, a simple expression for 1/q is given and its derivatives may be evaluated by this commutator technique. Also the matrix elements of a Gaussian-type operator $q^k e^{\lambda q^2 }$ has been evaluated. This revised version was published online in July 2006 with corrections to the Cover Date.

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