Harmonic oscillator tensors. III: Efficient algorithms for evaluating matrix elements of vibrational operators |
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Authors: | Pancracio Palting Shan Tao Lai Ying Nan Chiu Jorge Ricardo Letelier |
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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 |
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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
and
, 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
, 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
has been evaluated.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | |
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