Computational Chemistry and Molecular Modeling
Atomic, Molecular and Optical Physics
Wiley InterScience Backfile Collection 1832-2000
Chemistry and Pharmacology
A second-quantization formalism combined with a hypervirial theorem is used to derive new recurrence relations for one-dimensional harmonic oscillator matrix elements. The most general case of 〈m|f(â, â+)|n〉 is considered, and the recurrence relations forf(â, â) = Xk, exp(-βX), and exp(-X2) are given as examples. The relations obtained are considerably simpler than those derived by using only the hypervirial theorem; comparatively, the recurrence relations presented here have the advantage of avoiding the use of the quantum mechanical sum-rules when determining initial matrix elements. The proposed procedure can be used to determine the recurrence relations for other potentials as well as to evaluate the two-center integrals.
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