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A general expression for matrix elements of reciprocal powers of the displacement coordinateq in the harmonic oscillator basis |
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| Authors: | Pancracio Palting Shan Tao Lai Manzheng Fu |
| Institution: | (1) Center for Molecular Dynamics and Energy Transfer, Department of Chemistry, The Catholic University of America, 20064 Washington, DC, USA;(2) 8818 Keewatin Road, 20706 Lanham, MD, USA;(3) Vitreous State Laboratory, The Catholic University of America, 20064 Washington, DC, USA |
| Abstract: | A formula is derived that allows one to determine the matrix elements of an arbitrary integral reciprocal power of the dimensionless displacement coordinate q of the harmonic oscillator from those ofq –1 in an exact manner. This relation is obtained from the use of the chain rule and irreducible tensors expressed in terms of the creation and annihilation operators of the harmonic oscillator. |
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