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Mathematics and Computers in Simulation

The diatomic anharmonic oscillator according to matrix mechanics

Michael Monagan, John F. Ogilvie

Published Aug 1, 1999• 2 citations
Publisher
DOI
10.1016/s0378-4754(99)00046-4

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The ladder operators for the Goldman and Krivchenkov anharmonic potential have been derived within the algebraic approach. The method is extended to include the rotating oscillator. The coherent states for the Goldman and Krivchenkov oscillator, which are the eigenstates of the annihilation operator and minimize the generalized position-momentum uncertainty relation, are constructed within the framework of supersymmetric quantum mechanics. The constructed ladder operators can be a useful tool in quantum chemistry computations of non-trivial matrix elements. In particular, they can be employed in molecular vibrational–rotational spectroscopy of diatomic molecules to compute transition energies and dipole matrix elements.