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• W1977576169 abstract "This paper reports the development of several general recurrence relations that can be used to evaluate one-dimensional, three centre harmonic oscillator matrix elements of the operators and f = exp(−cx C ). The matrix elements have the general form ⟨φ m (a 1/2 x A )|g(or f)|φ n (b 1/2 x B )⟩; φ m is the harmonic oscillator basis function for an eigenstate m. The coordinates are x A  = x − A x , and so on, where A x , B x , and C x are points of reference for the displacement of a common atom whose instantaneous coordinate is x. A typical case might be that of a hydrogen atom referred to two wells located at A x and B x , and a second atom located at C x on the x axis. The recurrence relations apply to all cases including the two centre A x  = B x and overlap integrals, A x  ≠ B x , c = 0, and C x  = 0. Moreover, the recurrence relations can generate matrix elements to any order. The applications of some of these recursions are illustrated with several examples: (1) the variational treatment of the Morse ..." @default.
• W1977576169 created "2016-06-24" @default.
• W1977576169 creator A5089349816 @default.
• W1977576169 date "2012-05-10" @default.
• W1977576169 modified "2023-10-18" @default.
• W1977576169 title "Recurrence relations for one-dimensional harmonic oscillator matrix elements of Gaussian and exponential operators" @default.
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• W1977576169 doi "https://doi.org/10.1080/00268976.2012.668225" @default.
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