Abstract
We display the matrix elements for the vibrational operators q k sin( ω k q), q k cos( ω k q), q k sinh( ω k q) and q k cosh( ω k q) k = 0, 1, 2, 3, … derived using an irreducible tensor technique in the basis of the non-degenerate harmonic oscillator wave functions. We give an example of a variational eigenvalue calculation, using matrix elements calculated in this manner, of an arbitrary periodical and non-periodical potentials expanded in fourier series.
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