Abstract Occupation number representation and operator-technique are used in the calculation of harmonic oscillator matrixelements for one and two centres and for equal and different frequencies. The potentials treated are generalized Gauss-potentials of the form p̑k x̑l exp{a x̑2 }, x̑k p̑l exp{a p̑2 }, and p̑k x̑l exp{a x̑ p̑} which by application of an operator identity could be reduced to the same form. Applications in nuclear and molecular physics, in molecular spectroscopy and in quantum chemistry are discussed briefly.