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A Generalized Talmi–Moshinsky Transformation for 1D Harmonic Oscillator Functions and Interaction Matrix Elements

A generalized Talmi–Moshinsky transformation relating one-dimensional harmonic oscillator product states with different sets of Jacobian coordinates is derived for systems composed of an arbitrary number of particles with arbitrary masses. With the help of our method the multidimensional integral which must be performed to evaluate an -particle matrix element can be transformed into a sum of products of one-dimensional integrals.