Unitary Symmetry of Oscillators and the Talmi Transformation

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Abstract
The Hamiltonian of an isotropic harmonic oscillator is invariant under unitary transformations in three dimensions. This well‐known invariance is exploited in a treatment of the Talmi transformation, viz., the transformation of two‐particle oscillator functions to center‐of‐mass and relative coordinates. A simple and transparent form of this transformation in terms of rotation matrices and Wigner coefficients of SU3 is given. The calculation of these Wigner coefficients is described and the problem of degeneracies discussed.