Angular Momentum Eigenstates of the Isotropic 3-D Harmonic Oscillator: Phase-Space Distributions, Coalescence Probabilities and Applications to Meson Formation

The isotropic 3-dimensional harmonic oscillator potential can serve as an approximate description of many systems in atomic, solid state, nuclear, and particle physics. In particular, the question of 2 particles binding (or coalescing) into angular momentum eigenstates in such a potential has interesting applications. We compute the probabilities for coalescence of two distinguishable, non-relativistic particles into such a bound state, where the initial particles are represented by generic wave packets of given average positions and momenta. We use a phase-space formulation and thus utilize the Wigner distribution functions of angular momentum eigenstates in isotropic 3-dimensional harmonic oscillators, which we discuss in detail. We conclude by applying our formalism to the recombination of quark and antiquarks into excited and ground state meson states.