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arXiv · 2112.12269

Angular Momentum Eigenstates of the Isotropic 3-D Harmonic Oscillator: Phase-Space Distributions and Coalescence Probabilities

Michael Kordell II·Rainer J. Fries·Che Ming Ko
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Abstract

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 hence need the Wigner distribution functions of angular momentum eigenstates in isotropic 3-dimensional harmonic oscillators. These distribution functions have been discussed in the literature before but we utilize an alternative approach to obtain these functions. Along the way, we derive a general formula that expands angular momentum eigenstates in terms of products of 1-dimensional harmonic oscillator eigenstates.

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Michael Kordell II, Rainer J. Fries, Che Ming Ko. 2021-12-30. Angular Momentum Eigenstates of the Isotropic 3-D Harmonic Oscillator: Phase-Space Distributions and Coalescence Probabilities. https://doi.org/10.1016/j.aop.2022.168960

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