Angular Momentum Eigenstates of the Isotropic 3-D Harmonic Oscillator:
Phase-Space Distributions and Coalescence Probabilities
- URL: http://arxiv.org/abs/2112.12269v2
- Date: Thu, 30 Dec 2021 17:30:16 GMT
- Title: Angular Momentum Eigenstates of the Isotropic 3-D Harmonic Oscillator:
Phase-Space Distributions and Coalescence Probabilities
- Authors: Michael Kordell II, Rainer J. Fries, Che Ming Ko
- Abstract summary: We compute the probabilities for coalescence of two distinguishable, non-relativistic particles into a bound state.
We use a phase-space formulation and hence need the Wigner distribution functions of angular momentum eigenstates.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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