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.
Related papers
- Integral quantization based on the Heisenberg-Weyl group [39.58317527488534]
We develop a framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime.
The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group.
A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.
arXiv Detail & Related papers (2024-10-31T14:36:38Z) - Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators.
We find conditions for their strong continuity and establish properties of their generators.
arXiv Detail & Related papers (2024-06-15T17:39:32Z) - A non-hermitean momentum operator for the particle in a box [49.1574468325115]
We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example.
The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
arXiv Detail & Related papers (2024-03-20T12:51:58Z) - Ultracold Neutrons in the Low Curvature Limit: Remarks on the
post-Newtonian effects [49.1574468325115]
We apply a perturbative scheme to derive the non-relativistic Schr"odinger equation in curved spacetime.
We calculate the next-to-leading order corrections to the neutron's energy spectrum.
While the current precision for observations of ultracold neutrons may not yet enable to probe them, they could still be relevant in the future or in alternative circumstances.
arXiv Detail & Related papers (2023-12-30T16:45:56Z) - Employing an operator form of the Rodrigues formula to calculate
wavefunctions without differential equations [0.0]
The factorization method of Schrodinger shows us how to determine the energy eigenstates without needing to determine the wavefunctions in position or momentum space.
This approach can be used in either undergraduate or graduate classes in quantum mechanics.
arXiv Detail & Related papers (2023-12-14T20:21:17Z) - Energetics of the dissipative quantum oscillator [22.76327908349951]
We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap.
Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy.
We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
arXiv Detail & Related papers (2023-10-05T15:18:56Z) - Path distributions for describing eigenstates of the harmonic oscillator
and other 1-dimensional problems [0.0]
An integral expression is written that describes the wave function.
The resulting expression can be analyzed using a generalization of stationary-phase analysis.
A somewhat broad distribution is found, peaked at value of momentum that corresponds to a classical energy.
arXiv Detail & Related papers (2023-06-19T20:40:26Z) - Two dimensional non-Hermitian harmonic oscillator: coherent states [0.0]
The corresponding time independent Schr"odinger equation yields real eigenvalues with complex eigenfunctions.
We construct the coherent state of the system by using a superposition of 12 eigenfunctions.
arXiv Detail & Related papers (2020-12-08T16:16:04Z) - Exact solution of the position-dependent effective mass and angular
frequency Schr\"odinger equation: harmonic oscillator model with quantized
confinement parameter [0.0]
We present an exact solution of a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent on the position.
The position-dependent effective mass and angular frequency also become constant under this limit.
arXiv Detail & Related papers (2020-10-09T09:58:38Z) - The Entropic Dynamics of Spin [0.0]
In Entropic Dynamics (ED) approach the essence of theory lies in its probabilistic nature while the Hilbert space structure plays a secondary and optional role.
In this paper the ED framework is extended to describe a spin-1/2 point particle.
The updating of all constraints is carried out in a way that stresses the central importance of symmetry principles.
arXiv Detail & Related papers (2020-07-30T20:02:09Z) - Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range.
For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.