Coulomb Scattering in Non-Commutative Quantum Mechanics

Gáliková, Veronika; Prešnajder, P.

doi:10.14311/ap.2013.53.0427

Cited by 3 publications

(1 citation statement)

References 7 publications

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“…It would therefore be useful to establish a formalism for scattering in non-commutative space in order to identify possible systematic trends that could serve as indicators of non-commutativity. Scattering theory in two dimensional non-commutative space has been developed in detail in [12] and an analysis of the S-matrix for the Coulomb potential in three dimensions was performed in [8,13]. However, a detailed development of scattering theory and the phase shift analysis in three dimensional fuzzy space is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Scattering in a three-dimensional fuzzy space

2017

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We develop scattering theory in a non-commutative space defined by a su(2) coordinate algebra. By introducing a positive operator valued measure as a replacement for strong position measurements, we are able to derive explicit expressions for the probability current, differential and total cross-sections. We show that at low incident energies the kinematics of these expressions is identical to that of commutative scattering theory. The consequences of spacial non-commutativity are found to be more pronounced at the dynamical level where, even at low incident energies, the phase shifts of the partial waves can deviate strongly from commutative results. This is demonstrated for scattering from a spherical well. The impact of non-commutativity on the well's spectrum and on the properties of its bound and scattering states are considered in detail. It is found that for sufficiently large well-depths the potential effectively becomes repulsive and that the cross-section tends towards that of hard sphere scattering. This can occur even at low incident energies when the particle's wave-length inside the well becomes comparable to the non-commutative length-scale.

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Section: Introductionmentioning

confidence: 99%

Scattering in a three-dimensional fuzzy space

2017

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Eigenvalue problem for radial potentials in space with SU(2) fuzziness

Mirahmadi

Fatollahi

2014

Journal of Mathematical Physics

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The eigenvalue problem for radial potentials is considered in a space whose spatial coordinates satisfy the SU(2) Lie algebra. As the consequence, the space has a lattice nature and the maximum value of momentum is bounded from above. The model shows interesting features due to the bound, namely, a repulsive potential can develop bound-states, or an attractive region may be forbidden for particles to propagate with higher energies. The exact radial eigen-functions in momentum space are given by means of the associated Chebyshev functions. For the radial stepwise potentials the exact energy condition and the eigen-functions are presented. For a general radial potential it is shown that the discrete energy spectrum can be obtained in desired accuracy by means of given forms of continued fractions.Comment: 1+20 pages, 2 figs, LaTe

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Phenomenology of the dispersion law in a three-dimensional quantum space

Kováčik,

Ďuríšková,

Rusnák

2024

Int. J. Mod. Phys. A

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The concept of a quantum structure underlying space has been proposed for quite some time, yet it has largely eluded direct observation. There is a prevailing notion that the minuscule effects stemming from quantum space could, under certain astronomical conditions, accumulate to an observable magnitude. Typically, these effects are perturbative, limited to the first one or two orders. This study presents a full dispersion law derived from a three-dimensional quantum space model. Our primary focus is to investigate the in-vacuo dispersion phenomenon and the threshold anomaly. Furthermore, we briefly explore the implications of additional spatial dimensions within this framework and suggest a way of distinguishing between various theories that agree in the leading-order approximation.

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Coulomb Scattering in Non-Commutative Quantum Mechanics

Cited by 3 publications

References 7 publications

Scattering in a three-dimensional fuzzy space

Scattering in a three-dimensional fuzzy space

Eigenvalue problem for radial potentials in space with SU(2) fuzziness

Phenomenology of the dispersion law in a three-dimensional quantum space

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