Coulomb Problem

Benjamín Raziel Jaramillo Avila, R. P. Martı́nez-y-Romero, H. N. Núñez‐Yépez +1 more

Shi‐Hai Dong

Sami Ghazouani, Aymen Mannai

Abstract Motivated by the conclusion section of Ghazouani and Sboui (2020 J. Phys. A: Math. Theor. 53 035202), we merge together the invariance algebra of the Dunkl–Coulomb problem and the Lie algebra so ( 2 , 1 ) into a bigger new algebras. Next, we introduce several information theoretic measures of the Dunkl–Coulomb problem: Using the Dunkl transform and the canonical Dunkl transform, we obtain an analytical expression for the momentum wave functions of the Dunkl–Coulomb problem. We give an analytical expression for the expectation values of the position ⟨ r a ⟩ n m and momentum ⟨ λ a ⟩ n m in various bound states of the Dunkl–Coulomb problem. With these, a Heisenberg-type inequality for the three-dimensional linear canonical Dunkl transform is derived and is applied to the bound states of the Dunkl–Coulomb problem.

Piotr Garbaczewski, Robert Olkiewicz

S. Nouri

In this paper a set of generalized coherent states for the d-dimensional Coulomb problem in coordinate representation are constructed. A coordinate transformation in hyperspherical space is used that maps the d-dimensional Coulomb problem into the D-dimensional harmonic oscillator and the generalized coherent states for the d-dimensional Coulomb problem are then obtained. This exactly soluble model can provide an adequate means for a quantum coherency description of the Coulomb problem in arbitrary dimensions, specifically in the special case of the hydrogen atom, in many theoretical and applied related fields such as in coherent scattering.

Vojkan Jakšić, Eugene Kritchevski, Claude‐Alain Pillet