scholarly journals Some uncertainty Inequalities related to the multivariate Laguerre function

2020 ◽  
Vol 44 (3) ◽  
pp. 712-728
Author(s):  
Lotfi KAMOUN ◽  
Rim SELMI
Keyword(s):  
Laguerre Function ◽  
Uncertainty Inequalities

Applications of non-orthogonal Laguerre function basis in helium atom

2005 ◽  
Vol 163 (2) ◽  
pp. 879-893
Author(s):  
Agus Kartono ◽  
Toto Winata ◽  
Sukirno
Keyword(s):  
Helium Atom ◽  
Laguerre Function

A variety of uncertainty principles for the Dunkl transform on ℝd

2020 ◽  
pp. 2150077
Author(s):  
Fethi Soltani
Keyword(s):  
Dunkl Transform ◽  
Uncertainty Principles ◽  
Local Type ◽  
Heisenberg Type ◽  
Uncertainty Inequalities

In this work, we prove Clarkson-type and Nash-type inequalities in the Dunkl setting on [Formula: see text] for [Formula: see text]-functions. By combining these inequalities, we show Heisenberg-type inequalities for the Dunkl transform on [Formula: see text], and we deduce local-type uncertainty inequalities for the Dunkl transform on [Formula: see text].

Factorization method for exact solution of the non-central modified Killingbeck potential plus a ring-shaped-like potential

2019 ◽  
Vol 34 (10) ◽  
pp. 1950072 ◽  
Author(s):  
B. Tchana Mbadjoun ◽  
J. M. Ema’a Ema’a ◽  
Jean Yomi ◽  
P. Ele Abiama ◽  
G. H. Ben-Bolie ◽  
...  
Keyword(s):  
Exact Solution ◽  
Potential Problem ◽  
Energy Levels ◽  
Factorization Method ◽  
Spherically Symmetric ◽  
Laguerre Function ◽  
Radial Part ◽  
Raising And Lowering Operators ◽  
Structure Of Molecules ◽  
Lowering Operators

In this paper, we study the Schrödinger equation with non-central modified Killingbeck potential plus a ring-shaped-like potential problem, which is not spherically symmetric. The factorization method is used to solve the hypergeometric equation types which lead to solutions with the associate Laguerre function for the radial part and Jacobi polynomial for the polar part. We introduce the raising and lowering operators to calculate the energies eigenvalues, which show that the lack of spherical symmetry removes the degeneracy of second quantum number m which is completely expected. These obtained energies are better to explain the superposition of the energy levels of the atoms in the crystalline structure of molecules.

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