The Klein–Gordon equation with the Kratzer potential in the noncommutative space

Abstract

The Klein–Gordon equation is considered for the Kratzer potential in the spherical polar coordinate in laboratory frame in noncommutative space. The energy shift due to noncommutativity is obtained via the perturbation theory. After rather cumbersome algebra, we found the eigenfunctions and eigenvalues of the system for a noncommutative phase space.

Solutions of Klein-Gordon equation for the modified central complex potential in the symmetries of noncommutative quantum mechanics

“…The above equation allows us to obtain the operator (13) The new operator ( ) r V ccˆ can be expressed as [25][26][27][28][29] :…”

“…Up to our knowledge, no attempts to study the modified central complex potential using Bopp's shift method. The new structure of the relativistic noncommutative relativistic quantum mechanicsbased on new NC canonical commutations relations in Schrödinger, Heisenberg and interactions pictures, respectively, as follows [24][25][26][27][28][29] (Throughout this paper, the natural units 1 = =  c will be used):…”

Approximate eigensolutions of the attractive potential via parametric Nikiforov-Uvarov method

“…In a spherical potential model Vtrue(rtrue), the time independent Schrödinger equation is given by [28, 29, 30, 31, 32, 33]. true[−ℏ2∇22μ+Vtrue(rtrue)true]ψnℓmtrue(r,θ,ϕtrue)=Enkψnℓmtrue(r,θ,ϕtrue),where ℓ and n are orbital angular momentum and radial quantum number respectively, ψnℓmtrue(r,θ,ϕtrue) is the wave function, μ and ℏ are reduced mass and Planck constant respectively, r is the internuclear separation and Enℓ is the non-relativistic energy.…”

A New Approach to the Approximate Analytic Solution of the Three-Dimensional Schrӧdinger Equation for Hydrogenic and Neutral Atoms in the Generalized Hellmann Potential Model

“…Edet et al studied bound-state solutions of the Schrödinger equation for the modified Kratzer potential plus screened Coulomb potential [16]. In this work, motivated by several recent studies such as the non-renormalizable of the standard model, string theory, quantum gravity, the noncommutative quantum mechanics (NCQM) has attracted much attention (see, e.g., [17][18][19][20][21][22][23]). Recently, we are studied the KGE with modified Coulomb potential plus inverse-square-root potential and modified Coulomb plus inverse-square potential in the noncommutative three-dimensional space [18,19].…”

“…(1)) used in the present study was first proposed by Edet et al [8]. The structure of nonrelativistic noncommutative quantum mechanics (NRNCQM) based to NC canonical commutations relations in the Schrödinger, Heisenberg, and interaction pictures (SP, HP, and IP), respectively, as follows (throughout this paper, the natural units = = 1 will be used) (see, e.g., [20][21][22][23][24][25][26][27]):…”