Path Integral Solution of Noncentral Potential

2007

Int J Theor Phys

175

We show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in certain class of noncentral potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.

“…[19]. Further, for C = 0, it agrees with the corresponding energy spectrum already been calculated by the path integral solution of the system [18] and using KS transformation [36,37] …”

Section: A the Generalized Coulomb Systemsupporting

confidence: 87%

Polynomial Solution of Non-Central Potentials

Ikhdair¹,

2007

Int J Theor Phys

175

“…(41) and (42), we obtain = − −1 (43) Additionally, using Eqs. (24)- (26) and (29)- (30), we obtain the following useful parts of the wavefunctions:…”

Section: The Solutions Of the D-dimensional Angular Equationsmentioning

confidence: 95%

“…In most of this work, the eigenvalues and eigenfunctions are obtained by means of separation of variables in spherical or other orthogonal curvilinear coordinate systems. The path integral for particles moving in non-central potentials is evaluated to derive the energy spectrum of this system analytically [43]. In addition, the idea of SUSY and shape invariance is also used to obtain exact solutions of such non-central but separable potentials [44,45].…”

Section: Introductionmentioning

confidence: 99%

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Ikhdair¹,

2008

Open Physics

“…In most of these studies, the eigenvalues and eigenfunctions are obtained by means of seperation of variables in spherical or other orthogonal curvilinear coordinate systems. The path integral for particles moving in noncentral potentials is evaluated to derive the energy spectrum of this system analytically [43].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of the Modified Kratzer Potential Plus Ring-Shaped Potential in the D-Dimensional Schrödinger Equation by the Nikiforov–uvarov Method

Ikhdair¹,

2008

Int. J. Mod. Phys. C

We present analytically the exact energy bound-states solutions of the Schrödinger equation in D-dimensions for a recently proposed modified Kratzer potential plus ring-shaped potential by means of the conventional Nikiforov-Uvarov method. We give a clear recipe of how to obtain an explicit solution to the wave functions in terms of orthogonal polynomials. The results obtained in this work are more general and true for any dimension which can be reduced to the standard forms in three-dimensions given by other works.