Polynomial Solution of Non-Central Potentials

Abstract

We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central 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.

18 pages

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Cited by in corpus (18)

• A General Approach for the Exact Solution of the Schrodinger Equation
• Exact solutions of the modified Kratzer potential plus ring-shaped potential in the D-dimensional Schrodinger equation by the Nikiforov-Uvarov method
• Formula Method for Bound State Problems
• Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry
• Solution of the D-dimensional Klein-Gordon equation with equal scalar and vector ring-shaped pseudoharmonic potential
• Masses and Magnetic moments of Triply Heavy Flavour Baryons in Hypercentral Model
• Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials
• Physical applications of second-order linear differential equations that admit polynomial solutions
• Non-Central Potentials, Exact Solutions and Laplace Transform Approach
• Relativistic treatment in D-dimensions to a spin-zero particle with noncentral equal scalar and vector ring-shaped Kratzer potential
• Approximated l-states of the Manning-Rosen potential by Nikiforov-Uvarov method
• Approximate bound states of the Dirac equation with some physical quantum potentials
• Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential
• The Relativistic Bound States of a Non Central Potential
• The bound state solutions of the $D$-dimensional Schrödinger equation for the Woods-Saxon potential
• Novel Bound States Treatment of the Two Dimensional Schrodinger Equation with Pseudocentral Plus Multiparameter Noncentral Potential
• Solutions of Schrödinger Equation with Generalized Inverted Hyperbolic Potential
• Hartmann potential with a minimal length and generalized recurrence relations for matrix elements