Exactly complete solutions of the Schrödinger equation with a spherically harmonic oscillatory ring-shaped potential

We present analytically the exact energy bound-states solutions of the Schrodinger equation in D dimensions for a recently proposed modified Kratzer plus ring-shaped potential by means of the Nikiforov–Uvarov method. We obtain an explicit solution of the wave functions in terms of hyper-geometric functions (Laguerre polynomials). The results obtained in this work are more general and true for any dimension which can be reduced to the well-known three-dimensional forms given by other works.

Exact solutions of the modified kratzer potential plus ring-shaped potential in the d-dimensional schrödinger equation by the nikiforov–uvarov method

We propose a new exactly solvable potential which consists of the modified Kratzer potential plus a new ring-shaped potential βctg2θ/r2. The exact solutions of the bound states of the Schrodinger equation for this potential are presented analytically by using the Nikiforov–Uvarov method, which is based on solving the second-order linear differential equation by reducing to a generalized equation of hypergeometric type. The wavefunctions of the radial and angular parts are taken on the form of the generalized Laguerre polynomials and the total energy of the system is different from the modified Kratzer potential because of the contribution of the angular part.

http://iopscience.iop.org/1402-4896/75/3/008/pdf/1402-4896_75_3_008.pdf

Exact solution of the Schrödinger equation for the modified Kratzer potential plus a ring-shaped potential by the Nikiforov–Uvarov method

We present the exact solution of the Klein–Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov–Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular part of the potential becomes zero.

Exact bound states of the d-dimensional klein–gordon equation with equal scalar and vector ring-shaped pseudoharmonic potential

The approximately analytical scattering state solutions of the l-wave Schr?dinger equation for the Eckart potential are carried out by a proper approximation to the centrifugal term. The normalized radial wavefunctions of l-wave scattering states on the 'k/2? scale' are presented and the calculation formula of phase shifts is derived. It is interesting to find that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. We consider and verify two special cases: the l=0 and the s-wave Hulth?n potential.

https://iopscience.iop.org/article/10.1088/0031-8949/77/03/035001/pdf

Arbitrary l-wave scattering state solutions of the Schrödinger equation for the Eckart potential

Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential

We find that the analytical solutions to quantum system with a quartic potential V (x) = ax2 + bx4 (arbitrary a and b > 0 are real numbers) are given by the triconfluent Heun functions HT(α,β,γ; z)...

Chang Yuan Chen

Papers

Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential

Exact solutions of a quartic potential

Exact solutions of the rigid rotor in the electric field

The visualization of the angular probability distribution for the angular Teukolsky equation with m ≠ 0