Shi-Hai Dong

The series solutions of the non-relativistic equation with the Morse potential

In this Letter the analytical solutions of the two-dimensional Schrodinger equation with the Morse potential are obtained by the series expansion method. We then generalize this method to the D-dimensional Schrodinger equation case. The studied Morse potential itself is expanded in the series about the origin.

THE KLEIN GORDON EQUATION WITH A COULOMB PLUS SCALAR POTENTIAL IN D DIMENSIONS

The solutions of the Klein–Gordon equation with a Coulomb plus scalar potential in D dimensions are exactly obtained. The energy E(n,l,D) is analytically presented and the dependence of the energy E(n,l,D) on the dimension D is analyzed in some detail. The positive energy E(n,0,D) first decreases and then increases with increasing dimension D. The positive energy E(n,l D)(l≠0) increases with increasing dimension D. The dependences of the negative energies E(n,0,D) and E(n,l,D)(l≠0) on the dimension D are opposite to those of the corresponding positive energies E(n,0,D) and E(n,l,D)(l≠0). It is found that the energy E(n,0,D) is symmetric with respect to D=2 for D∈(0,4). It is also found that the energy E(n,l,D)(l≠0) is almost independent of the angular momentum quantum number l for large D and is completely independent of the angular momentum quantum number l if the Coulomb potential is equal to the scalar one. The energy E(n,l D) is almost overlapping for large D.

Exact solutions to the Dirac equation with a Coulomb potential in 2 + 1 dimensions

The (2 + 1)-dimensional Dirac equation with a Coulomb potential is investigated by studying a second-order differential equation obtained from a pair of coupled first-order ones. The solutions of the bound states expressed by the confluent hypergeometric functions are analytically obtained. The energy levels and their fine structures are also presented

THE HIDDEN SYMMETRY FOR A QUANTUM SYSTEM WITH A PÖSCHL–TELLER-LIKE POTENTIAL

The eigenvalues and eigenfunctions of the Schrodinger equation with a Poschl–Teller (PT)-like potential are presented. A realization of the creation and annihilation operators for the wave functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions, sin(ρ) and

Series solutions of the Schrödinger equation with position-dependent mass for the Morse potential

\cos(\rho) \frac{d}{d\rho}

Exactly solvable potentials for the Schrödinger equation with spatially dependent mass

with ρ=πx/L.