Guo-Hua Sun

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 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

The Schrödinger Equation with a Coulomb Plus Inverse-Square Potential in D Dimensions

cos(rho) frac{d}{drho}

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

with ρ=πx/L.

An algebraic approach to the ring-shaped non-spherical oscillator

A D-dimensional Schrodinger equation with a Coulomb plus inverse-square potential is carried out. The relationship between the energy E(n,l,D) and the dimension D is analyzed in great detail. It is shown that the E(n,0,D) first decreases for D (0,2] and then increases for D ≥ 2. The energy E(n,l,D) is almost independent of the quantum number l for large D, but the quantum number l plays some role in the energy E(n,l,D) when the dimension D is not too large.