Solutions of the Schr?dinger equation in the tridiagonal representation with the noncentral electric dipole plus a novel angle-dependent component

A noncentral ring-shaped potential is proposed in which the noncentral electric dipole and a novel angle-dependent component are included, the radial part is selected as the Coulomb potential or the harmonic oscillator potential. The exact solution of the Schr?dinger equation with this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relation for the expansion coefficients of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of the Jacobi/Laguerre polynomials. The discrete spectrum of the bound states is obtained by diagonalization of the radial recursion relation.