Solving Of The Schrodinger Equation For The Quantum System With Non-Center Coulomb Potential

In this paper, we've discussed an solved three different Schrodinger equations for the quantum system with non-center Coulomb potential, including:According to the idea of introducing non-spherical ring shaped oscillator potential in the Schrodinger equation, we study a new non-central potential which is called the spherical harmonic oscillatory ring shaped potentialThe exact solutions of Schrodinger equation with this potential are investigated by using Nikiforov-Uvarov method The bound-state solutions of both the angular and radial equations are expressed in terms of the Rodrigues formula or the generalized Ultraspheri polynomials and the generalized Laguerre polynomials;The first-order revision and the approximation analytical formula of the energy levels for hydrogen-like atoms in condition of the Debye shielding potential are achieved by means of the Rayleigh—Schrodinger perturbation theory and the power series;meanwhile,the corresponding recurrence relations are got with the use of the solution of power series. Basic on mentioned above and with the use of energy consistent method the equivalent value of second-order revision in condition of the Debye shielding potential as well be got and the result is compared with the data obtained by the numerical method. Beside, the critical bond-state and corresponding cut off of conditions are discussed; PmXIV,SmXV and EuXVI ions belong to CdI isoelectronic sequence havingground configuration4d¹⁰5s². With the relativistic Hartree-Fock(HFR) calculationsmethod,we calculate the energy levels of configuration5s²,5s5p,5s5d,5p²for CdIisoelectronic sequence on the energy intervals in the N=5complex from I VI to NdXIII.Based on the calculations and some experimental data, we predict the the energy levelsof configuration5s²,5s5p,5s5d,5p²for ions from PmXIV to EuXVI.Meanwhile, wecalculate the wavelengths and the corresponding oscillator strengths of transitions5s²-5s5p,5s5p-5p²,5s5p-5s5d.