Nonrelativistic Treatment of Schr¨odinger Particles Under Inversely Quadratic Hellmann Plus Ring-Shaped Potentials
We have solved approximately the Schr¨odinger equation with the inversely quadratic Hellmann plus ring-shaped potential in the framework of the Nikiforov–Uvarov method. The energy eigenvalues and corresponding wave functions of the radial and angular parts are obtained in terms of Jacobi polynomials. In special cases, our result reduces to the cases of three well-known potentials such as the Coulomb potential, inversely quadratic Yukawa potential, and Hartman potential. The energy eigenvalues are evaluated as well. Our numerical results can be useful for other physical systems.
S.M. Ikhdair, R. Sever. A perturbative treatment for the energy levels of neutral atom. Int. J. Mod. Phys. A. 21, 6465 (2006).
A.N. Ikot, L.E. Akpabio. Approximate solution of the Schr¨odinger equation with Rosen–Morse potential including the centrifugal term. Appl. Phys. Res. 2, 202 (2010).
B.I. Ita. Bound state solutions of Schr¨odinger equation for Rydberg potential energy function. Nig. J. Phys. 20, 221 (2008).
S.M. Ikhdair, R. Sever. On solutions of the Schr¨odinger equation for some molecular potentials: Wave function Ansatz. Cent. Eur. J. Phys. 6, 697 (2008).
B.I. Ita. Any -state solutions of the Schr¨odinger equation for a more general exponential screened Coulomb potential using Maclaurin's and Nikiforov–Uvarov method. Int. J. Phys. Sci. 2, 141 (2010).
A.D. Antia, A.N. Ikot, L.E. Akpabio. Exact solutions of the Schr¨odinger equation with Manning–Rosen plus ringshaped like potential by Nikiforov–Uvarov method. Eur. J. Sci. Res. 46, 107 (2010).
A.D. Antia, A.N. Ikot, E.E. Ituen, L.E. Akpabio. Analytical solution of Schr¨odinger equation with Eckart potential plus Hulthen potential via Nikiforov–Uvarov method. Pal. J. Math. 1, 104 (2012).
A.N. Ikot. Analytical solutions of Schr¨odinger equation with generalized hyperbolic potential using Nikiforov– Uvarov method. Afr. Rev. Phys. 60026, 211 (2011).
A.N. Ikot, L.E. Akpabio, E.B. Umoren. Exact solution of Schr¨odinger equation with inverted Woods–Saxon and Manning–Rosen potential. J. Sci. Res. 3, 25 (2011).
O.A. Awoga, A.N. Ikot, I.O. Akpan, A.D. Antia. Solution of Schr¨odinger equation with exponential coshine-screened potential Ind. J. Pure and Appl. Phys. 50, 217 (2012).
D. Agboola. Complete analytical solutions of the Mie-type potentials in -dimensions. Acta Phys. Polonica A 120(3), 371 (2011).
D.A. Morales. Supersymmetric improvement of the Pekeris approximation for the rotating Morse potential. Chem. Phys. Lett. 394, 68 (2004).
J. Saheghi, B. Pourhassan. Drag force of moving quark at sript = 2 supersgravity. Elect. J. Theor. Phys. 20, 1 (2008).
B.I. Ita, A.I. Ikeuba. Solutions to the Schr¨odinger equation with inversely quadratic Yukawa plus inversely quadratic Hellmann potential using Nikiforov–Uvarov method. J. At. and Mol. Phys. 20, 1 (2013).
A.D. Antia, E.A. Umo, C.C. Umoren, Solutions of nonrelativistic Schr¨odinger equation with Hulthen–Yukawa plus angle dependent potential within the framework of Nikiforov–Uvarov method. J. Theor. Phys. Crypt. 10, 1 (2015).
H. Hellmann. A combined approximation method for the energy calculation in the many-electron problem. Acta Physicochem. URSS 1, 913 (1934).
H. Hellmann, W. Kassatotchkin. Metallic Binding According to the Combined Approximation Procedure. Acta Physicochem. URSS 5, 23 (1936).
P. Gombas. Die Statistische Theorie des Atoms und ihre Anwendungen (Springer, 1949) [ISBN: 978-3-7091-2100-9].
J. Callaway, P.S. Laghos. Application of the pseudopotential method to atomic scattering. . Phys. Review 187, 192 (1969).
A. Arda, R. Sever. Effective-mass Klein–Gordon–Yukawa problem for bound and scattering states. J. Math. Phys. 52, 092101 (2011).
C. Grosche. Path integral solutions for deformed PoschlTeller-like and conditional solvable potentials. J. Phys. A: Math. Gen. 38, 2947 (2005).
S.H. Dong, G.H. Sun, M. Lozada-Cassou. An algebraic approach to the ring-shaped non-spherical oscillator. Phys. Lett. A 328, 299 (2005).
B.I. Ita. Solutions of the Schr¨odinger equation with inversely quadratic Hellmann plus Mie-type potential using Nikiforov–Uvarov method. Int. J. Rec. Adv. Phys. 2, 25 (2013).
M. Hamzavi, A.A. Rajabi. Tensor coupling and relativistic spin and pseudospin symmetries with the Hellmann potential. Can. J. Phys. 91, 411 (2013).
A.F. Nikiforov, V.B. Uvarov. Special Functions of Mathematical Physics (Birkh¨auser, 1988).
C. Tezan, R. Sever. A general approach for the exact solution of the Schr¨odinger equation. Int. J. Theor. Phys. 48, 337 (2009).
G. Kocak, O. Bayrak, I. Boztosun. Arbitrary -state solutions of the Hellmann potential. J. Theor. Comp. Chem. 6, 893 (2007).
W. Greiner. Relativistic Quantum Mechanics: Wave Equation (Springer, 2000).
A.D. Antia, I.E. Essien, E.B. Umoren, C.C. Eze. Approximate solutions of the non-relativistic Schr¨odinger equation with inversely quadratic Yukawa plus Mobius square potential via parametric Nikiforov–Uvarov method. Adv. Phys. Theor. Appl. 44, 1 (2015).
M. Hamzavi, H. Hassanabadi, A.A. Rajabi. Exact solutions of Dirac equation with Hartmann potential by Nikiforov–Uvarov method. Int. J. Mod. Phys. E. 19, 2189 (2010).