A General Approach for the Exact Solution of the Schrodinger Equation

Sever, Ramazan
The Schrodinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schrodinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.


Analytical solution of the Schrodinger equation for Makarov potential with any l angular momentum
Bayrak, O.; Karakoc, M.; Boztosun, I.; Sever, Ramazan (Springer Science and Business Media LLC, 2008-11-01)
We present the analytical solution of the Schrodinger Equation for the Makarov potential within the framework of the asymptotic iteration method for any n and l quantum numbers. Energy eigenvalues and the corresponding wave functions are calculated. We also obtain the same results for the ring shaped Hartmann potential which is the special form of the non-central Makarov potential.
Polynomial solution of non-central potentials
Ikhdair, Sameer M.; Sever, Ramazan (Springer Science and Business Media LLC, 2007-10-01)
We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.
New approach to conserved charges of generic gravity in AdS spacetimes
Altas, Emel; Tekin, Bayram (American Physical Society (APS), 2019-02-12)
Starting from a divergence-free rank-4 tensor of which the trace is the cosmological Einstein tensor, we give a construction of conserved charges in Einstein's gravity and its higher derivative extensions for asymptotically anti-de Sitter spacetimes. The current yielding the charge is explicitly gauge invariant, and the charge expression involves the linearized Riemann tensor at the boundary. Hence, to compute the mass and angular momenta in these spacetimes, one just needs to compute the linearized Riemann...
Bound State Solutions of Schrodinger Equation for Generalized Morse Potential with Position-Dependent Mass
Arda, Altug; Sever, Ramazan (IOP Publishing, 2011-07-15)
The effective mass one-dimensional Schrodinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.
Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potentials
IKHDAİR, SAMEER; Sever, Ramazan (Wiley, 2009-10-01)
The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P-n((mu,nu)) (x), where mu > -1, nu > -1 and x is an element of[-1, +1]. The s-waves analytic solution is obtained. Th...
Citation Formats
C. TEZCAN and R. Sever, “A General Approach for the Exact Solution of the Schrodinger Equation,” INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, pp. 337–350, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62576.