Exact Solution of Schrödinger Equation with Inverted Woods-Saxon and Manning-Rosen Potentials (original) (raw)

Scattering of the Woods–Saxon potential in the Schrödinger equation

Journal of Physics A: Mathematical and Theoretical, 2010

The scattering solutions of the one-dimensional Schrödinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in terms of Heun's function. These results are also studied for the constant mass case in detail.

Solutions of Schrödinger Equation with Generalized Inverted Hyperbolic Potential

Journal of Modern Physics, 2012

We present the bound state solutions of the Schrödinger equation with generalized inverted hyperbolic potential using the Nikiforov-Uvarov method. We obtain the energy spectrum and the wave function with this potential for arbitrary l -state. We show that the results of this potential reduced to the standard known potentials -Rosen-Morse, Poschl Teller and Scarf potential as special cases. We also discussed the energy equation and the wave function for these special cases.

Exact solutions of the radial Schrödinger equation for some physical potentials

Open Physics, 2007

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained.

Scattering of the Woods-Saxon potential in the Schr�dinger equation

J Phys a Math Theor, 2010

The scattering solutions of the one-dimensional Schrödinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in terms of Heun's function. These results are also studied for the constant mass case in detail.

The Scattering and Bound States of the Schrödinger Particle in Generalized Asymmetric Manning-Rosen Type Potential

Advances in High Energy Physics, 2014

We solve exactly one-dimensional Schrödinger equation for the generalized asymmetric Manning-Rosen (GAMAR) type potential containing the different types of physical potential that have many application fields in the nonrelativistic quantum mechanics and obtain the solutions in terms of the Gauss hypergeometric functions. Then we determine the solutions for scattering and bound states. By using these states we calculate the reflection and transmission coefficients for scattering states and achieve a correlation that gives the energy eigenvalues for the bound states. In addition to these, we show how the transmission and reflection coefficients depend on the parameters which describe shape of the GAMAR type potential and compare our results with the results obtained in earlier studies.

Exact solution of the Klein-Gordon equation for the PT-symmetric generalized Woods-Saxon potential by the Nikiforov-Uvarov method

Annalen der Physik, 2007

The one-dimensional Klein-Gordon (KG) equation has been solved for the PT-symmetric generalized Woods-Saxon (WS) potential. The Nikiforov-Uvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have also investigated the positive and negative exact bound states of the s-states for different types of complex generalized WS potentials.