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APPROXIMATE ANALYTICAL SOLUTIONS OF THE KLEIN-GORDON EQUATION FOR THE HULTHEN POTENTIAL WITH THE POSITION-DEPENDENT MASS

The Klein–Gordon equation is solved approximately for the Hulthen potential for any angular momentum quantum number l with the position-dependent mass. Solutions are obtained by reducing the Klein–Gordon equation into a Schrodinger-like differential equation using an appropriate coordinate transformation. The Nikiforov–Uvarov method is used in the calculations to get energy eigenvalues and the wavefunctions. It is found that the results in the case of constant mass are in good agreement with the ones obtained in the literature.

New exact solution of the one-dimensional Dirac equation for the Woods–Saxon potential within the effective mass case

We study the one-dimensional Dirac equation in the framework of a position-dependent mass under the action of a Woods?Saxon external potential. We find that by constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular, we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically.

Scattering and bound state solutions of the asymmetric Hulthén potential

The one-dimensional time-independent Schrodinger equation is solved for the asymmetric Hulthen potential. The reflection and transmission coefficients and bound state solutions are obtained in terms of the hypergeometric functions. It is observed that the unitary condition is satisfied in the non-relativistic region.

EXACT SOLUTIONS OF THE SCHRODINGER EQUATION VIA LAPLACE TRANSFORM APPROACH: PSEUDOHARMONIC POTENTIAL AND MIE-TYPE POTENTIALS

Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schrödinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are obtained and seen that they are the same with the ones obtained before. The energy eigenvalues of the inverse square plus square potential and three-dimensional harmonic oscillator are given as special cases. It is shown the variation of the first six normalized wavefunctions of the above potentials. It is also given numerical results for the bound states of two diatomic molecular potentials, and compared the results with the ones obtained in literature.

Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances

Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are calculated by using behavior of the wave functions at infinity. The same analysis is done for the constant mass case. It is also pointed out that our results are in agreement with those obtained in literature. Meanwhile, an analytic expression is obtained for the transmission resonance and it is observed that the expressions for bound states and resonances are equal for the energy values E = ±m.

Exact Solutions of the Morse-like Potential, Step-Up and Step-Down Operators via Laplace Transform Approach

We intend to realize the step-up and step-down operators of the potential

Scattering of the Woods–Saxon potential in the Schrödinger equation

V(x)=V_{1}e^{2\beta x}+V_{2}e^{\beta x}

Effective-mass Klein-Gordon-Yukawa problem for bound and scattering states

. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (

Non-central potentials, exact solutions and Laplace transform approach

\beta \rightarrow -\beta

Analytical Solutions to the Klein-Gordon Equation with Position-Dependent Mass for q-Parameter P？schl-Teller Potential

).