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The one-dimensional Hulthén potential in the quantum phase space representation

100%

Stanek J.

Open Physics

2014

tom 12

nr 2

90-96

The analytic expression of the Wigner function for bound eigenstates of the Hulthén potential in quantum phase space is obtained and presented by plotting this function for a few quantum states. In addition, the correct marginal distributions of the Wigner function in spherical coordinates are determined analytically.

Approximate analytical solutions for arbitrary l-state of the Hulthén potential with an improved approximation of the centrifugal term

80%

Stanek J.

Open Chemistry

2011

tom 9

nr 4

737-742

An approximate analytical solution of the radial Schrödinger equation for the generalized Hulthén potential is obtained by applying an improved approximation of the centrifugal term. The bound state energy eigenvalues and the normalized eigenfunctions are given in terms of hypergeometric polynomials. The results for arbitrary quantum numbers n r and l with different values of the screening parameter δ are compared with those obtained by the numerical method, asymptotic iteration, the Nikiforov-Uvarov method, the exact quantization rule, and variational methods. The results obtained by the method proposed in this work are in a good agreement with those obtained by other approximate methods. [...]

Transmission resonance for a Dirac particle in a one-dimensional Hulthén potential

80%

Guo J. , Yu Y. , Jin S.

Open Physics

2009

tom 7

nr 1

168-174

We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulthén potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have derived the reflection and transmission coefficients using the matching condition on the wavefunctions, and investigated the condition for the existence of transmission resonance. Furthermore, we have demonstrated how the transmission resonance depends on the shape of the potential.

Arbitrary /-state approximate solutions of the Hulthén potential through the exact quantization rule

80%

Qiang W.-C. , Gao Y. , Zhou R.-S.

Open Physics

2008

tom 6

nr 2

356-362

In this paper, using the Exact Quantization Rule, we present approximate analytical solutions of the radial Schrödinger equation with non-zero l values for the Hulthén potential in the frame of an approximation to the centrifugal potential for any l states. The energy levels of all bound states can be easily calculated from the Exact Quantization Rule. Specifically, the normalized analytical wave functions are also obtained. Some energy eigenvalues are numerically calculated and compared with those obtained by other methods such as asymptotic iteration, supersymmetry, numerical integration methods, and the schroedinger Mathematica package.

Approximate analytical solutions of scattering states for Klein-Gordon equation with Hulthén potentials for nonzero angular momentum

70%

Chen C.-Y. , Lu F.-L. , Sun D.-S.

Open Physics

2008

tom 6

nr 4

884-890

In this paper, using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthén potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of t-waves scattering states are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.