Bound and scattering states for a hyperbolic‐type potential in view of a new developed approximation

Abstract

A new developed approximation is used to obtain the arbitrary l-wave bound and scattering state solutions of Schr€ odinger equation for a particle in a hyperbolic-type potential. For bound state, the energy eigenvalue equation and unnormalized wave functions in terms of Jacobi polynomials are achieved using the Nikiforov-Uvarov (NU) method. Besides, energy eigenvalues are calculated numerically for some states and compared with those given in the literature to check accuracy of our results.For scattering state, the wave function is found in terms of hypergeometric functions. Furthermore, scattering amplitude and phase shifts are achieved using scattering solutions. Also it is shown that the energy eigenvalue equation obtained from analytic property of scattering amplitude is same with one obtained using NU method.

N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation

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Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

“…One of the most important tasks discussed in physics is to obtain the exact analytical solutions, which describe the bound and scattering states, of radial Schrödinger equation with arbitrary angular quantum numbers (l = 0 and l = 0) for various potentials. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] For the s-wave states (the case of l = 0), the analytical solutions for the bound states can be achieved directly. On the other hand, for the l-wave states (the case of l = 0), it is necessary to use a convenient approximation to the centrifugal term (l(l + 1)/r 2 ) such as the Pekeris approximation [17] and the approximation scheme proposed by Greene and Aldrich.…”

Scattering state of the multiparameter potential with an improved approximation for the centrifugal term in D‐dimensions

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