Exact solutions of scattering states for the s-wave Schrödinger equation with the Manning–Rosen potential

Abstract

The exact solutions of s-wave scattering states for the Schrödinger equation with the Manning–Rosen potential are presented by the standard method. The normalized radial wavefunctions of scattering states on the ‘k/2πscale’ and the calculation formula of phase shifts are found. We also study the special case for α = 1 and find that this potential will reduce to the Hulthén potential.

Indirect dark matter detection limits from the ultrafaint Milky Way satellite Segue 1

“…A useful analytical formula [68,78] that closely matches the numerical solution can be obtained by using the Hulthén potential V (r) = −α D m φ e −rm φ /(1 − e −rm φ ), which has similar behavior to the Yukawa potential for r → 0 and r → ∞. The solution is given by…”

The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

“…By comparing the above equation (45) with equation (18) and observing the relations of corresponding parameters, i.e., ↔ λ,δ ↔ δ andη = η, it is easy to find that equation (45) completely coincides with equation (18). It is well shown that the poles of S-matrix in the complex energy plane correspond to bound states for real poles and scattering states for complex poles in the lower half of the energy plane [28,29].…”

“…The energy level E is determined by the energy equation (18), which is rather complicated transcendental equation. The correspondingly analytical wave functions can be expressed as…”

“…It was first considered by Manning [15] and Rosen [16] in 1933 due to its importance in the description of vibration behavior of diatomic molecules model in physics and chemical physics. The −wave bound and scattering states of the Schrödinger equation for this potential have been carried out by using the factorization method [17], the function analysis method [18] and path integral approach [19], respectively. In addition, Ikhdair and Sever have also studied the arbitrary −wave solutions of the D-dimensional Schrödinger equation with the Manning-Rosen potential [20] by Nikiforov-Uvarov approach.…”

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

“…Recently, the study of exponential-type potentials has attracted much attention from many authors (for example, cf, ). These physical potentials include the Woods-Saxon [7,8], Hulthén [9][10][11][12][13][14][15][16][17][18][19][20][21][22], modified hyperbolic-type [23], ManningRosen [24][25][26][27][28][29][30][31], the Eckart [32][33][34][35][36][37], the Pöschl-Teller [38] and the Rosen-Morse [39,40] potentials.…”