New bound and scattering state solutions of the Manning–Rosen potential with the centrifugal term

Abstract

We proposed a new approximate scheme for a centrifugal term. Using new approximate formula for 1/r2, we obtained the bound state and scattering state solutions of the Manning–Rosen potential with centrifugal terms. All approximate analytical formulae of energy eigenvalues, normalized wavefunctions and scattering phase shifts are presented. In addition, we also suggested another much better approximate formula to 1/r2 for bound states. All data calculated by the above approximate analytical formulae are compared with those obtained by using the numerical integration method in the bound state and scattering state cases. Furthermore, the complete s-wave scattering state solutions for the Manning–Rosen potential are also naturally derived.

Bound state solutions of D‐dimensional schrödinger equation with exponential‐type potentials

“…It should be noticed, that the eigenvalues given in eq. coincide with those of Qiang et al after matching their parameter with our h L by means of as well as their , agrees with their approximation scheme of .…”

“…It should be noticed, that the eigenvalues given in eq. (61) coincide with those of Qiang et al [29] after matching their parameter a 0 with our h L by means of a 0 5ðh L 11Þ=2 as well as their exp ð1=bÞ51, agrees with their approximation scheme of 1=r 2 . Conversely, it is important to mention that another possibility for the A, B and C parameters is the choice…”

Analytic solutions of the Schrödinger equation with non-central generalized inverse quadratic Yukawa potential

“…Physicists over the years have developed strong interest in searching for the solution of the Schrödinger equation with some potentials [1][2][3][4][5][6][7]. This is because, finding the analytical solution of the Schrödinger equation is extremely crucial in nonrelativistic quantum mechanics and the eigenfunction contains all the necessary information required to describe a quantum system under consideration.…”

Bound state solutions of the generalized shifted Hulthén potential

“…The radial Schrödinger equation for these potentials can be solved exactly for ℓ = 0 (s-wave) but cannot be solved for these potentials for ℓ ≠ 0. To obtain the solution for ℓ ≠ 0, we employ the Pekeris-type approximation scheme to deal with the centrifugal term or solve numerically [21].The most widely used approximation was introduced by Pekeris [22] and another form was suggested by Greene and Aldrich [23] and Qiang et al [24].…”

“…The short range generalized shifted Hulthén potential will be solved within the framework of the Pekeris type approximations suggested by [24] to solve the Schrödinger equation(Non-relativistic Quantum Mechanics) for any arbitrary ℓ −state. These approximations are [32,48,49]: (3) is the commonly used approximation [24];…”