Supersymmetric solution of Schrödinger equation by using the asymptotic iteration method

Abstract

In this work, the exact analytical solutions of the radial Schrödinger equation are presented for the harmonic oscillator, Hulthén and Pöschl‐Teller potentials within the framework of the asymptotic iteration method by using supersymmetry. The energy eigenvalues and the corresponding eigenfunctions are obtained analytically.

The asymptotic iteration method revisited

“…Since the first publication [1] of the Asymptotic Iteration Method (AIM), it has enjoyed great success in many areas of physics, among them we refer the reader to the references [2][3][4][5][6][7]. Given the differential equation y (x) = λ 0 (x)y (x) + s 0 (x)y(x), (1) where λ 0 (x) and s 0 (x) are C ∞ functions.…”

“…Using (2), it easily follows that λ n (x)y (n+1) (x) − λ n−1 (x)y (n+2) (x) = δ n (x)y(x) (7) whence if y(x), the solution of (1), is a polynomial of degree at most n then δ n (x) ≡ 0. On the other hand, if δ n (x) ≡ 0, a particular solution of the differential equation ( 1) is given by y(x) = exp − x α n (t)dt .…”

Relativistic Energy Analysis of Five-Dimensionalq-Deformed Radial Rosen-Morse Potential Combined withq-Deformed Trigonometric Scarf Noncentral Potential Using Asymptotic Iteration Method

“…Eqs. (21)(22)(23)(24) are angular part of Dirac equation for 𝜃 1 until 𝜃 4 respectively. The D-dimensional relativistic wave functions and orbital quantum numbers are obtained from those equations.…”

“…In this study, the four angular part of Dirac equations are presented in Eqs. (21)(22)(23)(24), so we have to solve each equation of angular Dirac equation using AIM.…”