Analytical arbitrary ℓ‐wave solutions of the manning–rosen potential in the tridiagonalization program

Abstract

By working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator, the arbitrary '-wave solutions of the Schrö dinger equation for the Manning-Rosen potential is investigated with an approximation of centrifugal term. The resulting three-term recursion relation for the expansion coefficients of the wavefunction is presented. The bound-state wavefunctions are expressed in terms of the Jocobi polynomial, and the discrete spectrum of the bound states is obtained by diagonalization of the recursion relation.

Solutions of the Schrödinger equation in the tridiagonal representation with the deformed hyperbolic potentials

“…from which a tridiagonal matrix representation for the wave operator, ϕ m |H − E|ϕ n , is achievable by imposing the following conditions on the last term, which should either be eliminated by choosing (α, β) = 1 2 (ν, µ) or be proportional to δ m,n−1 ,which requires (α, β) be 1 2 (ν + 1, µ) or 1 2 (ν, µ + 1). It is shown that the last two cases correspond to the hyperbolic Rosen-Morse potential and the hyperbolic Pöschl-Teller potential [26,28]. Hence, we will only be concerned with the first case.…”