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The ladder operators of Rosen-Morse potential with centrifugal term by factorization method. (English) Zbl 1353.81130

Summary: In this paper, we have considered analytical solution of radial Schrödinger equation with Rosen-Morse potential by factorization method. In order to obtain bound states, we have approximated the centrifugal term (\(l \neq 0\)) as exponential function. By using associated Jacobi polynomial and comparing with radial part, we have obtained eigenvalues and eigenfunction for \(l\)-wave cases. The factorization method leads us to calculate the first order equations as the raising and lowering operators. These operators help us to Hamiltonian system which is written in terms of two first order differential equation with respect to parameters \(n\) and \(l\) as the raising and lowering operators. Finally we have been considered that there is not shape invariance condition proportional to parameters \(n\) and \(l\). Also the variations of energy spectrum has plotted in terms of \(n\).

MSC:

81V55 Molecular physics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
81U15 Exactly and quasi-solvable systems arising in quantum theory
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