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Study of the generalized quantum isotonic nonlinear oscillator potential. (English) Zbl 1238.81108

Summary: We study the generalized quantum isotonic oscillator Hamiltonian given by \(H = - d^2/dr^2 + l(l + 1)/r^2 + w^2r^2 + 2g(r^2 - a^2)/(r^2 + a^2)^2,~g > 0\). Two approaches are explored. A method for finding the quasipolynomial solutions is presented, and explicit expressions for these polynomials are given, along with the conditions on the potential parameters. By using the asymptotic iteration method, we show how the eigenvalues of this Hamiltonian for arbitrary values of the parameters \(g, w\), and \(a\) may be found to high accuracy.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
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References:

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