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Discrete spectra for confined and unconfined -a/r + b r^2 potentials in d dimensions
Richard L. Hall, Nasser Saad, Kalidas Sen
Exact solutions to the d-dimensional Schroedinger equation, d\geq 2, for Coulomb plus harmonic oscillator potentials V(r)=-a/r+br^2, b>0 and a\ne 0 are obtained. The potential V(r)…
Study of the generalized quantum isotonic nonlinear oscillator potential
Nasser Saad, Richard L. Hall, Hakan Ciftci +1
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 find…
Spectral characteristics for a spherically confined -1/r + br^2 potential
Richard L. Hall, Nasser Saad, K. D. Sen
We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r) = -a/r + br^2, b>0. In particular, scaling, monotonicity, and en…