Journal of Physics A: Mathematical and General
We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, Pöschl-Teller I and Pöschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.
Dutt, R.; Gangopadhyaya, Asim; Rasinariu, C.; and Sukhatne, Uday P., "New Solvable Singular Potentials " (2001). Physics: Faculty Publications and Other Works. 11.
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