New Solvable Singular Potentials
High Energy Physics - Theory
2008-11-26 v1 Mathematical Physics
math.MP
Quantum Physics
Abstract
We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, P\"oschl-Teller I and P\"oschl-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.
Cite
@article{arxiv.hep-th/0011096,
title = {New Solvable Singular Potentials},
author = {R. Dutt and A. Gangopadhyaya and C. Rasinariu and U. Sukhatme},
journal= {arXiv preprint arXiv:hep-th/0011096},
year = {2008}
}
Comments
19 pages, 4 figures