Physics – Mathematical Physics
Scientific paper
2011-06-10
Mod. Phys. Lett. A 26 (2011) 1843-1852
Physics
Mathematical Physics
14 pages, no figure, published version
Scientific paper
Exactly solvable rationally-extended radial oscillator potentials, whose wavefunctions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of $k$th-order supersymmetric quantum mechanics, with special emphasis on $k=2$. It is shown that for $\mu=1$, 2, and 3, there exist exactly $\mu$ distinct potentials of $\mu$th type and associated families of exceptional orthogonal polynomials, where $\mu$ denotes the degree of the polynomial $g_{\mu}$ arising in the denominator of the potentials.
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