Supersymmetric Partner Bessel Functions

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The partner Bessel functions are given by . The supersymmetry (SUSY) parameter determines the transition beween Bessel functions of different order, from to for arbitrary .

Contributed by: N. Barbosa-Cendejas, and M. A. Reyes (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The partner Bessel equation

is derived from a supersymmetric (SUSY) type of factorization of Bessel's equation, which also applies to other Sturm–Liouville equations. The partner Bessel functions show an interesting and unusual SUSY behavior: the SUSY parameter γ links these functions to a pair of Bessel functions differing by two orders

.

Since , this SUSY parameter takes the partner Bessel functions from to .

In the snapshots you can see the shape of the partner Bessel functions as they evolve from one order to another for different values of the SUSY parameter.

References:

[1] N. Barbosa-Cendejas and M. A. Reyes, "Damped Wave Equation from Isospectral Bessel Functions," Rev. Mex. Fís., 54, 2008 pp. 319–321. [2] M. A. Reyes, D. Jimenez, and H. C. Rosu, "One-Parameter Isospectral Special Functions," Rev. Mex. Fís., 49, 2003 pp. 358–363.



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