Supersymmetric features of the Error and Dawson's functions

M.A. Reyes and R. Arcos-Olalla

Departamento de Física, Universidad de Guanajuato, Apartado Postal E143, 37150 León, Gto., México.

Received 4 May 2015; ]]> accepted 14 September 2015

Abstract

Following a letter by Bassett, we show first that it is possible to find an analytical approximation to the error function in terms of a finite series of hyperbolic tangents from the supersymmetric (SUSY) solution of the Poschl-Teller eigenvalue problem in quantum mechanics (QM). Afterwards, we show that the second order differential equation for the derivatives of Dawson's function can be found in another SUSY related eigenvalue problem, where the factorization of the simple harmonic oscillator Hamiltonian renders the wrong-sign Hermite differential equation, and that Dawson's second order differential equation possess a singular SUSY type relation to this equation.

Keywords: Supersymmetry; error function; Dawson's function.

PACS: 02.30.Gp; 02.30.Mv; 05.10.Ln; 11.30.Pb

DESCARGAR ARTÍCULO EN FORMATO PDF

References

1. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (seventh edition), (Elsevier, 2007) p. 887, sect. 8.25.         [ Links ]

2. B. Bassett, Comput. Math Appl. 36 (1998) 37-45; also in Report-No-SISSA-64-96-A.         [ Links ]

3. S. Winitzki, Computational Science and Its Applications -ICCSA 2003, Lecture Notes in Computer Science 2667 (2003) 780-789.         [ Links ]

4. M. Chiani, D. Dardari, and M.K. Simon, IEEE Trans. Commun. 2 (2003) 840-845.         [ Links ]

5. G.K. Karagiannidis, A.S. Lioumpas, Commun. Lett., IEEE 11 (2007) 644-646.         [ Links ]

6. G. Poschl, E. Teller, Zeitschrift fur Physik 83 (1933) 143-151        [ Links ]

7. L. Infeld and T.E. Hull, Rev. Mod. Phys. 23 (1951) 21.         [ Links ]

8. J.I. Díaz, J. Negro, L.M. Nieto, and O. Rosas-Ortiz, J. Phys. A: Math. Gen. 32 (1999) 8447-8460.         [ Links ]

9. Erno Sajo, J. Phys. A: Math. Gen. 26 (1993) 2977-2987.         [ Links ]

10. W.J. Cody, A. Paciorek Kathleen, and C. Jr. Thacher Henry, Math. Comp. 24 (1970) 171-178.         [ Links ]

11. R. Arcos-Olalla, M.A. Reyes, and H.C. Rosu, Physics Letters A 376 (2012) 2860-2865.         [ Links ]

12. B. Mielnik, J. Math. Phys. 25 (1984) 3387-3389.         [ Links ]