Supersymmetric features of the Error and Dawson's functions

Following a letter by Bessett, 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.