Hidden SUSY features, and Dawson’s function and the wrong-sign Hermite functions

Abstract

We propose that some problems in mathematical physics show non-typical supersymmetric (SUSY) features which may still need to be thoroughly explored. In particular, we first show that the Pöschl-Teller problem posses some inherent ladder peculiarities which are not considered in the usual SUSY approach. Then we show that Dawson’s function and its derivatives show a SUSY type relation with the wrong-sign Hermite equation, found in a general factorization of the simple harmonic oscillator, which includes Mielnik’s SUSY partners as particular cases.