1111.1198 (Fabricio Marques et al.)

A new simple class of superpotentials in SUSY Quantum Mechanics    [PDF]

Fabricio Marques, Osvaldo Negrini, Adilson Jose da Silva

In this work we introduce the class of quantum mechanics superpotentials
$W(x)=g\epsilon(x) x^{2n}$ and study in details the cases $n=0$ and 1. The
$n=0$ superpotential is shown to lead to the known problem of two
supersymmetrically related Dirac delta potentials (well and barrier). The $n=1$
case result in the potentials $V_{\pm}(x)=g^{2}x^{4}\pm2g|x|$. For $V_{-}$ we
present the exact ground state solution and study the excited states by a
variational technic. Starting from the ground state of $V_{-}$ and using
logarithmic perturbation theory we study the ground states of $V_{+}$ and also
of $V(x)=g^2 x^4$ and compare the result got by this new way with other results
for this state in the literature.

View original: http://arxiv.org/abs/1111.1198