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arXiv · 1111.1198

A new simple class of superpotentials in SUSY Quantum Mechanics

Fabricio Marques·Osvaldo Negrini·Adilson Jose da Silva
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Abstract

In this work we introduce the class of quantum mechanics superpotentials $W(x)=gε(x) x^{2n}$ 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.

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Fabricio Marques, Osvaldo Negrini, Adilson Jose da Silva. 2012-02-22. A new simple class of superpotentials in SUSY Quantum Mechanics. https://doi.org/10.1088/1751-8113%2F45%2F11%2F115307

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