Ibort L.A , Landi G., Mar'in-Solano , J., Marmo G.
On the inverse problem of Lagrangian supermechanics
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ABSTRACT.  The inverse problem for Lagrangian supermechanics is investigated. 
A set of necessary and sufficient conditions for a system of second
order differential equations in superspace to derive from (a
possibly non regular) superlagrangian function are
given. The harmonic superoscillator is revisited and a family of
even and odd alternative superlagrangians are constructed for it.
Finally, we comment on the existence of recursion operators.