  The aim of this work is to use systematically the symmetries of the (one
dimensional) bacward heat equation with potentiel in order to solve certain one
dimensional It\^o's stochastic differential equations. The special form of the
drift (suggested by quantum mechanical considerations) gives, indeed, access to
an algebrico-geometric method due, in essence, to E.Cartan, and called the
Method of Isovectors. A V singular at the origin, as well as a one-factor
affine model relevant to stochastic finance, are considered as illustrations of
the method.
