AROUND SUPERSYMMETRY FOR SEMICLASSICAL SECOND ORDER DIFFERENTIAL OPERATORS.

Let P(h), h ∈]0, 1] be a semiclassical scalar differential operator of order 2. The existence of a supersymmetric structure given by a matrix G(x; h) was exhibited by H'erau, Hitrik, and Sj¨ostrand (2011) under rather general assumptions. In this paper we give a sufficient condition on the coefficients of P(h) so that the matrix G(x; h) enjoys some nice estimates with respect to the semiclassical parameter. [ABSTRACT FROM AUTHOR]