Spectral properties of non-self-adjoint operators in the semi-classical regime

We give a spectral description of the semi-classical Schrodinger operator with a piecewise-linear, complex-valued potential. Moreover, using these results, we give an example to show how an arbitrarily small fixed perturbation of a non-self-adjoint operator can completely change the asymptotic spectrum of the operator in the semi-classical limit. (C) 2001 Academic Press.