A Time Dependent Scattering Theory for a Class of Simply Characteristic Operators with Short Range Local Potentials

Let H = H 0 + W S (Q), where (i) H 0 = h 0 ( P ), (ii) h 0 is a real‐valued simply characteristic polynomial on R n with {0} = { n:h 0 (ξ + tη ) = h 0 (ξ) for all ξ and real t } and (iii) W s is a real‐valued short range potential with some local singularity. Using time dependent methods we prove, for the operator H (a) the absence of singular continuous spectrum, (b) asymptotic completeness and (c) accumulation of eigenvalues only at the critical values of the symbol h 0 . The class H 0 is precisely that for which a stationary theory is developed in [ 6 ].