Szegö limit theorems in quantum mechanics (Q801474)

This paper is devoted to the obtention of Szegö-type limit theorems for some Schrödinger operators of the form \(H=-(1/2)\Delta +V\) with V smooth, positive and growing like \(V_ 0| x|^ k\), \(k>0\). After one section on the calculus of symbols relative to H and one using weighted Sobolev spaces and some results of operator theory, an averaging theorem compare classical and quantum mean value in the high energy limit. This averaging theorem is then used to prove the announced Szegö type theorem.