Semiclassical asymptotics for the spectral shift function. (English) Zbl 0922.35108

Robert, Didier

Buslaev, V. (ed.) et al., Differential operators and spectral theory. M. Sh. Birman’s 70th anniversary collection. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 189(41), 187-203 (1999).

Summary: The spectral shift function was introduced at the beginning of the fifties, by I. M. Lifshits, to measure the change in the spectrum of a selfadjoint operator when it is perturbed by a trace class operator. The goal of this paper is to give a survey about results concerning asymptotic properties of the spectral shift function for perturbations of operators defined as observable in quantum mechanics, with respect to different parameters like energy, Planck constant (or masses). Some applications to trace formulas are discussed.
For the entire collection see [Zbl 0911.00011].

MSC:

35P20	Asymptotic distributions of eigenvalues in context of PDEs
35J10	Schrödinger operator, Schrödinger equation
81Q10	Selfadjoint operator theory in quantum theory, including spectral analysis

Keywords:

trace formulas