Semi-Classical States for Non-Self-Adjoint Schrödinger Operators
نویسندگان
چکیده
منابع مشابه
Resolvent estimates for non-self-adjoint operators via semi-groups
We consider a non-self-adjoint h-pseudodifferential operator P in the semi-classical limit (h → 0). If p is the leading symbol, then under suitable assumptions about the behaviour of p at infinity, we know that the resolvent (z − P )−1 is uniformly bounded for z in any compact set not intersecting the closure of the range of p. Under a subellipticity condition, we show that the resolvent extend...
متن کاملEigenvalue distributions and Weyl laws for semi-classical non-self-adjoint operators in 2 dimensions
In this note we compare two recent results about the distribution of eigenvalues for semi-classical pseudodifferential operators in two dimensions. For classes of analytic operators A. Melin and the author [6] obtained a complex Bohr-Sommerfeld rule, showing that the eigenvalues are situated on a distorted lattice. On the other hand, with M. Hager [4] we showed in any dimension that Weyl asympt...
متن کاملNon-self-adjoint Differential Operators
We describe methods which have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. We find that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the opera...
متن کاملNon-Self-Adjoint Operators and Pseudospectra
The theory of pseudospectra has grown rapidly since its emergence from within numerical analysis around 1990. We describe some of its applications to the stability theory of differential operators, to WKB analysis and even to orthogonal polynomials. Although currently more a way of looking at non-self-adjoint operators than a list of theorems, its future seems to be assured by the growing numbe...
متن کاملOn Eigenfunction Approximations for Typical Non-self-adjoint Schrödinger Operators
We construct efficient approximations for the eigenfunctions of non-selfadjoint Schrödinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schrödinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable ad...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1999
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200050521