Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256708 | Reports on Mathematical Physics | 2017 | 16 Pages |
Abstract
We analyze spectral properties of the operator H = â2/âx2 - â2/ây2 + Ï2y2 - λy2V(xy) in L2(â2), where Ï â 0 and V ⥠0 is a compactly supported and sufficiently regular potential. It is known that the spectrum of H depends on the one-dimensional Schrödinger operator L = -d2/dx2 + Ï2 - λV(x) and it changes substantially as infÏ(L) switches sign. We prove that in the critical case, infÏ(L) = 0, the spectrum of H is purely essential and covers the interval [0, â). In the subcritical case, inf Ï(L) > 0, the essential spectrum starts from Ï and there is a nonvoid discrete spectrum in the interval [0, Ï). We also derive a bound on the corresponding eigenvalue moments.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Diana Barseghyan, Pavel Exner,