Self-adjoint approximations of the degenerate Schrödinger operator
نویسندگان
چکیده
منابع مشابه
Correspondence of the eigenvalues of a non-self-adjoint operator to those of a self-adjoint operator
We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are infinitely many real eigenvalues which accumulate only at ±∞. We use this result to determine the asymptotic distribution of the eigenvalues and to compute some of ...
متن کاملApproximations of Strongly Continuous Families of Unbounded Self-Adjoint Operators
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations. However, it is shown that under an additional compactness assumption the spectrum does vary continuously, and a family of symmetric finite-dimensional approxi...
متن کاملFinite Element Approximations to the Discrete Spectrum of the Schrödinger Operator with the Coulomb Potential
In the present paper, the authors consider the Schrödinger operator H with the Coulomb potential defined in R3m, where m is a positive integer. Both bounded domain approximations to multielectron systems and finite element approximations to the helium system are analyzed. The spectrum of H becomes completely discrete when confined to bounded domains. The error estimate of the bounded domain app...
متن کاملSpectral Behaviour of a Simple Non-self-adjoint Operator
We investigate the spectrum of a typical non-selfadjoint differential operator AD = −d2/dx2 ⊗ A acting on L(0, 1) ⊗ C, where A is a 2 × 2 constant matrix. We impose Dirichlet and Neumann boundary conditions in the first and second coordinate respectively at both ends of [0, 1] ⊂ R. For A ∈ R we explore in detail the connection between the entries of A and the spectrum of AD, we find necessary c...
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: p-Adic Numbers, Ultrametric Analysis and Applications
سال: 2017
ISSN: 2070-0466,2070-0474
DOI: 10.1134/s2070046617010046