On Local Perturbations of Shr Odinger Operator in Axis

نویسنده

  • Rustem R. GADYL'SHIN
چکیده

We adduce the necessary and sufficient condition for arising of eigenvalues of Shrödinger operator in axis under small local perturbations. In the case of eigenvalues arising we construct their asymptotics.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Local Perturbations of Schr¨odinger Operator on Plane

We obtain necessary and sufficient conditions for emerging of small eigen-value for Schrödinger operator on plane under local operator perturbations. In the case the eigenvalue emerges we construct its asymptotics. The examples are given.

متن کامل

2 HANS { CHRISTOPH KAISER AND JOACHIM REHBERGOn Stationary Schr

We regard the Schrr odinger{Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three{ dimensional domain and establish the method of steepest descent. The electro-static potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrr odinger operator, the Fermi level and the quantum...

متن کامل

On Eigenvalues in Gaps for Perturbed Magnetic Schrr Odinger Operators

1 Introduction (1) We consider Schrr odinger operators with a spectral gap, perturbed by either a decreasing electric potential or a decreasing magnetic eld. The strength of these perturbations depends on a coupling parameter. With growing, eigenvalues may move into the gap or out of the gap. Most of our results concern (lower) bounds for the number of eigenvalues that cross a xed energy level ...

متن کامل

A Local Strong form Meshless Method for Solving 2D time-Dependent Schrödinger Equations

This paper deals with the numerical solutions of the 2D time dependent Schr¨odinger equations by using a local strong form meshless method. The time variable is discretized by a finite difference scheme. Then, in the resultant elliptic type PDEs, special variable is discretized with a local radial basis function (RBF) methods for which the PDE operator is also imposed in the local matrices. Des...

متن کامل

Absolutely Continuous Spectrum of One-dimensional Schrr Odinger Operators and Jacobi Matrices with Slowly Decreasing Potentials

We prove that for any one-dimensional Schrr odinger operator with potential V (x) satisfying decay condition jV (x)j C x ?3=4? ; the absolutely continuous spectrum lls the whole positive semi-axis. The description of the set in R + on which the singular part of the spectral measure might be supported is also given. Analogous results hold for Jacobi matrices.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007