All
All

What are you looking for?

All
Projects
Organizations

Quick search

  • Projects supported by TA ČR
  • Excellent projects
  • Projects with the highest public support
  • Current projects

Smart search

  • That is how I find a specific +word
  • That is how I leave the -word out of the results
  • “That is how I can find the whole phrase”

Asymptotics of the bound state induced by delta-interaction supported on a weakly deformed plane

Result description

In this paper, we consider the three-dimensional Schrodinger operator with a delta-interaction of strength alpha > 0 supported on an unbounded surface parametrized by the mapping R-2 (sic) x bar right arrow (x, beta f (x)), where beta is an element of [0, infinity) and f : R-2 -> R, f not equivalent to 0, is a C-2-smooth, compactly supported function. The surface supporting the interaction can be viewed as a local deformation of the plane. It is known that the essential spectrum of this Schrodinger operator coincides with [- 1/4 alpha(2), +infinity). We prove that for all sufficiently small beta > 0, its discrete spectrum is non-empty and consists of a unique simple eigenvalue. Moreover, we obtain an asymptotic expansion of this eigenvalue in the limit beta -> 0+. In particular, this eigenvalue tends to -1/4 alpha(2) exponentially fast as beta -> 0+.

Keywords

Schrodinger operatorinteractions

The result's identifiers

Alternative languages

  • Result language

    angličtina

  • Original language name

    Asymptotics of the bound state induced by delta-interaction supported on a weakly deformed plane

  • Original language description

    In this paper, we consider the three-dimensional Schrodinger operator with a delta-interaction of strength alpha > 0 supported on an unbounded surface parametrized by the mapping R-2 (sic) x bar right arrow (x, beta f (x)), where beta is an element of [0, infinity) and f : R-2 -> R, f not equivalent to 0, is a C-2-smooth, compactly supported function. The surface supporting the interaction can be viewed as a local deformation of the plane. It is known that the essential spectrum of this Schrodinger operator coincides with [- 1/4 alpha(2), +infinity). We prove that for all sufficiently small beta > 0, its discrete spectrum is non-empty and consists of a unique simple eigenvalue. Moreover, we obtain an asymptotic expansion of this eigenvalue in the limit beta -> 0+. In particular, this eigenvalue tends to -1/4 alpha(2) exponentially fast as beta -> 0+.

  • Czech name

  • Czech description

Classification

  • Type

    Jimp - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Result continuities

Others

  • Publication year

    2018

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Mathematical Physics

  • ISSN

    0022-2488

  • e-ISSN

  • Volume of the periodical

    59

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    17

  • Pages from-to

  • UT code for WoS article

    000424017000039

  • EID of the result in the Scopus database

    2-s2.0-85040712425

Result type

Jimp - Article in a specialist periodical, which is included in the Web of Science database

Jimp

OECD FORD

Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Year of implementation

2018