Theoretical and Mathematical Physics

, Volume 186, Issue 3, pp 333–345 | Cite as

Semiclassical asymptotic approximations and the density of states for the two-dimensional radially symmetric Schrödinger and Dirac equations in tunnel microscopy problems

  • J. Brüning
  • S. Yu. Dobrokhotov
  • M. I. Katsnelson
  • D. S. Minenkov


We consider the two-dimensional stationary Schrödinger and Dirac equations in the case of radial symmetry. A radially symmetric potential simulates the tip of a scanning tunneling microscope. We construct semiclassical asymptotic forms for generalized eigenfunctions and study the local density of states that corresponds to the microscope measurements. We show that in the case of the Dirac equation, the tip distorts the measured density of states for all energies.


axially symmetric two-dimensional Schrödinger operator axially symmetric two-dimensional Dirac operator generalized eigenfunction semiclassical approximation density of states tunnel microscopy 


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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • J. Brüning
    • 1
  • S. Yu. Dobrokhotov
    • 2
    • 3
  • M. I. Katsnelson
    • 4
    • 5
  • D. S. Minenkov
    • 2
  1. 1.Humboldt UniversityBerlinGermany
  2. 2.Institute for Problems in Mechanics, RASMoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyMoscowRussia
  4. 4.Institute for Molecules and MaterialsRadboud UniversityNijmegenthe Netherlands
  5. 5.Ural Federal UniversityEkaterinburgRussia

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