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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 186, Number 3, Pages 386–400
DOI: https://doi.org/10.4213/tmf8987 (Mi tmf8987) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

J. Brüninga, S. Yu. Dobrokhotovbc, M. I. Katsnel'sonde, D. S. Minenkovbc

a Humboldt University, Berlin, Germany
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russian
c Institute for Problems in Mechanics, RAS, Moscow, Russia
d Institute for Molecules and Materials, Radboud University, Nijmegen, the Netherlands
e Ural Federal University, Ekaterinburg, Russia
Full-text PDF (693 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf8987
Abstract: 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.
Keywords: axially symmetric two-dimensional Schrödinger operator, axially symmetric two-dimensional Dirac operator, generalized eigenfunction, semiclassical approximation, density of states, tunnel microscopy.
Funding agency Grant number
Deutsche Forschungsgemeinschaft 2436 RUS 113/990/0-1
Russian Foundation for Basic Research 12-01-31196
Ministry of Education and Science of the Russian Federation 02.A03.21.006
This research was supported by the DFG (Grant No. SFB 647/3), the Russian Foundation for Basic Research (Grant No. 14-01-00521), and the Russian Federation (Act 211, Contract No. 02.A03.21.0006).
Received: 10.06.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 186, Issue 3, Pages 333–345
DOI: https://doi.org/10.1134/S004057791603003X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: J. Brüning, S. Yu. Dobrokhotov, M. I. Katsnel'son, D. S. Minenkov, “Semiclassical asymptotic approximations and the density of states for the two-dimensional radially symmetric Schrödinger and Dirac equations in tunnel microscopy problems”, TMF, 186:3 (2016), 386–400; Theoret. and Math. Phys., 186:3 (2016), 333–345
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v186/i3/p386
    • This publication is cited in the following 2 articles:
    1. V. V. Rykhlov, “Efficient semiclassical approximation for bound states in graphene in magnetic field with a small trigonal warping correction”, Math. Notes, 116:6 (2024), 1339–1349  mathnet  crossref  crossref
    2. A. A. Tolchennikov, “Behavior of the solution of the Klein–Gordon equation with a localized initial condition”, Theoret. and Math. Phys., 199:2 (2019), 761–770  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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