Geodesic
Semiclassical asymptotic approximations and the~density of states for the~two-dimensional radially symmetric Schr\"odinger and Dirac equations in tunnel microscopy problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 386-400

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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. 
@article{TMF_2016_186_3_a2,
     author = {J. Br\"uning and S. Yu. Dobrokhotov and M. I. Katsnel'son and D. S. Minenkov},
     title = {Semiclassical asymptotic approximations and the~density of states for the~two-dimensional radially symmetric {Schr\"odinger} and {Dirac} equations in tunnel microscopy problems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {386--400},
     publisher = {mathdoc},
     volume = {186},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a2/}
}
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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 Schr\"odinger and Dirac equations in tunnel microscopy problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 3, pp. 386-400. http://geodesic.mathdoc.fr/item/TMF_2016_186_3_a2/