Semiclassical asymptotic approximations and the density of states for the two-dimensional radially symmetric Schrödinger and Dirac equations in tunnel microscopy problems
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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.
Keywordsaxially symmetric two-dimensional Schrödinger operator axially symmetric two-dimensional Dirac operator generalized eigenfunction semiclassical approximation density of states tunnel microscopy
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- 7.A. I. Baz’, Ya. B. Zeldovich, and A. M. Perelomov, Scattering, Reactions, and Decay in Nonrelativistic Quantum Mechanics [in Russian], Nauka, Moscow (1971); English transl. prev. ed., Wiley, New York (1969).Google Scholar
- 8.V. M. Babich, “On the short-wave asymptotic behavior of the Green’s function for the Helmholtz equation,” Mat. Sb., ns., 65(107), 576–630 (1964).Google Scholar
- 10.V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973); English transl.: Operational Methods, Mir, Moscow (1976).Google Scholar