Dirac equation transfer matrix,
WKB-approach,
Wannier–Stark problem,
functional equations,
self-similar fractal potential,
Cantor staircase,
scale invariance,
tunneling time,
coherent superposition of microscopically distinct (sub)states.
Subject:
1. Relativistic quantum mechanics.
2. Quantum-classical problem.
3. Tunneling time problem. Hartman paradox in quantum mechanics and classical electrodynamics.
4. Wannier–Stark problem.
5. Scattering a quantum particle on fractal potentials.
6. Even WKB-series involving classical turning points.
Main publications:
The Stationary Dirac Equation as a Generalized Pauli Equation for Two Quasiparticles. Foundations of Physics, 10.1007/s10701-015-9888-3
From a 1D Completed Scattering and Double Slit Diffraction to the Quantum-Classical Problem for Isolated Systems. Foundations of Physics, DOI: 10.1007/s10701-011-9564-1
Stationary states of an electron in periodic structures in a constant uniform electrical field, J. of Phys.: Condens. Matt., 1998, v. 10, no. 30, p. 6707–6716.
The transfer matrices of the self-similar fractal potential on the Cantor set, J. of Phys. A: Mathematical and General, 2000, v. 33, no. 23, p. 4293–4308.
On the Transfer-Matrix Approach to the Scattering Problem for the Self-Similar Fractal Potential and Cantor Staircase. p-Adic Numbers, Ultrametric Analysis and Applications, 2010, Vol. 2, No. 3, pp. 179–186.
N. L. Chuprikov, “On the Hartman effect and velocity of propagating the electromagnetic wave in the tunneling process”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(31) (2013), 215–222
2011
2.
N. L. Chuprikov, “The WKB Method and Differential Consequences of the Riccati Equation”, Mat. Zametki, 89:6 (2011), 929–937; Math. Notes, 89:6 (2011), 885–892
3.
N. L. Chuprikov, “On the compatibility of the corpuscular and wave properties of a particle in the two-slit experiment”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(23) (2011), 235–242
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