Geodesic
The energy levels and eigen wave functions of electrons in quantum rings in the magnetic field
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 130 (2013) no. 1, pp. 326-333 Cet article a éte moissonné depuis la source Math-Net.Ru

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The solution of the eigenvalue problem for non interacting electrons of the quantum ring in the magnetic field is discussed. The potential shape of the quantum ring permitting analytical solution was proposed. The solution of the appropriate eigenvalue problem was found in the terms of the Heun functions and expression for the energy levels was obtained. It was pointed out that proposed potential might be considered as a single-well or double-well potential of concentric quantum rings.
Keywords: quantum ring, magnetic field, quasi-exactly solvable models of quantum mechanics. 
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E. V. Antropova; A. A. Bryzgalov; F. I. Karmanov. The energy levels and eigen wave functions of electrons in quantum rings in the magnetic field. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 130 (2013) no. 1, pp. 326-333. http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a32/

[1] A. G. Ushveridze Quasi-exactly solvable models in quantum mechanics, Soviet J. Particles and Nuclei, 20:5 (1989), 504–528 | MR

[2] W.-C. Tan, J. C. Inkson, “Electron states in a two-dimensional ring — an exactly soluble model”, Semicond. Sci. Technol., 11:11 (1996), 1635–1641 | DOI

[3] H. A. Mavromatis, “Generalization of Casas–Plastino potentials to three dimensions”, Amer. J. Phys., 68:3 (2000), 287–288 | DOI | MR

[4] A. A. Bryzgalov, F. I. Karmanov, “Method for splitting into physical processes in the problem on the time dynamics of electron wave functions of a two-dimensional quantum ring”, Math. Models Comput. Simul., 3:1 (2011), 25–34 | DOI | Zbl

[5] S. Yu. Slavyanov, W. Lay, Special functions. A unified theory based on singularities., Oxford University Press, New York, 2000, xvi+293 pp. ; S. Yu. Slavyanov, V. Lai, Spetsialnye funktsii: Edinaya teoriya, osnovannaya na analize, Nevskii Dialekt, SPb., 2002, 312 pp. | MR | Zbl

[6] E. R. Arriola, J. S. Dehesa, A. Zarzo, “Spectral properties of the biconfluent Heun differential equation”, J. Comput. Appl. Math., 37:1–3 (1991), 161–169 | DOI | MR | Zbl

[7] A. F. Nikiforov, V. B. Uvarov, Special functions of mathematical physics, Nauka, Moscow, 1984, 344 pp. | MR