Asymptotic behavior of the eigenvalues of the Schrödinger operator in thin closed tubes

Author:

Grushin V. V.

Publisher

Pleiades Publishing Ltd

Subject

General Mathematics

Reference25 articles.

1. V. P. Maslov, “An asymptotic expression for the eigenfunctions of the equation Δu + k 2 u = 0 with boundary conditions on equidistant curves and the scattering of electromagnetic waves in a waveguide,” Dokl. Akad. Nauk SSSR 123(3), 631–633 (1958) [Soviet Phys. Dokl. 3, 1132–1135 (1959)].

2. V. P. Maslov, “Mathematical aspects of integral optics,” Russ. J. Math. Phys. 8(1), 83–105 (2001).

3. V. P. Maslov and E. M. Vorob’ev, “On single-mode open resonators,” Dokl. Akad. Nauk SSSR 179(3), 558–561 (1968).

4. V. V. Belov, S. Yu. Dobrokhotov, and S. O. Sinitsyn, “Asymptotic solutions of the Schrödinger equation in thin tubes,” Trudy Inst. Matem. Mekh. Ural Otd. RAS 9(1), 1–11 (2003).

5. V. V. Belov, S. Yu. Dobrokhotov, S. O. Sinitsyn, and T. Y. Tudorovskii, “Semiclassical approximation and the canonical Maslov operator for nonrelativistic equations of quantum mechanics in nanotubes,” Dokl. Ross. Akad. Nauk 393(4), 460–464 (2003) [Russian Acad. Sci. Dokl. Math.].

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