@article{ZNSL_2018_471_a8,
author = {A. Ya. Kazakov},
title = {{\textquotedblleft}Separation of variables{\textquotedblright} in the model problems of the diffraction theory. {Formal} scheme},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {124--139},
year = {2018},
volume = {471},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a8/}
}
A. Ya. Kazakov. “Separation of variables” in the model problems of the diffraction theory. Formal scheme. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 124-139. http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a8/
[1] V. M. Babich, V. S. Buldyrev, Short-Wavelength Diffraction Theory, Asymptotic Methods, Springer, Berlin, 1991 | MR
[2] V. M. Babich, N. Ya. Kirpichnikova, The Boundary-Layer Method in Diffraction Theory, Leningrad University, Leningrad, 1974 | MR
[3] Yu. A. Kravtsov, Yu. I. Orlov, Caustics, catasrophes and wave fields, Springer, Heidelberg, 1999 | MR
[4] A. N. Oraevsky, “Whispering-gallery waves”, Quantum Electron, 32:5 (2002), 377–400 | DOI
[5] M. M. Popov, “K zadache o volnakh shepchuschei galerei v okrestnosti prostogo nulya effektivnoi krivizny granitsy”, Zap. nauchn. semin. LOMI, 62, 1976, 197–206 | MR | Zbl
[6] M. M. Popov, “Volnovoe pole v kausticheskoi teni v okrestnosti tochki peregiba granitsy”, Zap. nauchn. semin. LOMI, 89, 1979, 246–260 | MR
[7] V. M. Babich, V. P. Smyshlyaev, “Scattering problem for the Schrödinger equation in the case of a potential linear in time and coordinate. I. Asymptotics in the shadow zone”, Journ. of Soviet Math., 32:2 (1986), 103–112 | DOI | Zbl
[8] V. P. Smyshlyaev, “Concentration of the solutions near a limit ray in the neighborhood of an inflection point of the boundary”, J. Soviet Math., 55:3 (1991), 1757–1760 | DOI | MR | Zbl
[9] A. Ya. Kazakov, “Special function related to the concave-convex boundary problem of the diffraction theory”, J. Phys. A: Math.Gen., 36:14 (2003), 4127–4142 | DOI | MR
[10] A. Ya. Kazakov, “Special Function Related to the Scattering of the Whispering Gallery Mode at a Point of Local Straightening”, J. Math. Sci., 128:2 (2005), 2782–2786 | DOI | MR | Zbl
[11] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST Hanbook of Mathematical Functions, NIST and Cambride University Press, 2010 | MR
[12] K. Husimi, “Miscellanea in Elementary Quantum Mechanics. II”, Progr. Theor. Phys., 9:4 (1953), 381–402 | DOI | MR | Zbl
[13] A. M. Perelomov, V. S. Popov, “Gruppovye aspekty zadachi ob ostsillyatore s peremennoi chastotoi”, Teoret. mat. fiz., 1:3 (1969), 360–374 | MR
[14] C. F. Lo, “Propagator of the general driven time-dependent oscillator”, Phys. Rev. A, 47:1 (1993), 115–118 | DOI
[15] Sang Pyo Kim, “A class of exactly solved time-dependent quantum harmonic oscillators”, J. Phys. A: Math. Gen., 27:11 (1994), 3927–3926 | DOI | MR
[16] H. Kanasugi, H. Okada, “Systematic Treatment of General Time-Dependent Harmonic Oscillator in Classical and Quantum Mechanics”, Progr. Theoret. Phys., 93:5 (1995), 949–960 | DOI | MR
[17] O. Vallee, M. Soares, Airy functions and application to physics, Imperial College Press, London, 2010 | MR