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Spectral asymptotics for a-interactions on sharp cones

Abstract: We investigate the spectrum of three-dimensional Schrödinger operators with a-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues below the threshold of the essential spectrum. We focus on spectral properties for sharp cones, that is when the cone aperture goes to zero, and we describe the asymptotic behavior of the eigenvalues and of the eigenvalue counting function. A part of the results are given in terms of numerical constants appearing as solutions of transcendental equations involving modified Bessel functions.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Journal of Mathematical Analysis and Applications, 2018, 458(1), 566-589

Editorial: Academic Press Inc.

 Fecha de publicación: 01/02/2018

Nº de páginas: 24

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jmaa.2017.09.026

ISSN: 0022-247X,1096-0813

 Proyecto español: MTM2014-53145-P

Url de la publicación: https://doi.org/10.1016/j.jmaa.2017.09.026