TY - JOUR

T1 - Discrete Spectrum of Cross-Shaped Quantum Waveguides

AU - Nazarov, S.A.

PY - 2014

Y1 - 2014

N2 - We study the discrete spectrum of the Dirichlet problem for the Laplace operator on the cross of two strips with widths 1 and H which are perpendicular to each other. We verify that for any parameter H > 0 the discrete spectrum consists of the only point μ1 H while the function H {mapping} μ1 H is strictly monotone decreasing. We consider other cross-shaped junctions of quantum waveguides and, in particular, construct asymptotics of eigenvalues as H → +0. © 2014 Springer Science+Business Media New York.

AB - We study the discrete spectrum of the Dirichlet problem for the Laplace operator on the cross of two strips with widths 1 and H which are perpendicular to each other. We verify that for any parameter H > 0 the discrete spectrum consists of the only point μ1 H while the function H {mapping} μ1 H is strictly monotone decreasing. We consider other cross-shaped junctions of quantum waveguides and, in particular, construct asymptotics of eigenvalues as H → +0. © 2014 Springer Science+Business Media New York.

U2 - 10.1007/s10958-014-1662-0

DO - 10.1007/s10958-014-1662-0

M3 - Article

SP - 346

EP - 376

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

ER -