Bound states of a converging quantum waveguide
作者： Giuseppe Cardone , Sergei A. Nazarov , Keijo Ruotsalainen
DOI: 10.1051/M2AN/2012033
关键词: Spectrum (functional analysis) 、 Mathematics 、 Discrete spectrum 、 Bound state 、 Continuous spectrum 、 Quantum 、 Quantum mechanics 、 Upper and lower bounds 、 Waveguide (acoustics) 、 Eigenvalues and eigenvectors
摘要: We consider a two-dimensional quantum waveguide composed of two semi-strips width 1 and 1 − e, where e > 0 is small real parameter, i.e. the gently converging. The junction zone for + O (√e). will present sufficient condition existence weakly coupled bound state below π 2 , lower continuous spectrum. This eigenvalue in discrete spectrum unique its asymptotics constructed justified when → 0+ .
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