2009/02/21 by Samir Ben Hariz, Hariz, S. Ben, Mounir Ben Salah +3
Computer Science · Mathematics · #47B80 #81Q10 #81Q15 #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.0902.3731
openalex publication_date 2009/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d. We impose the Neumann boundary condition on a disc window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete eigenvalues below the essential spectrum for any a>0. We give also a numeric estimation of the number of discrete eigenvalue as a function of (a)/(d). When a tends to the infinity, the asymptotic of the eigenvalue is given.