2012/11/10 by Hatem Najar, Najar, H., Monia Raissi +1
Mathematics · Physics and Astronomy · #47B80 #81Q10 #81Q15 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1211.2343
openalex publication_date 2012/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous study \citen 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 proved that such system exhibits discrete eigenvalues below the essential spectrum for any a>0. In the present work we study the effect of a magnetic filed of Aharonov-Bohm type when the magnetic field is turned on this system. Precisely we prove that in the presence of such magnetic filed there is some critical values of a0>0, for which we have absence of the discrete spectrum for 0