Physics – Mathematical Physics
Scientific paper
2007-02-08
Physics
Mathematical Physics
Scientific paper
We consider the Dirichlet Laplacian in a domain two three-dimensional parallel layers having common boundary and coupled by a window. The window produces the bound states below the essential spectrum; we obtain two-sided estimates for them. It is also shown that the eigenvalues emerge from the threshold of essential spectrum as the window passes through certain critical shapes. We prove the necessary condition for the window to be of critical shape. Under an additional assumption we show that this condition is sufficient and obtain the asymptotic expansion for the emerging eigenvalue as well as for the associated eigenfunction.
No associations
LandOfFree
On the spectrum of two quantum layers coupled by a window does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the spectrum of two quantum layers coupled by a window, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the spectrum of two quantum layers coupled by a window will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-433164