Bound states due to a strong $δ$ interaction supported by a curved surface

Details Bound states due to a strong $δ$ interaction supported by a curved surface Bound states due to a strong $δ$ interaction supported by a curved surface

2002-07-19

arxiv.org/abs/math-ph/0207025v2

J. Phys. A36 (2003), 443-457

Physics

Mathematical Physics

LaTeX 2e, 21 pages

Scientific paper

10.1088/0305-4470/36/2/311

We study the Schr\"odinger operator $-\Delta -\alpha \delta (x-\Gamma)$ in $L^2(\R^3)$ with a $\delta$ interaction supported by an infinite non-planar surface $\Gamma$ which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if $\Gamma $ is asymptotically planar in a suitable sense and $\alpha>0$ is sufficiently large this operator has a non-empty discrete spectrum and derive an asymptotic expansion of the eigenvalues in terms of a ``two-dimensional'' comparison operator determined by the geometry of the surface $\Gamma$. [A revised version, to appear in J. Phys. A]

Affiliated with

Also associated with

No associations

Rating

Bound states due to a strong $δ$ interaction supported by a curved surface 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 Bound states due to a strong $δ$ interaction supported by a curved surface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bound states due to a strong $δ$ interaction supported by a curved surface will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-397442