Spectral asymptotics of a strong ${\delta }^{\prime }$ interaction supported by a surface

Abstract

We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive ${\delta }^{\prime }$ interaction supported by a smooth surface in ${\mathbb{R}}^3$, either infinite and asymptotically planar, or compact and closed. Its second term is found to be determined by a Schrödinger type operator with an effective potential expressed in terms of the interaction support curvatures.

13 pages, no figures

References in corpus (4)

• Schrödinger operators with delta and delta'-potentials supported on hypersurfaces
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Cited by in corpus (6)

• Dirac operators with Lorentz scalar shell interactions
• Spectral asymptotics for ${\delta }^{\prime }$ interaction supported by a infinite curve
• On eigenvalue asymptotics for strong delta-interactions supported by surfaces with boundaries
• On absence of bound states for weakly attractive ${\delta }^{\prime }$-interactions supported on non-closed curves in ${\mathbb{R}}^2$
• 2D Schrödinger operators with singular potentials concentrated near curves
• Singular Schrödinger operators and Robin billiards. Spectral properties and asymptotic expansions