Schrödinger operators with $\delta$-interactions supported on conical surfaces

Abstract

We investigate the spectral properties of self-adjoint Schrödinger operators with attractive $\delta$-interactions of constant strength $\alpha >0$ supported on conical surfaces in ${\mathbb{R}}^3$. It is shown that the essential spectrum is given by $[-{\alpha }^2/4,+\infty )$ and that the discrete spectrum is infinite and accumulates to $-{\alpha }^2/4$. Furthermore, an asymptotic estimate of these eigenvalues is obtained.

References in corpus (2)

• Schrödinger operators with delta and delta'-potentials supported on hypersurfaces
• A class of rotationally symmetric quantum layers of dimension 4