Schrödinger operators with $δ$-interactions supported on conical surfaces

Abstract

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