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Schrödinger operators with $δ$-interactions supported on conical surfaces (1404.1764v1)
Published 7 Apr 2014 in math.SP, math-ph, and math.MP
Abstract: We investigate the spectral properties of self-adjoint Schr\"odinger 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 $[-\alpha2/4,+\infty)$ and that the discrete spectrum is infinite and accumulates to $-\alpha2/4$. Furthermore, an asymptotic estimate of these eigenvalues is obtained.