Schrödinger operators with δ-interactions supported on conical surfaces

We investigate the spectral properties of self-adjoint Schrödinger operators with attractive δ-interactions of constant strength \alpha \gt 0 supported on conical surfaces in {{{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 -{\mkern 1mu} {{\alpha }^{2}}/4. Furthermore, an asymptotic estimate of these eigenvalues is obtained.