Spectral Series of the Schrödinger Operator with Delta Potential at the Poles of Two- and Three-Dimensional Surfaces of Revolution

This article is devoted to the construction of spectral series of the Schrödinger operator with double delta potential of the form \(H=-(h^2/2)\Delta+\delta_{x_1}(x)+\delta_{x_2}(x)\) , \(x\in M\) , where \(x_j\) are the poles of 2- or 3-surface of revolution \(M\) , in the semiclassical limit as \(h\to 0\) . The operator is considered to be an arbitrary self-adjoint extension of the Laplace–Beltrami operator.