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.