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