ИСТИНА

We consider the spectral problem for the Schr\"odinger operator $$ H \psi = E \psi,\qquad H = -\frac{h^2}{2}\Delta + \delta_{x_1}(x) + \delta_{x_2} (x),\qquad x\in M, $$ where $-\Delta$ denotes the Laplace--Beltrami operator on a surface of revolution $M$, and $\delta_{x_j}$ represents the Dirac delta function centered at $x_j$, in the semiclassical limit as $h\to +0$. The operator $H$ is defined as a self-adjoint extension of the Laplace--Beltrami operator with extensions being parametrized by the unitary group. We obtain an explicit form of the quantization conditions, which allow one to establish the asymptotic behavior of the spectrum of $H$, and derive a representation for asymptotic eigenfunctions in terms of the Bessel and Neumann functions of zero order (two-dimensional case) or the Bessel functions of half-integer order (three-dimensional case). This representation offers a~comprehensive understanding of the structural characteristics and behavior of the eigenfunctions as $h\to +0$.