Zero-range potential model for the study of the ground states near the vortex core in the quantum limit

We propose the treatment of the lowest bound states near the vortex core on the basis of the self-adjoint extension of the Hamiltonian with the localized magnetic flux of Aaronov-Bohm type. It is shown that in the limit {\varkappa} >> 1 the potential for the vortex core excitations can be treated in terms of the generalized zero-range potential method. The spectrum of the Caroli-de Gennes-Matricon states is obtained and the comparison with the numerical calculations of Hayashi, N. et al. [Phys. Rev. Lett. 80, p. 2921 (1998)] is performed. The analytical expression for the ground state energy depending on the boundary condition parameter b was obtained by us.