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We propose the treatment of the lowest bound states near the vortex core onthe basis of the self-adjoint extension of the Hamiltonian with the localizedmagnetic 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 ofthe generalized zero-range potential method. The spectrum of the Caroli-deGennes-Matricon states is obtained and the comparison with the numericalcalculations of Hayashi, N. et al. [Phys. Rev. Lett. 80, p. 2921 (1998)] isperformed. The analytical expression for the ground state energy depending onthe boundary condition parameter b was obtained by us.

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