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In this paper, the study of canonical quantization of a free real massivescalar field in the Schwarzschild spacetime is continued. The normalizationconstants for the eigenfunctions of the corresponding radial equation arecalculated, providing the necessary coefficients for the doubly degeneratescatteringlike states that are used in the expansion of the quantum field. Itis shown that one can pass to a new type of states such that the spectrum ofstates with energies larger than the mass of the field splits into two parts.The first part consists of states that resemble properly normalized plane wavesfar away from the black hole, so they just describe the theory for an observerlocated in that area. The second part consists of states that live relativelyclose to the horizon and whose wave functions decrease when one goes away fromthe black hole. The appearance of the second part of the spectrum, whichfollows from the initial degeneracy of the scatteringlike states, is aconsequence of the topological structure of the Schwarzschild spacetime.

Asymptotic behavior of solutions and spectrum of states in the quantum scalar field theory in the Schwarzschild spacetime