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Quantum devices based on Josephson effect in superconductors are usuallydescribed by a Hamiltonian obtained by commonly used canonical quantization.However, this recipe has not been yet rigorously justified. We show that thisapproach is indeed correct in certain range of parameters. We find thecondition of the validity of such quantization and the lowest corrections tothe Josephson energy.

Justification of the canonical quantization of the Josephson effect