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We prove explicitly that to every discrete, semibounded Hamiltonian withconstant degeneracy and with finite sum of the squares of the reciprocal of itseigenvalues and whose eigenvectors span the entire Hilbert space there exists acharacteristic self-adjoint time operator which is canonically conjugate to theHamiltonian in a dense subspace of the Hilbert space. Moreover, we show thateach characteristic time operator generates an uncountable class of self-adjoint operators canonically conjugate with the same Hamiltonian in the samedense subspace.Comment: accepted for publication in the Proceedings of the Royal Society of  London

Self–adjoint time operator is the rule for discrete semi–bounded Hamiltonians