What Could Have We Been Missing While Pauli's Theorem Was in Force? *

Pauli’s theorem asserts that the canonical commutation relation [T,H] = iI only admits Hilbert space solutions that form a system of imprimitivities on the real line, so that only non-self-adjoint time operators exist in single Hilbert quantum mechanics. This, however, is contrary to the fact that there is a large class of solutions to [T, H] = iI, including self-adjoint time operator solutions for semibounded and discrete Hamiltonians. Consequently the theorem has brushed aside and downplayed the rest of the solution set of the time-energy canonical commutation relation.