On Heisenberg's Uncertainty Principle and the CCR
نویسنده
چکیده
Realizing the canonical commutation relations (CCR) [N, 0] = — i as N = — i d/d9 and 0 to be the multiplication by 9 on the Hilbert space of square integrable functions on [0, 27t], in the physical literature there seems to be some contradictions concerning the Heisenberg uncertainty principle (AN) (A0) > 1/4. The difficulties may be overcome by a rigorous mathematical analysis of the domain of state vectors, for which Heisenberg's inequality is valid. It is shown that the exponentials exp {it N} and e x p { i s 0 } satisfy some commutation relations, which are not the Weyl relations. Finally, the present work aims at a better understanding of the phase and number operators in non-Fock representations.
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