On Some Difficulties Concerning Heisenberg Uncertainty and Quantum Mechanical Relations

Román Ingarden

Jascha Zander, Roman Schnabel

Reinhard Honegger

Abstract Realizing the canonical commutation relations (CCR) [N, Θ] = - i as N = - i d/dϑ and Θ to be the multiplication by ϑ on the Hilbert space of square integrable functions on [0, 2π], in the physical literature there seems to be some contradictions concerning the Heisenberg uncertainty principle ⟨ΔN⟨ ⟨ΔΘ⟨ ≥ 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 {i t N} and exp{i sΘ} 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.

P. Marmet

Rodolfo A. Frino

The present paper is concerned with the derivation of the Einstein's formula of equivalence of mass and energy, E = mc^2, from the Heisenberg uncertainty relations. Thus, this paper unifies two of the most important laws of physics as provides the proof of the quantum mechanical nature of the above famous formula.

D. A. Trifonov