Using the conventional Haberkorn approach, it is evaluated the recombination of the radical pair (RP) singlet spin state to study theoretically the cytoprotective effect of an extremely-low-frequency electromagnetic field (ELF-EMF) on early stages of hepatic cancer chemically induced in rats. The proposal is that ELF-EMF modulates the interconversion rate of singlet and triplet spin states of the RP populations modifying the products from the metabolization of carcinogens. Previously, we found that the daily treatment with ELF-EMF 120 Hz inhibited the number and area of preneoplastic lesions in chemical carcinogenesis. The singlet spin population is evaluated diagonalizing the spin density matrix through the Lanczos method in a radical pair mechanism (RPM). Using four values of the interchange energy, we have studied the variations over the singlet population. The low magnetic field effect as a test of the influence over the enzymatic chemical reaction is evaluated calculating the quantum yield. Through a bootstrap technique the range is found for the singlet decay rate for the process. Applying the quantum measurements concept, we addressed the impact toward hepatic cells. The result contributes to improving our understanding of the chemical carcinogenesis process affected by charged particles that damage the DNA.

In this article we argue that the state-vector phase-space representation recently proposed by Torres-Vega and co-workers ͓introduced in J. Chem. Phys. 98, 3103 ͑1993͔͒ coincides with the totality of coherent-state representations for the Heisenberg-Weyl group. This fact leads to ambiguities when one wants to solve the stationary Schrödinger equation in phase space and we devise two schemes for the removal of these ambiguities. The physical interpretation of the phase-space wave functions is discussed and a procedure for computing expectation values as integrals over phase space is presented. Our formal points are illustrated by two examples. © 1997 American Institute of Physics. ͓S0021-9606͑97͒02317-9͔

We introduce a marginal picture of the evolution of quantum systems, in which the representation vectors are the quantities that evolve and operators and wave packets remain static. The representation vectors can be seen as probe functions that are the evolution of a ␦ function with initial support on q = X in coordinate space. This picture of the dynamics is suited for the determination of intrinsic arrival distributions for quantum systems, providing a clear physical meaning to the "time eigenstates" used in these calculations. We also analyze Galapon et al.'s "confined time eigenstates" ͓Phys. Rev. Lett. 93, 180406 ͑2004͔͒ from this point of view, and propose alternative probe functions for confined systems without the need of a quantized time.

We study translations in quantum mechanics for the case of a point spectrum, including translations by non-allowed amounts. We find that we obtain a copy of the original interval if we want to move to the outside of it, or to a mixture of states when moving to non-spectrum values (i.e., an interpolation eigenfunction). These results will clarify the meaning of the Pauli statement about the existence of a time operator in quantum mechanics.

Contrary to the conviction expressed by J. Kijowski [Phys. Rev. A 59, 897 (1999)] and shared in some other papers, the reasons to look for the 'time operator' in the context of the standard quantum doctrine of orthogonal projectors and self-adjoint observables are highly questionable. Some improved solutions in terms of POV measures invite critical discussions as well. This paper appeared as Concepts of Physics 2, 81 (2005).