Given an ensemble of systems in an unknown state, as well as an observable $hat A$ and a physical apparatus which performs a measurement of $hat A$ on the ensemble, whose detailed working is unknown (black box), how can one test whether the Luders or von Neumann reduction rule applies?
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time distribution of a f
ree particle is generalized and extended. Interestingly, the resulting arrival time distribution operator is connected to a particular, positive, quantization of the classical current. For particles in a potential we also introduce and study the notion of conditional arrival-time distribution.
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion of possibl
e operators and their physical meaning. Criteria to define unique, optimal operators for specific cases are given.
Through tunneling, or barrier penetration, small wavefunction tails can enter a finitely shielded cylinder with a magnetic field inside. When the shielding increases to infinity the Lorentz force goes to zero together with these tails. However, it is
shown, by considering the radial derivative of the wavefunction on the cylinder surface, that a flux dependent force remains. This force explains in a natural way the Aharonov-Bohm effect in the idealized case of infinite shielding.
A natural approach to measure the time of arrival of an atom at a spatial region is to illuminate this region with a laser and detect the first fluorescence photons produced by the excitation of the atom and subsequent decay. We investigate the actua
l physical content of such a measurement in terms of atomic dynamical variables, taking into account the finite width of the laser beam. Different operation regimes are identified, in particular the ones in which the quantum current density may be obtained.
For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated region. T
he resulting temporal distribution is explicitly calculated for the one-dimensional case and compared with axiomatically proposed expressions. As a main result we show that by means of a deconvolution one obtains the well known quantum mechanical probability flux of the particle at the location as a limiting distribution.
