Moller operators and Lippmann-Schwinger equations for step-like potentials

The Moller operators and the asociated Lippman-Schwinger equations obtained from different partitionings of the Hamiltonian for a step-like potential barrier are worked out, compared and related.Comment: 15 pages, 1 inlined figure, iopart.cl

Sources of quantum waves

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the wave function in all space at a given instant. We compare this standard approach to "source boundary conditions'' that fix the wave at all times in a given region, in particular at a point in one dimension. In contrast to the well-known physical interpretation of the initial-value-problem approach, the interpretation of the source approach has remained unclear, since it introduces negative energy components, even for ``free motion'', and a time-dependent norm. This work provides physical meaning to the source method by finding the link with equivalent initial value problems.Comment: 12 pages, 7 inlined figures; typos correcte

A measurement-based approach to quantum arrival times

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. The 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.Comment: 11 pages, 4 figures, submitted to Phys. Rev.

Comment on "Measurement of time of arrival in quantum mechanics"

The analysis of the model quantum clocks proposed by Aharonov et al. [Phys. Rev. A 57 (1998) 4130 - quant-ph/9709031] requires considering evanescent components, previously ignored. We also clarify the meaning of the operational time of arrival distribution which had been investigated.Comment: 3 inlined figures; comment on quant-ph/970903

Transient response of a quantum wave to an instantaneous potential step switching

The transient response of a stationary state of a quantum particle in a step potential to an instantaneous change in the step height (a simplified model for a sudden bias switch in an electronic semiconductor device) is solved exactly by means of a semianalytical expression. The characteristic times for the transient process up to the new stationary state are identified. A comparison is made between the exact results and an approximate method.Comment: 8 pages, 8 figures, Revtex

Quantum times of arrival for multiparticle states

Using the concept of crossing state and the formalism of second quantization, we propose a prescription for computing the density of arrivals of particles for multiparticle states, both in the free and the interacting case. The densities thus computed are positive, covariant in time for time independent hamiltonians, normalized to the total number of arrivals, and related to the flux. We investigate the behaviour of this prescriptions for bosons and fermions, finding boson enhancement and fermion depletion of arrivals.Comment: 10 a4 pages, 5 inlined figure

Generalizations of Kijowski's time-of-arrival distribution for interaction potentials

Several proposals for a time-of-arrival distribution of ensembles of independent quantum particles subject to an external interaction potential are compared making use of the ``crossing state'' concept. It is shown that only one of them has the properties expected for a classical distribution in the classical limit. The comparison is illustrated numerically with a collision of a Gaussian wave packet with an opaque square barrier.Comment: 5 inlined figures: some typo correction

Atomic time-of-arrival measurements with a laser of finite beam width

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 actual 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.Comment: 7 figure