Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

Lasers - An effective artificial source of radiation for the cultivation of anoxygenic photosynthetic bacteria

The laser diode (LD) is a unique light source that can efficiently produce all radiant energy within the narrow wavelength range used most effectively by a photosynthetic microorganism. We have investigated the use of a single type of LID for the cultivation of the well-studied anoxygenic photosynthetic bacterium, Rhodobacter capsulatus (Rb. capsulatus). An array of vertical-cavity surface-emitting lasers (VCSELs) was driven with a current of 25 mA, and delivered radiation at 860 nm with 0.4 nm linewidth. The emitted light was found to be a suitable source of radiant energy for the cultivation of Rb. capsulatus. The dependence of growth rate on incident irradiance was quantified. Despite the unusual nearly monochromatic light source used in these experiments, no significant changes in the pigment composition and in the distribution of bacteriochlorophyll between LHII and LHI-RC were detected in bacterial cells transferred from incandescent light to laser light. We were also able to show that to achieve a given growth rate in a light-limited culture, the VCSEL required only 30% of the electricity needed by an incandescent bulb, which is of great significance for the potential use of laser-devices in biotechnological applications and photobioreactor construction. (c) 2006 Wiley Periodicals, Inc.