A new method is developed for treating atoms and molecules in a magnetic field in a gauge-invariant way using the Rayleigh-Ritz energy variational principle. The energy operator depends on the vector potential which must be chosen in some gauge. In order to adapt the trial wave function to the gauge of the vector potential, the trial wave function can be multiplied by a phase factor which depends on the spatial coordinates. When the energy expectation value is minimized with respect to the phase function, the equation for charge conservation for stationary states is obtained. This equation can be solved for the phase function, and the solution used in the energy expectation value to obtain a gauge-invariant energy. The method is applicable to all quantum mechanical systems for which the variational principle can be applied. It ensures satisfaction of the charge conservation condition, a gauge-invariant energy, and the best upper bound to the ground-state energy which can be obtained for the form of trial wave function chosen.

A 10.6 ym C02 laser operating a power range S P 200 watts was used to pump some select vibrational transitions in the NO2 molecule while monitoring the rotational transitions (91/9—'100/10), (232f 22 ~~"*242,23> ' (402,38 "393,37) in the (0, 0, 0) vibrational level and the (8q,8—*"^1,7) rotational transition in the (0, 1, 0) vibrational level. These rotational transitions were monitored by microwave probing to determine how the population of states in the rotational manifolds were being altered by the laser. Coincidences between some components of the V3-V2 band of N02 and the C02 infrared laser lines in the 10 um region appeared to be responsible for the strong interaction between the continuous laser beams and the molecular states.

We present a comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments. Signals in both the probe and conjugate directions are discussed. The effects of recombination, non-radiative scattering and spatial and orientational diffusion are included. The analysis is applied to both a molecular and to a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. The theory is used to explain our recent observations in germanium. Included are discussions of picosecond transient grating self-diffraction measurements that can be understood in terms of an orientational grating produced by anisotropic (in k-space) state-filling. Though there have been predictions and indirect experimental evidence for isotropic state-filling in germanium, this is the first direct experimental indication of anisotropic state-filling in a semiconductor.