This year marks the 50th anniversary of the birth of the celebrated Wigner distribution function. Many advances made in various areas of science during the 50 year period can be attributed to the physical insights that the Wigner distribution function provides when applied to specific problems. In this paper the usefulness of the Wigner distribution function in collision theory is described.

Trajectories along which phase-space points of the Wigner distribution function move are computed for a Gaussian wave packet moving under the influence of a weak perturbative potential. The potentials considered are a potential step, a potential barrier, and a periodic potential. Trajectories computed exhibit the complex, nonlocal nature of quantum dynamics. It is seen that quantum interference, which takes place in the time development of the wave packet, is taken care of in a simple way by the Wigner trajectory method (...) presented here. (shrink)

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief (...) that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed. (shrink)