Quantum Momentum Distributions

MANFRED L. RISTIG, J. W. Clark

В. А. Головко

The hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system obtained earlier by the author is investigated in the momentum representation. In the paper it is shown that the use of the momentum representation opens up new opportunities in studies of macroscopic quantum systems both nonsuperfluid and superfluid. It is found that the distribution over momenta in a quantum fluid is not a Bose or Fermi distribution even in the limit of practically noninteracting particles. The distribution looks like a Maxwellian one although, strictly speaking, it is not Maxwellian. The momentum distribution in a quantum crystal depends upon the interaction potential and the crystalline structure. The momentum distribution in a superfluid contains a delta function. The momentum distribution for the condensate in a superfluid crystal consists of delta peaks that are arranged periodically in momentum space. The periodical structure remains if the condensate crystal is not superfluid.

Eliade N. Stefanescu

Henri H. Arsenault, Pascuala Garcı́a-Martı́nez

Diffraction mathematical theory of light can be derived from Quantum Mechanics and Relativity. Using the duality between position and momentum variables, we show that the momentum distribution of light coincides with the well-known angular spectrum distribution. The momentum distribution links quantum theory and relativity to classical diffraction theory. We also show that the Huygens Principle and the momentum distribution are conjugate expressions at the diffraction aperture. These considerations lead to the geometrical theory of diffraction.

Paul E. Sokol, Richard N. Silver, J. W. Clark

Henri H. Arsenault, Pascuala Garcı́a-Martı́nez

Diffraction properties of light can be derived from Quantum Mechanics and Relativity. Using the fact that position and momentum are conjugate variables, we show that the momentum distribution of light coincides with the well-known angular spectrum distribution. The momentum distribution links quantum theory and relativity to classical diffraction theory. We also show that the Huygens Principle and the momentum distribution are conjugate expressions at the diffraction aperture. These considerations lead to the geometrical theory of diffraction.