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Calculations of the phonon dispersion relations and specific heats for two transition metals are made using Krebs approach, in which the dynamical matrix is split into a closed-shell part and an ionic part. The ionic contribution to the elements of the dynamical matrix is calculated from a screened Coulomb interaction of the metal ions embedded in the sea of Bloch electrons. Computed vibration frequencies from this approach are periodic in the reciprocal space. The phonon dispersion relations along the [0001], [01–10] and [11–20] symmetry directions for yttrium and hafnium are computed. These and the calculated specific heats compare well with the experimental results.

In this paper, we discuss the quantum Kaluza-Klein cosmological model in the Vilenkin theory, and give the corresponding tunnelling wave function.

The motion of singularities in the classical Yang-Mills field is derived from the field equations of general relativity. It is pointed out that in Yang-Mills field by itself does not determine the motion of its sources in spite of its being a nonlinear theory.

We use the relativistic 2-body Dirac Hamiltonian with a square-well vector interaction, to investigate how the finite mass of the source of the external field changes the behavior of the bound-state spectrum from that of one Dirac particle in an attractive square well. Limiting ourselves for simplicity to states of total spin zero, we find that, as long as the massm 2 of the heavier particle is smaller than some critical massm c, the total energyE of the system does not reach the particle-antiparticle continuum, so that no difficulty of interpretation arises. If, however,m 2 is greater thanm c, there exists, as in the one-body Dirac equation, one value of the coupling strengthV c for whichE reaches the antiparticle continuum. Then, when the coupling strength exceedsV c, the bound-state level disappears. Furthermore, for some coupling strengthV>V c, there is a 2-particle bound-state level emerging from the particle-antiparticle continuum, whose total energyE increases until it reaches the particle-particle continuum. This latter result shows that, form 2>m c, a 2-body analysis actually further complicates the interpretation of deep bound states in relativistic quantum mechanics.

The cocoon model for X sources is examined. It is shown that inverse Compton scattering of relativistic electrons which are emitted from the central pulsar causes an appreciable flux of gamma radiation emitted in the MeV range. The same electrons give, by collisions with the plasma, the energy necessary to mantain the X flux. The ratio of X to gamma luminosity, dependent only on the shape of the electron spectrum, is computed for both power law and monochromatic spectra. The results are consistent with the gamma observations from the Cygnus region.

The problem of divergences associated with point particles in electrodynamics is overcome by associating an extreme probability density for their smallest radial extent. Infinite self-energies leading to an infinite displacement of spectral lines are thereby avoided. Dynamic equilibrium selects out a particular frequency rather than a sum over an infinite number leading to logarithmic divergences. Stochastic processes associated with the classical Bohr theory, together with his quantum conditions, are sufficient to derive the Lamb shift and the magnetic moment of electron spin caused by irregular circular fluctuations (Zitterbewegung) of an electron.

This work reports measurements of the differences of potential ΔV that are generated in crystals of NaCl subjected to unidirectional compression for loads such as to remain within the limits of validity of Hooke’s law and beyond them, and furthermore, the law of variation of ΔV with time, depending on the stresses applied to the crystal and the temperature.

In this paper conditions have been obtained for regular stationary reflection of a hydromagnetic shock on a rigid wall. Certain other theorems in the same connection have also been derived.