Vol. 7, No. 4 (1949)
1949, 13 (4): 1-23. doi: 10.7498/aps.7.1
Wang's generalization of Bethe's theory of snperlattices is applied to the cases of quadratic and simple cubic lattice. Only neighbour interaction is taken into consideration. All the calculations are carried out to the second approximation.The variation of the critical temperature with composition is calculated. The degree of order, the energy and the specific heat are calculated for the special case of equal numbers of A and B atoms at various temperatures. It is found that the results differ very little from those obtained by Bethe in the second approximation. In the case of the simple cubic lattice the discontinuity of the specific heat is found to be only slightly larger than that obtained by Bethe.
The density of heavy water has been determined between 25° and 100℃. Using the known data below 25°, we are able to construct a density table for heavy water between its freezing and boiling points with an accuracy of five units in the fifth decimal place. Figures are given to show the density difference between heavy water and ordinary water and also their density ratio, which tends to pass over a maximum at a temperature not far above the boiling point.
1949, 13 (4): 35-42. doi: 10.7498/aps.7.35
The quantized energy values of an electron enclosed in a spherical box are calculated by solving Schrodinger's wave equation. The energy levels are very close together if the sphere is of ordinary dimensions. But as the radius of the sphere decreases toward atomic dimensions, the value of every energy level increases and the spread between the levels also increases.
1949, 13 (4): 43-51. doi: 10.7498/aps.7.43
This paper presents several considerations which are usually overlooked by designers of power oscillators. Effects of the shape of the path of operation upon the plate efficiency of the oscillators are discussed and methods of improving the plate efficiency are mentioned.
1949, 13 (4): 52-58. doi: 10.7498/aps.7.52
This paper presents a simple method by which the phase angle between the fundamental components of two non-sinusoidal waves can be measured. Applications of this method in an electron tube amplifier and oscillator arc discussed.
Weiss's theory on the change of Schr?dinger wave functional on a surface as the surface changes is given in a complete form, allowing the Lagrangian of the field to contain all derivatives of the field quantities. The integrability of the resulting equation is proved by making use of the fact that the corresponding Hamilton-Jacobi equation is integrable. This gives at the same time a proof of the Lorentz invariancy of the commutation relations between the various conjugate variables, which so far remained obscure as soon as we allow derivatives higher than the second of the field quantities to appear in the Lagrangian.
1949, 13 (4): 72-93. doi: 10.7498/aps.7.72
The hydrodynamic theory of viscous lubrication is studied from Navier-Stokes differential equations ,by the method of successive approximation based upon the smallness of the film thickness. It is found that the first approximation gives the Reynolds equation of viscous lubrication. To simplify the numerical nature of the solution of Reynolds equation, the equivalent variational problem is formulated. The approximate solution obtained from the variational problem involves only a very small error, but much less amount of numerical work.