Periodic nodal surfaces

Mathematical approximations to the periodic minimal surfaces can be constructed from terms which are each the result of adding symmetry-related sinusoidal density waves for the appropriate symmetry group, and then taking the nodal surface the boundary between regions of positive and of negative density. The waves that correspond to a face-centred figure in real space are the body-centred terms in reciprocal space, namely ... 

DPMS, PMS, PCS, PNS All abbreviations for periodic hyperbolic surfaces infinite periodic minimal surfaces, periodic minimal surfaces, periodic cubic surfaces and periodic nodal surfaces respectively. (The abbreviations P-, D-and G- prepended to these indicate the topology and symmetry of the periodic surface, corresponding to the relative tuimel arangements and black-white sub-group of the P-surface, the D-surface and the gyroid respectively. 

Interpreted in terms of the symmetrical form of the periodic table (Fig. 3), the quantum numbers that define the radial distances of r = n a specify the nodal surfaces of spherical waves that define the electronic shell structure. Knowing the number of electrons in each shell, the density at the crests of the spherical waves that represent periodic shells, i.e., at 1.5,3, etc. (a), can be calculated. This density distribution, shown in Fig. 7, decreases exponentially with Z and, like the TF central-field potential, is valid for all atoms and also requires characteristic scale factors to generate the density functions for specific atoms. The Bohr-Schrodinger... 

However, in terms of the known periodic structure, the Bohr interpretation cannot apply. In order to generate the periodic table, it is necessary to interpret the extremum condition as satisfied by the nodal surfaces of the spherical electron wave, as shown in Fig. 2. The detailed periodic structure, together with subshell... 

The standing wave has nodal and antinodal planes of intensity parallel to the mirror surface, the period of which is a function of the angle of incidence, 0. On increasing 8 from 0 to 0C, the period between the antinodes decreases... 

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