Volume 18: Pages 196-206, 2005

The Nodal Structure of Standing Spherical Waves and the Periodic Law: What Do They Have in Common?

George P. Shpenkov

Institute of Mathematics and Physics, UTA, Kaliskiego 7, Bydgoszcz 85‐796 Poland

The dialectical symmetry of opposite properties is the fundamental law of the universe. The wave potential‐kinetic structure of all fields of matter‐space‐time is the manifestation of such a symmetry, which is described by the three‐dimensional wave equation. One of the particular solutions of the wave equation leads to sinusoidal spherical standing waves. Their nodal structure recalls the ordered elementary atomic structures. The quasi‐periodical shell‐nodal feature of standing waves reflects the periodic regularity inherent in atomic spaces. On this basis Mendeleev's periodic law gives and makes precise the new theoretical justification. The above points at issue, resulting in the clarification of the origin of the periodic law, are considered in this paper.

Keywords: imaginary numbers, complex numbers, dialectical symmetry, potential‐kinetic fields, wave‐function, spherical standing waves, wave equation, polar‐azimuth functions, nodes and antinodes, periodic law

Received: September 10, 2004; Published online: December 15, 2008