Causality and dispersion relations in wave mechanics

D. H. Delphenich

Louis de Broglie, Arthur J. Knodel, Jack C. Miller

H. M. Nussenzveig

T. Mátrai

P Marquardt, G. Galeczki

ynamical wave theory instead of the space-time invariant r from special relativity. Now the waves can be understood in terms of action, which traces the origin of particle motion to the potential, in line with physical causality. Key Words: Action, Wave Mechanics, Special Relativity, Dispersion Relations, Wave Propagation, Bound Systems, Quantization 1. Minimal action in bound systems 1.1. Action variables According to the opinion now prevailing, quantum mechanics originated with the hypothesis, made by Planck in 1900: E h = n (1) Planck stipulated that emission and absorption of electromagnetic radiation occurs in discrete quanta of energy E given by the frequency of the radiation, n , multiplied by a universal constant h with the dimensions of action. This was in line with Poincar's picture of the atom as providing the "vestibule" for the quantization of (free) radiation (Poincar 1924). It was, however, a less radical assumption than Einstein's dictum (in colorful south Germ

Partha Pratim Banerjee, Georges T. Nehmetallah, Rola Aylo +1 more

In this work we theoretically model continuous and pulse wave propagation using the underlying dispersion relations. We also derive the dispersion relations of the underlying wave equations based on the real and imaginary parts of the propagation constant which are related through Hilbert transformation to ensure causality. Also, in this paper we show that by using a model of photorefractive two wave coupling, we can derive the dispersion relation for pulsed propagation and coupling in a diffusion dominated photorefractive material. We note that the dispersion relation we have found in photorefractive material also obeys the Hilbert transform property. Finally, we show that the group velocity of light can be slowed down by means of phase coupling in the photorefractive two-wave mixing process.