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Springer eBooks

Wave Aspects of Matter

Walter Greiner

Published Jan 1, 1989• 0 citations
Publisher
DOI
10.1007/978-3-662-00707-5_3

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In this paper, we demonstrate the significance of Non-Einsteinian view of relativity in relation to wave model of particle and particle model of wave. To accommodate wave-particle dualism, we have considered de-Broglie’s matter wave concept and Compton Effect. The kinematics of the photon and the photon emitter particle (photon-gun) are taken into consideration. Then, we have correlated the motion related parameters of the gun with the characteristics of the photon. This provides a correlation between wave aspect of particle (matter wave) and particle aspect of wave.
A Bose–Einstein condensate with time varying scattering length in time-dependent harmonic trap is analytically investigated and soliton-like solutions of the Gross–Pitaeviskii equation are obtained to describe single soliton, bisoliton and N -soliton properties of the matter wave. The influences of the geometrical property and modulate frequency of trapping potential on soliton behaviour are discussed. When the trap potential has a very small trap aspect ratio or oscillates with a high frequency, the matter wave preserves its shape nearly like a soliton train in propagation, while the breathing behaviour, which displays the periodic collapse and revival of the matter wave, is found for a relatively large aspect ratio or slow varying potential. Meanwhile mass centre of the matter wave translates and/or oscillates for different trap aspect ratio and trap frequencies.
A Bose-Einstein condensate with time varying scattering length in time-dependent harmonic trap is analytically investigated and soliton-like solutions of the Gross-Pitaeviskii equation are obtained to describe single soliton, bisoliton and N-soliton properties of the matter wave. The influences of the geometrical property and modulate frequency of trapping potential on soliton behaviour are discussed. When the trap potential has a very sinall trap aspect ratio or oscillates with a high frequency, the matter wave preserves its shape nearly like a soliton train in propagation, while the breathing behaviour, which displays the periodic collapse and revival of the matter wave, is found for a relatively large aspect ratio or slow varying potential. Meanwhile mass centre of the matter wave translates and/or oscillates for different trap aspect ratio and trap frequencies.