China
Africa
Explore chapters and articles related to this topic
An Introductory Review of Quantum Mechanics
Published in Ramaswamy Jagannathan, Sameen Ahmed Khan, Quantum Mechanics of Charged Particle Beam Optics, 2019
Ramaswamy Jagannathan, Sameen Ahmed Khan
The first term gives the initial value of r→. The second term gives correctly the position at time t corresponding to the constant velocity c2pˆ→(0)/HˆD or c2p(0)/E(p). The last term indicates a complicated oscillatory motion with an extremely small amplitude ℏc/2E ~ ℏ/2mc and extremely high frequency 2E ~ ℏ/2mc2/ℏ. This rapid oscillation is called Zitterbewegung (German word meaning trembling motion). The amplitude of this oscillation is ~ h/mc, the Compton wavelength of the electron, and hence it is meaningless to specify the position of an electron to an accuracy less than its Compton wavelength.
Photonic realization of the deformed Dirac equation via the segmented graphene nanoribbons under inhomogeneous strain
Published in Journal of Modern Optics, 2019
M. R. Setare, P. Majari, C. Noh, Sh. Dehdashti
In this work, we propose a 1D periodic array of coupled waveguides in which separations between the waveguides are controlled in order to simulate deformed Dirac equation. We first construct the deformed relativistic wave equation making use of deformed Lie algebras. This deformation plays the role of nonlinearities in our model. We then discuss Zitterbewegung (ZB), an extremely fast oscillation of relativistic particles. We compare the ZB effect in the deformed model against the original one, showing that the amplitude and frequency change with the deformation parameter. The paper is organized as follows. In Section 2, we introduce segmented graphene nanoribbons under strain which provides an experimental tool to realize a generalized Dirac equation. We then show how the same model arises in engineered photonic waveguides in Section 3, and study the ZB in the deformed scenario in Section 4. We conclude in Section 5.