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Grossert, C., Leder, M. and Weitz, M. (2016) Phase Dependent Loading of Bloch Bands and Quantum Simulation of Relativistic Wave Equation Predictions with Ultracold Atoms in Variably Shaped Optical Lattice Potentials. Journal of Modern Optics, 63, 1805-1813.
https://doi.org/10.1080/09500340.2015.1137370

has been cited by the following article:

• TITLE: On the Relativistic Harmonic Oscillator

  AUTHORS: Yair Zarmi

  KEYWORDS: Relativistic Harmonic Oscillator, Weak-Relativistic Limit, Extreme-Relativistic Limit

  JOURNAL NAME: Applied Mathematics, Vol.14 No.1, January 10, 2023

  ABSTRACT: The relativistic harmonic oscillator represents a unique energy-conserving oscillatory system. The detailed characteristics of the solution of this oscillator are displayed in both weak- and extreme-relativistic limits using different expansion procedures, for each limit. In the weak-relativistic limit, a Normal Form expansion is developed, which yields an approximation to the solution that is significantly better than in traditional asymptotic expansion procedures. In the extreme-relativistic limit, an expansion of the solution in terms of a small parameter that measures the proximity to the limit (v/c) → 1 yields an excellent approximation for the solution throughout the whole period of oscillations. The variation of the coefficients of the Fourier expansion of the solution from the weak- to the extreme-relativistic limits is displayed.