Author(s)

Yair Zarmi

Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion, Israel.

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.

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

Zarmi, Y. (2023) On the Relativistic Harmonic Oscillator. Applied Mathematics, 14, 1-20. doi: 10.4236/am.2023.141001.