RELATIVISTIC (AN)HARMONIC OSCILLATOR

Authors
MOREAU W EASTHER R NEUTZE R
Citation
W. Moreau et al., RELATIVISTIC (AN)HARMONIC OSCILLATOR, American journal of physics, 62(6), 1994, pp. 531-535
Citations number
8
Categorie Soggetti
Physics
Journal title
American journal of physics → ACNP
ISSN journal
00029505
Volume
62
Issue
6
Year of publication
1994
Pages
531 - 535
Database
ISI
SICI code
0002-9505(1994)62:6<531:R(O>2.0.ZU;2-X
Abstract
The relativistic extension of one-dimensional simple harmonic motion i s developed in the Lagrangian formalism. The relativistic equations of motion are derived and solved analytically. The motion with respect t o proper time is analyzed in terms of an effective potential energy. W hile the motion remains bounded and periodic, the effect of time dilat ion along the world line is to cause it to become anharmonic with the period increasing with amplitude and the curvature concentrated at the turning points.