Noncovariant Lagrangians Are Presented Which Yield Two-Component Equations of Motion for a Class of Relativistic Mechanical Systems in 1 + 1 Dimensions Including the Harmonic Oscillator

• 作者: Robert L. Anderson
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Harmonic Oscillator
• 年，卷（期）: 2020,（9）
• 页码范围: 917-921
• 页数: 5页
• 分类号: O17

摘要

First, a Lagrangian is presented and authenticated for a Relativistic Harmonic Oscillator in 1 + 1 dimensions. It yields a two-component set of equations of motion. The time-component is the missing piece in all previous discussions of this system! The second result is that this Oscillator Langrangian generalizes to Langrangians for a class of particles in 1 + 1 dimensions subject to an arbitrary potential <em>V</em> which is space dependent only.