Relativistic harmonic oscillator, the associated equations of motion, and algebraic integration methods

被引：19

作者：

Babusci, D. ^{[1
]}

Dattoli, G. ^{[2
]}

Quattromini, M. ^{[2
]}

Sabia, E. ^{[2
]}

机构：

[1] Ist Nazl Fis Nucl, Lab Nazl Frascati, IT-00044 Rome, Italy

[2] ENEA, Ctr Ric Frascati, IT-00044 Rome, Italy

来源：

PHYSICAL REVIEW E | 2013年 / 87卷 / 03期

关键词：

TWISS PARAMETERS; INVARIANT;

D O I：

10.1103/PhysRevE.87.033202

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique is used to solve the associated Liouville equations, yielding the phase-space evolution of an ensemble of relativistic particles, subject to a "harmonic" potential. The nonharmonic distortion of the spatial and momentum distributions due to the intrinsic nonlinear nature of the relativistic contributions is discussed. We analyze the relativistic dynamics induced by two types of Hamiltonian, which can be ascribed to those of harmonic oscillator type. Finally, we briefly discuss the quantum aspects of the problem by considering possible strategies for the solution of the associated Salpeter equation. DOI: 10.1103/PhysRevE.87.033202

引用

页数：7

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