Note on the relativistic harmonic oscillator
โ Scribed by Louis Gold
- Publisher
- Elsevier Science
- Year
- 1957
- Tongue
- English
- Weight
- 148 KB
- Volume
- 264
- Category
- Article
- ISSN
- 0016-0032
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โฆ Synopsis
The relativistic harmonic oscillator is solved by an inverse fractional power series as has been done for the simple pendulum.
The striking similarity of these two kinds of non-linear motion is thus demonstrated. The entire analysis is amply dealt with, without resort to elliptic integrals.
๐ SIMILAR VOLUMES
Arguments have been given by Greenspan [1] to suggest that the equation of motion for a relativistic harmonic oscillator is (1)
The step operators of the two-dimensional isotropic harmonic oscillator are shown to be separable into the basis elements of two disjoint Heisenberg Lie algebras. This separability leads to two sets of irreducible tensors, each of which is based upon its associated underlying Heisenberg Lie algebra.
The recurrance relation method is employed to determine the dynamic structure factor for the single harmonic oscillator and a linear chain of harmonic oscillators. Approximative schemes based on this approach are proposed. Comparison is made with exactly known results.