Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator

Details Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator

2006-11-06

arxiv.org/abs/quant-ph/0611062v1

Am. J. Phys. 75, 208 (2007)

Physics

Quantum Physics

9 pages, 3 figures; to appear in Am. J. Phys

Scientific paper

10.1119/1.2402157

The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic oscillator with incommensurate frequencies and the isotropic oscillator to the case with commensurate frequencies for which the Lissajous curves appear as classical periodic orbits. Because of the three different scenarios depending on the ratio of its frequencies, the two-dimensional harmonic oscillator offers a unique way to explicitly analyze the role of symmetries in classical and quantum mechanics.

Affiliated with

Also associated with

No associations

Rating

Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-297725