The Classical and Quantum Mechanics of a Particle on a Knot
| Autor: | Sreedhar, V. V. |
|---|---|
| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aop.2015.04.004 |
| Popis: | A free particle is constrained to move on a knot obtained by winding around a putative torus. The classical equations of motion for this system are solved in a closed form. The exact energy eigenspectrum, in the thin torus limit, is obtained by mapping the time-independent Schrodinger equation to the Mathieu equation. In the general case, the eigenvalue problem is described by the Hill equation. Finite-thickness corrections are incorporated perturbatively by truncating the Hill equation. Comparisons and contrasts between this problem and the well-studied problem of a particle on a circle (planar rigid rotor) are performed throughout. Comment: 9 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|