On Quasi-Exact Solvability of the Schrödinger Equation for a Free Particle on the Surface of a Spindle Torus
- 86 Downloads
We show that the Schrödinger equation for a free particle on the surface of a spindle torus is quasi-exactly solvable. Our result complements former ones in an interesting way: it is known that the Schrödinger equation for a free particle on a ring torus is non-solvable, whereas it is exactly solvable for a particle on a horn torus.
Key words:Schrödinger equation quasi-exact solvability free particle spindle torus
Unable to display preview. Download preview PDF.
- 2.2. M. Encinosa and F. Sales-Mayor, “Bohmian trajectories on a toroidal surface,” quant-ph/0304047y.Google Scholar
- 7.7. T. S. McGrath, “Axial atomic model for determination of elemental particle field structure and energy levels,” United States patent application 9 #20040082074, kind code A1 (2003).Google Scholar
- 8.8. S. Midgley and J. B. Wang, “Time-dependent quantum waveguide theory: a study of nano ring structures,” Aus. J. Phys. 53, no. 1, 77–85 (2000).Google Scholar
- 10.10. A. Schulze-Halberg, “Non-existence of liouvillian solutions for a free quantum particle on a torus surface, part 1: polar states,” to appear in Found. Phys. Lett. (2004).Google Scholar