Superintegrability and higher order integrals for quantum systems
| dc.contributor.author | Kalnins, Ernie G. | |
| dc.contributor.author | Kress, Jonathan M. | |
| dc.contributor.author | Miller, W., Jr. | |
| dc.date.accessioned | 2010-06-28T03:07:42Z | |
| dc.date.available | 2010-06-28T03:07:42Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | We refine a method for finding a canonical form of symmetry operators of arbitrary order for the Schrödinger eigenvalue equation HΨ ≡ (Δ2 + V)Ψ = EΨ on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal coordinate system. The flat space equations with potentials V = α(x + iy)k − 1/(x − iy)k + 1 in Cartesian coordinates, and V = αr² + β/r²cos ²kθ + γ/r²sin ²kθ (the Tremblay, Turbiner and Winternitz system) in polar coordinates, have each been shown to be classically superintegrable for all rational numbers k. We apply the canonical operator method to give a constructive proof that each of these systems is also quantum superintegrable for all rational k. We develop the classical analog of the quantum canonical form for a symmetry. It is clear that our methods will generalize to other Hamiltonian systems. | en_NZ |
| dc.identifier.citation | Kalnins, E.G., Kress, J.M. & Miller, W., Jr. (2010). Superintegrability and higher order integrals for quantum systems. Journal of Physics A: Mathematical and Theoretical, 43(26), Art. No. 265205. | en_NZ |
| dc.identifier.doi | 10.1088/1751-8113/43/26/265205 | en_NZ |
| dc.identifier.uri | https://hdl.handle.net/10289/4050 | |
| dc.language.iso | en | |
| dc.relation.uri | http://iopscience.iop.org/1751-8121/43/26/265205 | en_NZ |
| dc.subject | mathematics | en_NZ |
| dc.subject | Schrödinger eigenvalue equation | en_NZ |
| dc.title | Superintegrability and higher order integrals for quantum systems | en_NZ |
| dc.type | Journal Article | en_NZ |
Files
License bundle
1 - 1 of 1
No Thumbnail Available
- Name:
- license.txt
- Size:
- 1.71 KB
- Format:
- Item-specific license agreed upon to submission
- Description: