Abstract
We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators in ℝ2. Furthermore, we find all algebras which are quasi-exactly solvable, along with the associated finite-dimensional modules of analytic functions. The resulting real Lie algebras are used to construct new quasi-exactly solvable Schrödinger operators on ℝ2.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1165-1193 |
| Number of pages | 29 |
| Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 354 |
| Issue number | 1710 |
| DOIs | |
| State | Published - May 15 1996 |
Fingerprint
Dive into the research topics of 'Real Lie algebras of differential operators and quasi-exactly solvable potentials'. Together they form a unique fingerprint.Cite this
- APA
- Standard
- Harvard
- Vancouver
- Author
- BIBTEX
- RIS