Publication: New quasi-exactly solvable hamiltonians in 2 dimensions
Loading...
Official URL
Full text at PDC
Publication Date
1994-01
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Citations
Exportar
Abstract
Quasi-exactly solvable Schrodinger operators have the remarkable property that a part of their spectrum can be computed by algebraic methods. Such operators lie in the enveloping algebra of a finite-dimensional Lie algebra of first order differential operators-the" hidden symmetry algebra. "In this paper we develop some general techniques for constructing quasi-exactly solvable operators. Our methods are applied to provide a wide variety of new explicit two-dimensional examples (on both flat and curved spaces) of quasi-exactly solvable Hamiltonians, corresponding to both semisimple and more general classes of Lie algebras.
Description
© Springer
UCM subjects
Unesco subjects
Keywords
Citation
1.Alhassid, Y., Engel, J., Wu, J.: Algebraic approach to the scattering matrix. Phys. Rev. Lett.53, 17–20 (1984)View Article.
2. Alhassid, Y., Gürsey, F., Iachello, F.: Group theory approach to scattering. Ann. Phys.148, 346–380 (1983)View Article
3. Alhassid, Y., Gürsey, F., Iachello, F.: Group theory approach to scattering. II. The Euclidean connection. Ann. Phys.167, 181–200 (1986)
4. Balazs, N.L., Voros, A.: Chaos on the pseudosphere. Phys. Rep.143, 109–240 (1986)View Article
5. Cotton, É.: Sur les invariants différentiels de quelques équations linéaires aux dérivées partielles du second ordre. Ann. École Norm.17, 211–244 (1900)
6. González-López, A., Kamran, N., Olver, P.J.: Lie algebras of differential operators in two complex variables. Am. J. Math.114, 1163– 1185 (1992)
7. González-López, A., Kamran, N., Olver, P.J.: Quasi-exactly solvable Lie algebras of first order differential operators in two complex variables. J. Phys.A 24, 3995–4008 (1991)View Article
8. Gorsky, A.: Relationship between exactly solvable and quasi-exactly solvable versions of quantum mechanics with conformal block equations in 2D theories. JETP Lett.54, 289– 292 (1991)
9. Kamran, N., Olver, P.J.: Equivalence of differential operators. SIAM J. Math. Anal.20, 1172–1185 (1989)View Article
10. Kamran, N., Olver, P.J.: Lie algebras of differential operators and Lie-algebraic potentials. J. Math. Anal. Appl.145, 342–356 (1990)View Article
11. Losev, A., Turbiner, A.: Multidimensional exactly solvable problems in quantum mechanics and pullbacks of affine co-ordinates on the Grassmannian. Int. J. Mod. Phys.A7, 1449–1466 (1992)View Article
12. Levine, R.D.: Lie-algebraic approach to molecular structure and dynamics. In: Mathematical Frontiers in Computational Chemical Physics. Truhlar D.G. (ed.) IMA Volumes in Mathematics and its Applications, Vol.15, Berlin, Heidelberg, New York: Springer 1988, pp. 245–261
13. Miller, Jr., W.: Lie Theory and Special Functions. New York: Academic Press 1968
14. Morozov, A.Y., Perelomov, A.M., Rosly, A.A., Shifman, M.A., Turbiner, A.V.: Quasi-exactly solvable quantal problems: One-dimensional analogue of rational conformal field theories. Int. J. Mod. Phys.A5, 803–832 (1990)View Article
15. Shifman, M.A.: New findings in quantum mechanics (partial algebraization of the spectral problem). Int. J. Mod. Phys.A4, 2897–2952 (1989)View Article
16. Shifman, M.A.: Quasi-exactly solvable spectral problems and conformal field theory. Contemp. Math., to appear
17. Shifman, M.A., Turbiner, A.V.: Quantal problems with partial algebraization of the spectrum. Commun. Math. Phys.126, 347–365 (1989)View Article
17. Turbiner, A.V.: Quasi-exactly solvable problems andsl(2) algebra. Commun. Math. Phys.118, 467–474 (1988)View Article
18. Turbiner, A.V.: On polynomial solutions of differential equations. J. Math. Physics33, 3989–3993 (1992)View Article
19. Turbiner, A.V.: Personal communication
20. Ushveridze, A.G.: Quasi-exactly solvable models in quantum mechanics. Sov. J. Part. Nucl.20, 504–528 (1989)