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Fokas, A. S.; Lagerstrom, P. A.

On the use of Lie-Bäcklund operators in quantum mechanics. (English) Zbl 0439.70018

J. Math. Anal. Appl. 74, 342-358 (1980).
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Cited in 2 Documents

MSC:

70H05 Hamilton’s equations
76G25 General aerodynamics and subsonic flows
70H20 Hamilton-Jacobi equations in mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
22E70 Applications of Lie groups to the sciences; explicit representations
83C40 Gravitational energy and conservation laws; groups of motions

Keywords:

Lie-Bäcklund operators; quantum mechanics; cubic invariants; quadratic invariants; classical and quantum-mechanical invariants; symmetry; separation of variables; Hamilton-Jacobi equation; Schrödinger equation

Citations:

Zbl 0408.70013; Zbl 0432.70027
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Full Text: DOI

References:

[1] Fokas, A. S., Group theoretical aspects of constants of motion and separable solutions in classical mechanics, J. Math. Anal. Appl., 68, 347 (1979) · Zbl 0408.70013
[2] Fokas, A. S.; Lagerstrom, P. A., Quadratic and cubic invariants in classical mechanics, J. Math. Anal. Appl., 74, 325 (1980) · Zbl 0432.70027
[3] Fokas, A. S., Lie-Bäcklund Theory of Separation of Variables and Conservation Laws In Classical and Quantum Mechanics, (presented at the International Joint IUTAM-IMU Symposium, Group Theoretical Methods in Mechanics. presented at the International Joint IUTAM-IMU Symposium, Group Theoretical Methods in Mechanics, Novosibirsk, USSR (August 25-29, 1978)) · Zbl 0435.70016
[4] Makarov, A. A.; Smorodinsky, J. A.; Valiev, K. H.; Winternitz, P., Nuovo Cimento L, 11a, 1061 (1967)
[5] Weyl, H., The Theory of Groups and Quantum Mechanisc (1932), Dutton: Dutton New York, reprinted, Dover, New York, 1950
[6] de Groot, S. R.; Suttorp, L. G., Foundations of Electrodynamics (1972), North-Holland: North-Holland Amsterdam
[7] Smorodinsky, J. A.; Tugov, I. I., Soviet Physics JETP, 23, 434 (1966)
[8] Winternitz, P.; Smorodinsky, J. A.; Uhlir, M.; Fris, I., Soviet J. Nuclear Phys., 4, 444 (1967)
[9] Miller, W. J., Symmetry and Separation of Variables, (Encyclopedia of Mathematics and Its Applications (1977), Addison-Wesley: Addison-Wesley Reading, Mass) · Zbl 0368.35002
[10] Fokas, A. S., (Ph. D. thesis (1979), California Institute of Technology: California Institute of Technology Pasadena)
[11] Anderson, R. L.; Ibragimov, N. H., Lie-Bäcklund Transformations in Applications, SIAM Monograph (January 1979) · Zbl 0447.58001
[12] Hermann, R., Lie Groups for Physicists (1966), Benjamin: Benjamin New York · Zbl 0135.06901
[13] Dirac, P. A.M, The Principles of Quantum Mechanics (1935), Oxford Univ. Press: Oxford Univ. Press London-New York · Zbl 0012.18104
[14] Van Hove, L., Sur certaines représentations unitaires d’un groupe infini de transformations, Mém. Acad. Roy. Belg., 26 (1951) · Zbl 0045.38701
[15] Fronsdal, C., Some Ideas about Quantization (1977), preprint · Zbl 0418.58011
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