Quantum mechanics with difference operators

Reports on Mathematical Physics

Volumn 50, Issue 3, 2002, Pages 409-431

  Dobrev, V K ^a,b   Doebner, H D ^c   Twarock, R ^d  

^a INSTITUTE FOR NUCLEAR RESEARCH AND NUCLEAR ENERGY   (Bulgaria)

^b ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^c CLAUSTHAL UNIVERSITY OF TECHNOLOGY   (Germany)

^d CITY UNIVERSITY   (United Kingdom)

Author keywords

Discrete derivative; Nonlinear Schr dinger equation; q deformation; Witt algebra

Indexed keywords

EID: 0036980131     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(02)80069-6     Document Type: Review

References (26)

1. W. Heisenberg: The Physical Principles of Quantum Theory, 1930.
2. T. D. Palev: J. Math. Phys. 23 (1982), 1778.
3. T. D. Palev and N. I. Stoilova: J. Math. Phys. 38 (1997), 2506.
4. J. Wess: "q-deformed phase space and its lattice structure", in: H.-D. Doebner and V. K. Dobrev (eds.): Quantum Group Symposium at Group 21, Proc. of the Quantum Groups Symposium at the XXI International Colloquium on Group Theoretical Methods in Physics, Heron Press, Sofia, pp. 3-10 (1997).
5. B. L. Cerchiai and J. Wess: Eur Phys. J. C 5 (1998), 553-566,.
6. V. G. Drinfel'd, Quantum groups, in Proceedings of the International Congress of Mathematicians, Berkeley, California, USA, 1986, pp. 798-820, Academic Press, 1987.
7. V. K. Dobrev, H.-D. Doebner and C. Mrugalla: J. Phys. A29 (1996), 5909.
8. B. Angermann, H.-D. Doebner, and J. Tolar: Quantum Kinematics on Smooth Manifolds, Lect. Not. Math. vol. 1037, Springer, New York 1983.
9. H.-D. Doebner and J. Tolar: Ann. Phys. Leipzig 47 (1990), 116-122.
10. R. Dashen and D. H. Sharp: Phys. Rev. 165 (1968), 1867,.
11. G. A. Goldin and D. H. Sharp: Lie algebras of local currents and their representations, in: 1969 Battelle Rencontres: Group Representations, Lecture Notes in Physics 6, V. Bargmann, ed., Berlin 1970.
12. H.-D. Doebner and J. D. Hennig: A quantum mechanical evolution equation for mixed states from symmetry and kinematics, in Symmetries in Science VIII, B. Gruber ed., Plenum Publ., New York 1995.
13. H.-D. Doebner and G. A. Goldin: Phys. Lett. A162 (1992), 397-401.
14. H.-D. Doebner and G. Goldin: in Proceedings of the First German-Polish Symposium on Particles and Fields, p. 115, World Scientific, Singapore 1993.
15. H.-D. Doebner and G. A. Goldin: J. Phys. A27 (1994), 1771-1780.
16. V. K. Dobrev, H.-D. Doebner and R. Twarock: J. Phys. A30 (1997), 6841-6859.
17. 1 with q-Difference Operators, Ph.D. thesis, TU Clausthal 1997.
18. N. Aizawa and H. Sato: Phys. Lett. B256 (1991), 185.
19. M. Chaichian, A. P. Isaev, J. Lukierski, Z. Popowicz and P. Prešnajder: Phys. Lett. B262 (1991), 32.
20. C. H. Oh and K. Singh: J. Phys. 7 (1994), 3439.
21. R. Kemmoku and S. Saito: J. Phys. A29 (1996), 4141.
22. H. Sato: Z. f. Phys. C70 (1996), 349.
23. F. Jackson, On q-definite integrals, Quarterly journal of pure and applied mathematics, (1910), 193-203.
24. N. Aizawa, V. K. Dobrev and H.-D. Doebner, Intertwining operators for Schrödinger algebras and hierarchy of invariant equations, in: Quantum Theory and Symmetries II, Proceedings of a Symposium, World Scientific 2002, to appear.
25. R. Twarock: J. Phys. A32 (1999), 4971-4981.
26. N. E. Mavromatos and R. J. Szabo: Int. J. Mod. Phys. A16 (2001), 209-250.