Quantum mechanics on the cylinder

Journal of Optics B: Quantum and Semiclassical Optics

Volumn 5, Issue 3, 2003, Pages

  González, José A ^a   Del Olmo, Mariano A ^a   Tosiek, Jaromir ^a,b  

^a UNIVERSITY OF VALLADOLID   (Spain)

^b LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Deformation quantization; Moyal formalism; Quantum mechanics

Indexed keywords

COMPUTATIONAL METHODS; CYLINDERS (SHAPES); INTEGRATION; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING;

DEFORMATION QUANTIZATION;

QUANTUM THEORY;

EID: 0037898449     PISSN: 14644266     EISSN: None     Source Type: Journal    
DOI: 10.1088/1464-4266/5/3/362     Document Type: Conference Paper

References (46)

1. Moyal J E 1949 Proc. Camb. Phil. Soc. 45 99
2. Weyl H 1931 The Theory of Groups and Quantum Mechanics (New York: Dover)
3. Wigner E P 1932 Phys. Rev. 40 749
4. Groenewold H J 1946 Physica 12 405
5. de Groot S R 1974 La Transformation de Weyl et la Fonction de Wigner: une Forme Alternative de la Mécanique Quantique (Montréal: Les Presses de l'Université de Montréal)
6. Amiet J P and Huguenin P 1981 Mécaniques Classique et Quantique dans l'espace de Phase (Neuchâtel: Université de Neuchâtel)
7. Gadella M 1995 Fortschr. Phys. 43 229
8. Berezin F A 1974 Math. URSS Izv. 38 1116
9. Berezin F A 1975 Math. URSS Izv. 39 363 Berezin F A 1975 Commun. Math. Phys. 40 153
10. Berezin F A 1975 Math. URSS Izv. 39 363 Berezin F A 1975 Commun. Math. Phys. 40 153
11. Bayen F, Flato M, Fronsdal C, Lichnerowicz A and Sternheimer D 1978 Ann. Phys., NY 111 61 Bayen F, Flato M, Fronsdal C, Lichnerowicz A and Sternheimer D 1978 Ann. Phys., NY 111 111
12. Bayen F, Flato M, Fronsdal C, Lichnerowicz A and Sternheimer D 1978 Ann. Phys., NY 111 61 Bayen F, Flato M, Fronsdal C, Lichnerowicz A and Sternheimer D 1978 Ann. Phys., NY 111 111
13. Souriau J M 1970 Structure des Systèmes Dynamiques (Paris: Dunod)
14. Woodhouse N 1980 Geometric Quantization (Oxford: Clarendon)
15. Perelomov A M 1986 Generalized Coherent States and Their Applications (Berlin: Springer)
16. Weil A 1964 Acta Math. 111 143
17. Brezin J 1970 Trans. Am. Math. Soc. 150 611
18. Zak J 1967 Phys. Rev. Lett. 19 1385
19. Berry M V 1977 Phil. Trans. R. Soc. A 287 237
20. Mukunda N 1979 Am. J. Phys. 47 182
21. Kasperkovitz P, Foidl C and Dirl R 1987 The Physics of Phase Space (Berlin: Springer) p 267
22. Arnold A, Degond P, Markowich P A and Steinrück H 1989 Appl. Math. Lett. 2 187
23. Kasperkovitz P and Peev M 1994 Ann. Phys., NY 230 21
24. Arratia O, Martín M A and del Olmo M A 1996 Rend. Sem. Mat. Univ. Pol. Torino 54 191
25. Arratia O and del Olmo M A 1997 Rep. Math. Phys. 40 149
26. Plebański J F, Przanowski M, Tosiek J and Turrubiates F J 2000 Acta Phys. Pol. B 31 561
27. Janssen A J E M 1982 J. Math. Phys. 23 720
28. Folland G B 1989 Harmonic Analysis in Phase Space (Princeton, NJ: Princeton University Press)
29. Reed M and Simon B 1978 Methods of Modern Mathematical Physics IV: Analysis of Operators (New York: Academic)
30. Voros A 1977 Developpements semi-classiques PhD Thesis Université de Paris-Sud
31. Voros A 1978 J. Funct. Anal. 29 104
32. Plebański J F, Przanowski M and Tosiek J 1996 Acta Phys. Pol. B 27 1961
33. Grossmann A 1976 Commun. Math. Phys. 48 191
34. Royer A 1977 Phys. Rev. A 15 449
35. Stratonovich R L 1956 Sov. Phys.-JETP 31 1012
36. de Biévre S and González J A 1993 Semiclassical behaviour of coherent states on the circle Quantization and Coherent States Methods (Singapore: World Scientific)
37. González J A 1996 Coherent states and quantization on the cylinder PhD Thesis Universidad de Valladolid
38. Klauder J R and Skagerstam B S 1985 Coherent States: Applications in Physics and Mathematical Physics (Singapore: World Scientific)
39. González J A and del Olmo M A 1998 J. Phys. A: Math. Gen. 31 8841
40. Mumford D 1983 Tata Lectures on Theta vol 1, (Boston, MA: Birkhäuser)
41. Erdélyi A ed 1981 Higher Transcendental Functions vol 2, (Malabar, FL: Krieger)
42. Kowalski K, Rembieliński J and Papaloucas L C 1996 J. Phys. A: Math. Gen. 29 4149
43. Kowalski K and Rembieliński J 2002 J. Phys. A: Math. Gen. 35 1405
44. Ali S T, Antoine J P and Gazeau J P 1991 Ann. Inst. H. Poincaré 55 829 Ali S T, Antoine J P and Gazeau J P 1991 Ann. Inst. H. Poincaré 55 857
45. Ali S T, Antoine J P and Gazeau J P 1991 Ann. Inst. H. Poincaré 55 829 Ali S T, Antoine J P and Gazeau J P 1991 Ann. Inst. H. Poincaré 55 857
46. Reed M and Simon B 1975 Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness (New York: Academic)