메뉴 건너뛰기




Volumn 51, Issue 2, 2004, Pages 229-243

Remarks on geometric quantum mechanics

Author keywords

Complete integrability; Geometric phases; Geometric quantum mechanics; Quantum measurement theory

Indexed keywords


EID: 1942444500     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2003.10.008     Document Type: Article
Times cited : (23)

References (47)
  • 1
    • 30244508244 scopus 로고
    • Phase change during a cyclic quantum evolution
    • Ahronov Y. Anandan J. Phase change during a cyclic quantum evolution Phys. Rev. Lett. 58 1987 1593-1596
    • (1987) Phys. Rev. Lett. , vol.58 , pp. 1593-1596
    • Ahronov, Y.1    Anandan, J.2
  • 2
    • 4243233467 scopus 로고
    • Geometry of quantum evolution
    • Ahronov Y. Anandan J. Geometry of quantum evolution Phys. Rev. Lett. 65 1990 1697-1700
    • (1990) Phys. Rev. Lett. , vol.65 , pp. 1697-1700
    • Ahronov, Y.1    Anandan, J.2
  • 5
    • 84874962985 scopus 로고
    • Convexity and commuting Hamiltonians
    • Atiyah M.F. Convexity and commuting Hamiltonians Bull. Lond. Math. Soc. 14 1982 1-15
    • (1982) Bull. Lond. Math. Soc. , vol.14 , pp. 1-15
    • Atiyah, M.F.1
  • 7
    • 0002207807 scopus 로고
    • Quantal phase factors accompanying adiabatic changes
    • M.V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. Roy. Soc. Lond. A 392 (1984) 45-57.
    • (1984) Proc. Roy. Soc. Lond. A , vol.392 , pp. 45-57
    • Berry, M.V.1
  • 8
    • 33845940811 scopus 로고
    • Classical adiabatic phase and quantal adiabatic phase
    • M.V. Berry, Classical adiabatic phase and quantal adiabatic phase, J. Phys. A 18 (1985) 15-27.
    • (1985) J. Phys. A , vol.18 , pp. 15-27
    • Berry, M.V.1
  • 9
    • 0003864761 scopus 로고
    • Prentice-Hall, New York, 1951 and Dover, New York
    • D. Bohm, Quantum Theory, Prentice-Hall, New York, 1951 and Dover, New York, 1989.
    • (1989) Quantum Theory
    • Bohm, D.1
  • 10
    • 0032336278 scopus 로고    scopus 로고
    • The quantum canonical ensemble
    • Brody D.C. Hughston L.P. The quantum canonical ensemble J. Math. Phys. 39 1998 2586-2592
    • (1998) J. Math. Phys. , vol.39 , pp. 2586-2592
    • Brody, D.C.1    Hughston, L.P.2
  • 11
    • 0034347339 scopus 로고    scopus 로고
    • Information content for quantum states
    • Brody D.C. Hughston L.P. Information content for quantum states J. Math. Phys. 41 2000 6502-6508
    • (2000) J. Math. Phys. , vol.41 , pp. 6502-6508
    • Brody, D.C.1    Hughston, L.P.2
  • 13
    • 0032622945 scopus 로고    scopus 로고
    • On the non-linear extension of quantum superposition and uncertainty principles
    • Cirelli R. Gatti M. Manià A. On the non-linear extension of quantum superposition and uncertainty principles J. Geom. Phys. 29 1999 64-86
    • (1999) J. Geom. Phys. , vol.29 , pp. 64-86
    • Cirelli, R.1    Gatti, M.2    Manià, A.3
  • 14
    • 0037346439 scopus 로고    scopus 로고
    • The pure state space of quantum mechanics as Hermitian symmetric space
    • Cirelli R. Gatti M. Manià A. The pure state space of quantum mechanics as Hermitian symmetric space J. Geom. Phys. 45 2003 267-284
    • (2003) J. Geom. Phys. , vol.45 , pp. 267-284
    • Cirelli, R.1    Gatti, M.2    Manià, A.3
  • 15
    • 36549101248 scopus 로고
    • Quantum mechanics as an infinite dimensional Hamiltonian system with uncertainty structure. Parts I and II
    • 2891-2897
    • R. Cirelli, A. Manià, L. Pizzocchero, Quantum mechanics as an infinite dimensional Hamiltonian system with uncertainty structure. Parts I and II, J. Math. Phys. 31 (1990) 2891-2897, 2898-2903.
    • (1990) J. Math. Phys. , vol.31 , pp. 2898-2903
    • Cirelli, R.1    Manià, A.2    Pizzocchero, L.3
  • 16
    • 0346411326 scopus 로고
    • On the integrability of quantum mechanics as an infinite-dimensional Hamiltonian system
    • Cirelli R. Pizzocchero L. On the integrability of quantum mechanics as an infinite-dimensional Hamiltonian system Nonlinearity 3 1990 1057-1080
    • (1990) Nonlinearity , vol.3 , pp. 1057-1080
    • Cirelli, R.1    Pizzocchero, L.2
  • 17
    • 34250229086 scopus 로고
    • On the variation in the cohomology of the symplectic form of the reduced phase space
    • Duistermaat J.J. Heckman G.J. On the variation in the cohomology of the symplectic form of the reduced phase space Inv. Math. 69 1982 259-268
    • (1982) Inv. Math. , vol.69 , pp. 259-268
    • Duistermaat, J.J.1    Heckman, G.J.2
  • 18
    • 0010170052 scopus 로고
    • Remarks on the geometric quantization of the Kepler problem
    • Gaeta G. Spera M. Remarks on the geometric quantization of the Kepler problem Lett. Math. Phys. 16 1988 187-192
    • (1988) Lett. Math. Phys. , vol.16 , pp. 187-192
    • Gaeta, G.1    Spera, M.2
  • 21
    • 0000567544 scopus 로고
    • Convexity properties of the moment map. I
    • Guillemin V. Sternberg S. Convexity properties of the moment map. I Inv. Math. 67 1982 491-513
    • (1982) Inv. Math. , vol.67 , pp. 491-513
    • Guillemin, V.1    Sternberg, S.2
  • 22
    • 34250231714 scopus 로고
    • Geometric quantization and multiplicity of group representations
    • Guillemin V. Sternberg S. Geometric quantization and multiplicity of group representations Inv. Math. 67 1982 515-538
    • (1982) Inv. Math. , vol.67 , pp. 515-538
    • Guillemin, V.1    Sternberg, S.2
  • 24
    • 0000977878 scopus 로고
    • Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian
    • Hannay J.H. Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian J. Phys. A 18 1985 221-230
    • (1985) J. Phys. A , vol.18 , pp. 221-230
    • Hannay, J.H.1
  • 25
    • 33846632986 scopus 로고
    • Quantum mechanics as a classical theory
    • Heslot A. Quantum mechanics as a classical theory Phys. Rev. D 31 1985 1341-1348
    • (1985) Phys. Rev. D , vol.31 , pp. 1341-1348
    • Heslot, A.1
  • 27
    • 0001092198 scopus 로고
    • Geometrization of quantum mechanics
    • Kibble T.W.B. Geometrization of quantum mechanics Commun. Math. Phys. 65 1979 189-201
    • (1979) Commun. Math. Phys. , vol.65 , pp. 189-201
    • Kibble, T.W.B.1
  • 31
    • 0003772469 scopus 로고
    • Mécanique quantique. I and II
    • Dunod, Paris, 1959
    • A. Messiah, Mécanique quantique. I and II, Dunod, Paris, 1959, 1962.
    • (1962)
    • Messiah, A.1
  • 32
    • 0002368839 scopus 로고
    • The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case
    • Montgomery R. The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case Commun. Math. Phys. 120 1988 269-294
    • (1988) Commun. Math. Phys. , vol.120 , pp. 269-294
    • Montgomery, R.1
  • 34
    • 0000518598 scopus 로고    scopus 로고
    • Symplectic topology of integrable Hamiltonian systems. I. Arnold-Liouville with singularities
    • Zung N.T. Symplectic topology of integrable Hamiltonian systems. I. Arnold-Liouville with singularities Compos. Math. 101 1996 179-215
    • (1996) Compos. Math. , vol.101 , pp. 179-215
    • Zung, N.T.1
  • 35
    • 0003694417 scopus 로고    scopus 로고
    • Symplectic Topology of Integrable Hamiltonian Systems. II. Topological Classification
    • arXiv:math.DG/OO10181 v2
    • N.T. Zung, Symplectic Topology of Integrable Hamiltonian Systems. II. Topological Classification. arXiv:math.DG/OO10181 v2.
    • Zung, N.T.1
  • 36
    • 1942495205 scopus 로고
    • Coherent States
    • Springer, Berlin
    • A. Perelomov, Coherent States, Springer, Berlin, 1986.
    • (1986)
    • Perelomov, A.1
  • 37
    • 77957176704 scopus 로고
    • Coherent states and Kähler manifolds
    • Rawnsley J. Coherent states and Kähler manifolds Quart. J. Math. 28 1977 403-415
    • (1977) Quart. J. Math. , vol.28 , pp. 403-415
    • Rawnsley, J.1
  • 38
    • 0003923885 scopus 로고    scopus 로고
    • Geometry of quantum mechanics
    • Ph.D. Thesis, The Pennsylvania State University
    • T.A. Schilling, Geometry of quantum mechanics, Ph.D. Thesis, The Pennsylvania State University, 1996.
    • (1996)
    • Schilling, T.A.1
  • 39
    • 0001345770 scopus 로고
    • Holonomy, the quantum adiabatic theorem, and Berry's phase
    • B. Simon, Holonomy, the quantum adiabatic theorem, and Berry's phase, Phys. Rev. Lett. 51 (1983) 2167-2170.
    • (1983) Phys. Rev. Lett. , vol.51 , pp. 2167-2170
    • Simon, B.1
  • 40
    • 0000018511 scopus 로고
    • On a generalized uncertainty principle, coherent states, and the moment map
    • Spera M. On a generalized uncertainty principle, coherent states, and the moment map J. Geom. Phys. 12 1993 165-182
    • (1993) J. Geom. Phys. , vol.12 , pp. 165-182
    • Spera, M.1
  • 42
    • 84909829910 scopus 로고
    • Integrabilität beim geodëtish Fluss
    • A. Thimm, Integrabilität beim geodëtish Fluss, Bonner Math. Schrift. B 10 (1978)
    • (1978) Bonner Math. Schrift. B , vol.10
    • Thimm, A.1
  • 43
    • 1942495203 scopus 로고
    • Dissertation, Universität Bonn
    • A. Thimm, Dissertation, Universität Bonn, 1980
    • (1980)
    • Thimm, A.1
  • 44
    • 84958431035 scopus 로고
    • Integrable geodesic flows
    • Thimm A. Integrable geodesic flows Ergod. Theor. Dyn. Syst. 1 1981 495-517
    • (1981) Ergod. Theor. Dyn. Syst. , vol.1 , pp. 495-517
    • Thimm, A.1
  • 47
    • 1942527112 scopus 로고    scopus 로고
    • Quantization of integrable systems and Bohr-Sommerfeld varieties
    • Preprint
    • T. Wurzbacher, Quantization of integrable systems and Bohr-Sommerfeld varieties, Preprint, 1996.
    • (1996)
    • Wurzbacher, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.