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Volumn 344, Issue 2, 2008, Pages 1005-1017

Space-time fractional Schrödinger equation with time-independent potentials

Author keywords

Caputo fractional derivative; Fractional Schr dinger equation; Heisenberg equation; Mittag Leffler function; Riesz fractional operator

Indexed keywords


EID: 43449090362     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.03.061     Document Type: Article
Times cited : (199)

References (37)
  • 1
    • 17144403633 scopus 로고
    • The Fractional Calculus: Theory and Applications, Differentiation and Integration to Arbitrary Order
    • Academic Press, New York
    • Oldham K.B., and Spanier J. The Fractional Calculus: Theory and Applications, Differentiation and Integration to Arbitrary Order. Math. Sci. Eng. (1974), Academic Press, New York
    • (1974) Math. Sci. Eng.
    • Oldham, K.B.1    Spanier, J.2
  • 6
    • 0036887936 scopus 로고    scopus 로고
    • Chaos, fractional kinetics, and anomalous transport
    • Zaslavsky G.M. Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371 (2002) 461-580
    • (2002) Phys. Rep. , vol.371 , pp. 461-580
    • Zaslavsky, G.M.1
  • 7
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler R., and Klafter J. The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339 (2000) 1-77
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 8
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Mainardi F., Luchko Yu., and Pagnini G. The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4 (2001) 153-192
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , pp. 153-192
    • Mainardi, F.1    Luchko, Yu.2    Pagnini, G.3
  • 11
    • 31744447506 scopus 로고    scopus 로고
    • Hamiltonian formalism of fractional systems
    • Stanislavsky A.A. Hamiltonian formalism of fractional systems. Eur. Phys. J. B 49 (2006) 93-101
    • (2006) Eur. Phys. J. B , vol.49 , pp. 93-101
    • Stanislavsky, A.A.1
  • 12
    • 0000735791 scopus 로고    scopus 로고
    • Nonconservative Lagrangian and Hamiltonian mechanics
    • Riewe F. Nonconservative Lagrangian and Hamiltonian mechanics. Phys. Rev. E 53 (1996) 1890
    • (1996) Phys. Rev. E , vol.53 , pp. 1890
    • Riewe, F.1
  • 13
    • 4243530410 scopus 로고    scopus 로고
    • Mechanics with fractional derivatives
    • Riewe F. Mechanics with fractional derivatives. Phys. Rev. E 55 (1997) 3581
    • (1997) Phys. Rev. E , vol.55 , pp. 3581
    • Riewe, F.1
  • 14
    • 33750541076 scopus 로고    scopus 로고
    • Fractional Hamiltonian analysis of higher order derivatives systems
    • Baleanu D., Muslih S., and Tas K. Fractional Hamiltonian analysis of higher order derivatives systems. J. Math. Phys. 47 10 (2006) 103503
    • (2006) J. Math. Phys. , vol.47 , Issue.10 , pp. 103503
    • Baleanu, D.1    Muslih, S.2    Tas, K.3
  • 15
    • 37549039833 scopus 로고    scopus 로고
    • Hamilton-Jaccobi formulation of systems with Caputo's fractional derivative
    • Rabei E.M., Almayteh I., Muslih S.I., and Baleanu D. Hamilton-Jaccobi formulation of systems with Caputo's fractional derivative. Phys. Scr. 77 1 (2008) 015101
    • (2008) Phys. Scr. , vol.77 , Issue.1 , pp. 015101
    • Rabei, E.M.1    Almayteh, I.2    Muslih, S.I.3    Baleanu, D.4
  • 16
    • 33845669957 scopus 로고    scopus 로고
    • Fractional Hamilton formalism within Caputo's derivative
    • Baleanu D., and Agrawal O.P. Fractional Hamilton formalism within Caputo's derivative. Czechoslovak J. Phys. 56 10-11 (2006) 1087-1092
    • (2006) Czechoslovak J. Phys. , vol.56 , Issue.10-11 , pp. 1087-1092
    • Baleanu, D.1    Agrawal, O.P.2
  • 17
    • 0036701004 scopus 로고    scopus 로고
    • Formulation of Euler-Lagrange equations for fractional variational problems
    • Agrawal O.P. Formulation of Euler-Lagrange equations for fractional variational problems. J. Math. Anal. Appl. 272 (2002) 368-379
    • (2002) J. Math. Anal. Appl. , vol.272 , pp. 368-379
    • Agrawal, O.P.1
  • 18
    • 33746876366 scopus 로고    scopus 로고
    • Fractional variational calculus and the transversality conditions
    • Agrawal O.P. Fractional variational calculus and the transversality conditions. J. Phys. A 39 (2006) 10375-10384
    • (2006) J. Phys. A , vol.39 , pp. 10375-10384
    • Agrawal, O.P.1
  • 19
    • 33745514693 scopus 로고    scopus 로고
    • Hamiltonian formulation of classical fields within Riemann-Liouville fractional derivatives
    • Muslih S., Baleanu D., and Rabei E. Hamiltonian formulation of classical fields within Riemann-Liouville fractional derivatives. Phys. Scr. 73 (2006) 436-438
    • (2006) Phys. Scr. , vol.73 , pp. 436-438
    • Muslih, S.1    Baleanu, D.2    Rabei, E.3
  • 21
    • 4544250038 scopus 로고    scopus 로고
    • Time fractional Schrödinger equation
    • Naber M. Time fractional Schrödinger equation. J. Math. Phys. 45 8 (2004) 3339-3352
    • (2004) J. Math. Phys. , vol.45 , Issue.8 , pp. 3339-3352
    • Naber, M.1
  • 22
    • 34247620479 scopus 로고    scopus 로고
    • Generalized fractional Schrödinger equation with space-time fractional derivatives
    • Wang S.W., and Xu M.Y. Generalized fractional Schrödinger equation with space-time fractional derivatives. J. Math. Phys. 48 (2007) 043502
    • (2007) J. Math. Phys. , vol.48 , pp. 043502
    • Wang, S.W.1    Xu, M.Y.2
  • 23
    • 41349084761 scopus 로고    scopus 로고
    • Fractional Schrödinger equation
    • Laskin N. Fractional Schrödinger equation. Phys. Rev. E 66 (2002) 056108
    • (2002) Phys. Rev. E , vol.66 , pp. 056108
    • Laskin, N.1
  • 24
    • 0000415309 scopus 로고    scopus 로고
    • Fractional quantum mechanics and Lévy path integrals
    • Laskin N. Fractional quantum mechanics and Lévy path integrals. Phys. Lett. A 298 (2000) 298-305
    • (2000) Phys. Lett. A , vol.298 , pp. 298-305
    • Laskin, N.1
  • 25
    • 0034271488 scopus 로고    scopus 로고
    • Fractional quantum mechanics
    • Laskin N. Fractional quantum mechanics. Phys. Rev. E 62 (2000) 3135-3145
    • (2000) Phys. Rev. E , vol.62 , pp. 3135-3145
    • Laskin, N.1
  • 26
    • 0034363921 scopus 로고    scopus 로고
    • Fractals and quantum mechanics
    • Laskin N. Fractals and quantum mechanics. Chaos 10 (2000) 780-790
    • (2000) Chaos , vol.10 , pp. 780-790
    • Laskin, N.1
  • 27
    • 33748296360 scopus 로고    scopus 로고
    • Some physical applications of fractional Schrödinger equation
    • Guo X.Y., and Xu M.Y. Some physical applications of fractional Schrödinger equation. J. Math. Phys. 47 (2006) 082104
    • (2006) J. Math. Phys. , vol.47 , pp. 082104
    • Guo, X.Y.1    Xu, M.Y.2
  • 28
    • 34547601480 scopus 로고    scopus 로고
    • Some solutions to the space fractional Schrödinger equation using momentum representation method
    • Dong J.P., and Xu M.Y. Some solutions to the space fractional Schrödinger equation using momentum representation method. J. Math. Phys. 48 (2007) 072105
    • (2007) J. Math. Phys. , vol.48 , pp. 072105
    • Dong, J.P.1    Xu, M.Y.2
  • 30
    • 17444414887 scopus 로고    scopus 로고
    • Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions
    • Xu M.Y., and Tan W.C. Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions. Sci. China Ser. G 46 2 (2003) 145-157
    • (2003) Sci. China Ser. G , vol.46 , Issue.2 , pp. 145-157
    • Xu, M.Y.1    Tan, W.C.2
  • 32
    • 0000145521 scopus 로고    scopus 로고
    • On Mittag-Leffler-type functions in fractional evolution processes
    • Mainardi F., and Gorenflo R. On Mittag-Leffler-type functions in fractional evolution processes. J. Comput. Appl. Math. 118 (2000) 283-299
    • (2000) J. Comput. Appl. Math. , vol.118 , pp. 283-299
    • Mainardi, F.1    Gorenflo, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.