메뉴 건너뛰기




Volumn 187, Issue 1, 2006, Pages 1-28

Fast calculation of energy and mass preserving solutions of Schrödinger-Poisson systems on unbounded domains

Author keywords

Difference equation; Discrete transparent boundary conditions; Finite differences; Newton potential; Schr dinger equation; Schr dinger Poisson system

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENCE EQUATIONS; ENERGY CONSERVATION; FINITE DIFFERENCE METHOD; POISSON DISTRIBUTION; PROBLEM SOLVING;

EID: 27344459965     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.03.026     Document Type: Article
Times cited : (28)

References (25)
  • 1
    • 0031632570 scopus 로고    scopus 로고
    • Numerically absorbing boundary conditions for quantum evolution equations
    • A. Arnold Numerically absorbing boundary conditions for quantum evolution equations VLSI Design 6 1998 313 319
    • (1998) VLSI Design , vol.6 , pp. 313-319
    • Arnold, A.1
  • 2
    • 4444331530 scopus 로고    scopus 로고
    • Discrete transparent boundary conditions for the Schrödinger equation: Fast calculation, approximation, and stability
    • A. Arnold, M. Ehrhardt, and I. Sofronov Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability Comm. Math. Sci. 1 2003 501 556
    • (2003) Comm. Math. Sci. , vol.1 , pp. 501-556
    • Arnold, A.1    Ehrhardt, M.2    Sofronov, I.3
  • 5
    • 0038392329 scopus 로고    scopus 로고
    • A mathematical model for the transient evolution of a resonant tunneling diode
    • N.B. Abdallah, and O. Pinaud A mathematical model for the transient evolution of a resonant tunneling diode C. R. Math. Acad. Sci. Paris 334 2002 283 288
    • (2002) C. R. Math. Acad. Sci. Paris , vol.334 , pp. 283-288
    • Abdallah, N.B.1    Pinaud, O.2
  • 6
    • 0001661079 scopus 로고    scopus 로고
    • Linear algebra, rational approximation and orthogonal polynomials
    • North-Holland, Amsterdam
    • A. Bultheel, M. Van Barel, Linear algebra, rational approximation and orthogonal polynomials, in: Studies in Computational Mathematics, vol. 6, North-Holland, Amsterdam, 1997.
    • (1997) Studies in Computational Mathematics , vol.6
    • Bultheel, A.1    Van Barel, M.2
  • 7
    • 0040522777 scopus 로고    scopus 로고
    • 2-solutions to the Schrödinger-Poisson system: Existence, uniqueness, time behaviour and smoothing effects
    • F. Castella L 2 -solutions to the Schrödinger-Poisson system: existence, uniqueness, time behaviour and smoothing effects Math. Mod. Meth. Appl. Sci. 7 1997 1051 1083
    • (1997) Math. Mod. Meth. Appl. Sci. , vol.7 , pp. 1051-1083
    • Castella, F.1
  • 9
    • 0011764695 scopus 로고    scopus 로고
    • Discrete transparent boundary conditions for the Schrödinger equation
    • M. Ehrhardt, and A. Arnold Discrete transparent boundary conditions for the Schrödinger equation Riv. Mat. Univ. Parma 6 2001 57 108
    • (2001) Riv. Mat. Univ. Parma , vol.6 , pp. 57-108
    • Ehrhardt, M.1    Arnold, A.2
  • 11
    • 0001449110 scopus 로고    scopus 로고
    • Solving ordinary differential equations II: Stiff and differential-algebraic problems
    • 2nd rev. ed., Springer, Berlin
    • E. Hairer, G. Wanner, Solving ordinary differential equations II: stiff and differential-algebraic problems, Springer Series in Computational Mathematics, vol. 14, 2nd rev. ed., Springer, Berlin, 1996.
    • (1996) Springer Series in Computational Mathematics , vol.14
    • Hairer, E.1    Wanner, G.2
  • 12
    • 84988144301 scopus 로고
    • Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and Schrödinger-Poisson systems
    • R. Illner, P.F. Zweifel, and H. Lange Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and Schrödinger- Poisson systems Math. Meth. Appl. Sci. 17 1994 349 376
    • (1994) Math. Meth. Appl. Sci. , vol.17 , pp. 349-376
    • Illner, R.1    Zweifel, P.F.2    Lange, H.3
  • 13
    • 0016927322 scopus 로고
    • Generating Bessel functions in Mie scattering calculations using continued fractions
    • W.J. Lentz Generating Bessel functions in Mie scattering calculations using continued fractions Appl. Opt. 15 1976 668 671
    • (1976) Appl. Opt. , vol.15 , pp. 668-671
    • Lentz, W.J.1
  • 14
    • 0000071243 scopus 로고
    • Electron confinement in quantum nanostructures: Self-consistent Poisson-Schrödinger theory
    • J.H. Luscombe, A.M. Bouchard, and M. Luban Electron confinement in quantum nanostructures: self-consistent Poisson-Schrödinger theory Phys. Rev. B 46 1992 10262 10268
    • (1992) Phys. Rev. B , vol.46 , pp. 10262-10268
    • Luscombe, J.H.1    Bouchard, A.M.2    Luban, M.3
  • 17
    • 0032203076 scopus 로고    scopus 로고
    • Asymptotic properties of solutions to discrete Coulomb equations
    • R.E. Mickens Asymptotic properties of solutions to discrete Coulomb equations Comput. Math. Appl. 36 1998 285 289
    • (1998) Comput. Math. Appl. , vol.36 , pp. 285-289
    • Mickens, R.E.1
  • 18
    • 0032349239 scopus 로고    scopus 로고
    • Spherically-symmetric solutions of the Schrödinger-Newton equations
    • I.M. Moroz, R. Penrose, and P. Tod Spherically-symmetric solutions of the Schrödinger-Newton equations Class. Quantum Grav. 15 1998 2733 2742
    • (1998) Class. Quantum Grav. , vol.15 , pp. 2733-2742
    • Moroz, I.M.1    Penrose, R.2    Tod, P.3
  • 19
    • 27344442586 scopus 로고    scopus 로고
    • private communication
    • C. Ringhofer, private communication.
    • Ringhofer, C.1
  • 20
    • 8644220121 scopus 로고    scopus 로고
    • Schrödinger-Poisson model for very-high-pressure cold helium
    • G. Reinisch, J. de Freitas Pacheo, and P. Valiron Schrödinger- Poisson model for very-high-pressure cold helium Phys. Rev. A 63 2001 042505
    • (2001) Phys. Rev. A , vol.63 , pp. 042505
    • Reinisch, G.1    De Freitas Pacheo, J.2    Valiron, P.3
  • 21
    • 0041026785 scopus 로고    scopus 로고
    • Discrete Schrödinger-Poisson systems preserving energy and mass
    • C. Ringhofer, and J. Soler Discrete Schrödinger-Poisson systems preserving energy and mass Appl. Math. Lett. 13 2000 27 32
    • (2000) Appl. Math. Lett. , vol.13 , pp. 27-32
    • Ringhofer, C.1    Soler, J.2
  • 22
    • 0035536412 scopus 로고    scopus 로고
    • A variational approach to the Schrödinger-Poisson system: Asymptotic behaviour, breathers, and stability
    • E. Ruíz Arriola, and J. Soler A variational approach to the Schrödinger-Poisson system: asymptotic behaviour, breathers, and stability J. Stat. Phys. 103 2001 1069 1106
    • (2001) J. Stat. Phys. , vol.103 , pp. 1069-1106
    • Arriola, E.R.1    Soler, J.2
  • 23
    • 0033096510 scopus 로고    scopus 로고
    • An analytical approach to the Schrödinger-Newton equations
    • P. Tod, and I.M. Moroz An analytical approach to the Schrödinger- Newton equations Nonlinearity 12 1999 201 216
    • (1999) Nonlinearity , vol.12 , pp. 201-216
    • Tod, P.1    Moroz, I.M.2
  • 24
    • 0012993065 scopus 로고
    • Asymptotic expansions for second-order linear difference equations
    • R. Wong, and H. Li Asymptotic expansions for second-order linear difference equations J. Comput. Appl. Math. 41 1992 65 94
    • (1992) J. Comput. Appl. Math. , vol.41 , pp. 65-94
    • Wong, R.1    Li, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.