Spectral differentiation matrices for the numerical solution of Schrodinger's equation

被引：10
作者：
Weideman, J. A. C. [1 ]
机构：
[1] Univ Stellenbosch, ZA-7600 Stellenbosch, South Africa
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2006年 / 39卷 / 32期
关键词：
D O I：
10.1088/0305-4470/39/32/S21
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Schrodinger's equation is solved numerically using the spectral collocation (pseudospectral) method based on Hermite weighted polynomial interpolants. Several sets of numerical results from the literature are reproduced using this approach. MATLAB codes that can serve as templates for further exploration are provided both in the paper and online. A new proposal is made for solving Schrodinger's equation in Stokes wedges.
引用
收藏
页码：10229 / 10237
页数：9
相关论文
共 16 条
  • [1] Bender C. M., 1999, ADV MATH METHODS SCI, DOI DOI 10.1007/978-1-4757-3069-2
  • [2] Quasi-exactly solvable quartic potential
    Bender, CM
    Boettcher, S
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1998, 31 (14): : L273 - L277
  • [3] Generalized PT symmetry and real spectra
    Bender, CM
    Berry, MV
    Mandilara, A
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2002, 35 (31): : L467 - L471
  • [4] Complex WKB analysis of energy-level degeneracies of non-Hermitian Hamiltonians
    Bender, CM
    Berry, M
    Meisinger, PN
    Savage, VM
    Simsek, M
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (06): : L31 - L36
  • [5] ASYMPTOTIC COEFFICIENTS OF HERMITE FUNCTION SERIES
    BOYD, JP
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1984, 54 (03) : 382 - 410
  • [6] Fornberg B., 1996, A Practical Guide to Pseudospectral Methods
  • [7] Spectral bounds for the PT-breaking Hamiltonian p2+x4+iax
    Handy, CR
    Wang, XQ
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (45): : 11513 - 11532
  • [8] On the numerical inversion of the Laplace transform of certain holomorphic mappings
    López-Fernández, M
    Palencia, C
    [J]. APPLIED NUMERICAL MATHEMATICS, 2004, 51 (2-3) : 289 - 303
  • [9] Quartic, sextic, and octic anharmonic oscillators: Precise energies of ground state and excited states by an iterative method based on the generalized Bloch equation
    Meissner, H
    Steinborn, EO
    [J]. PHYSICAL REVIEW A, 1997, 56 (02): : 1189 - 1200
  • [10] Pryce JD, 1997, LECT NOTES PURE APPL, V191, P349
12