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

Journal of Physics A: Mathematical and General

Volumn 39, Issue 32, 2006, Pages 10229-10237

  Weideman, J A C ^a  

^a STELLENBOSCH UNIVERSITY   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746728249     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/32/S21     Document Type: Conference Paper

References (17)

1. Bender C M, Berry M, Meisinger P N, Savage V M and Simsek M 2001 Complex WKB analysis of energy-level degeneracies of non-Hermitian Hamiltonians J. Phys. A: Math. Gen. 34 L31-6
2. Bender C M, Berry M V and Mandilara A 2002 Generalized PT symmetry and real spectra J. Phys. A: Math. Gen. 35 L467-71
3. Bender C M and Boettcher S 1998 Quasi-exactly solvable quartic potential J. Phys. A: Math. Gen. 31 L273-7
4. Bender C M and Orszag S A 1999 Advanced Mathematical Methods for Scientists and Engineers (New York: Springer)
5. Boyd J P 1984 Asymptotic coefficients of Hermite function series J. Comput. Phys. 54 382-410
6. Fornberg B 1996 A Practical Guide to Pseudospectral Methods (Cambridge: Cambridge University Press)
7. Handy C R and Wang X 2003 Spectral bounds for the PT-breaking Hamiltonian J. Phys. A: Math. Gen. 36 11513-32
8. López-Fernández M and Palencia C 2004 On the numerical inversion of the Laplace transform of certain holomorphic mappings Appl. Numer. Math. 51 289-303
9. Meissner H and Steinborn E O Quartic, sextic, and octic anharmonic oscillators: precise energies of ground state and excited states by an iterative method based on the generalized Bloch equation Phys. Rev. A 56 1189-200
10. Pryce J D 1997 SLDRIVER: A tool for exploring SL solvers and SL problems Spectral Theory and Computational Methods of Sturm-Liouville Problems (Knoxville, TN, 1996) (Lecture Notes in Pure and Appl. Math. vol 191) (New York: Dekker) pp 349-76
11. Trefethen L N 2000 Spectral methods in MATLAB (Philadelphia, PA: SIAM)
12. Weideman J A C 2006 http://dip.sun.ac.za/weideman/schrodinger/
13. Weideman J A C 1992 The eigenvalues of Hermite and rational spectral differentiation matrices Numer. Math. 61 409-32
14. Weideman J A C 1999 Spectral methods based on nonclassical orthogonal polynomials Applications and Computation of Orthogonal Polynomials (Oberwolfach, 1998) (Int. Ser. Numer. Math. vol 131) (Basel: Birkhäuser) pp 239-51
15. Weideman J A C and Reddy S C 2000 A MATLAB differentiation matrix suite ACM Trans. Math. Software 26 465-519 Codes available at http://www.mathworks. com/matlabcentral/fileexchange/ and at http://dip.sun.ac.za/weideman/research/ differ.html
16. Welfert B D 1997 Generation of pseudospectral differentiation matrices: I SIAM J. Numer. Anal. 34 1640-57
17. Wright T 2002 EigTool http://www.comlab.ox.ac.uk/pseudospectra/eigtool/