A finite-difference method for the numerical solution of the Schrödinger equation

A new approach, which is based on a new property of phase-lag for computing eigenvalues of Schrödinger equations with potentials, is developed in this paper. We investigate two cases: (i) The specific case in which the potential V( x) is an even function with respect to x. It is assumed, also, that...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 1997-03, Vol.79 (2), p.189-205
Main Authors: Simos, T.E., Williams, P.S.
Format: Article
Language:English
Subjects:
Eigenvalue problem
Exact sciences and technology
Finite differences
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Phase-lag
Schrödinger equation
Sciences and techniques of general use
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Summary:A new approach, which is based on a new property of phase-lag for computing eigenvalues of Schrödinger equations with potentials, is developed in this paper. We investigate two cases: (i) The specific case in which the potential V( x) is an even function with respect to x. It is assumed, also, that the wave functions tend to zero for x → ±∞. (ii) The general case of the Morse potential and of the Woods-Saxon or optical potential. Numerical and theoretical results show that this new approach is more efficient compared to previously derived methods.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(96)00156-2