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The Journal of Chemical Physics
Volumn 69, Issue 10, 1978, Pages 4678-4688
The renormalized Numerov method applied to calculating bound states of the coupled-channel Schroedinger equation
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Indexed keywords

EID: 2642543510     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.436421     Document Type: Article
Times cited : (429)
References (28)
  • 2
    • 85034688623 scopus 로고    scopus 로고
    • See the appendix by L. Fox in Ref. (18).
  • 9
    • 4243564558 scopus 로고
    • In a recent publication implied that numerical methods which invert matrices at each step are inefficient compared to those which multiply matrices at each step. Actually, the inversion of a symmetric matrix by Gaussian elimination requires fewer operations (and by actual test calculations uses less computer time) than the multiplication of two matrices of the same dimensions.
    • (1977) J. Phys. B , vol.10 , pp. L35
    • LeDourneuf, M.1    Ky Lan, Vo.2
  • 10
    • 85034690224 scopus 로고    scopus 로고
    • In the limit [formula omitted] it is obvious from Eq. (17) that [formula omitted] If this determinant deviates too far from its limiting value, it means that the grid spacing h is too large, producing a large truncation error. In the extreme case in which [formula omitted] the numerical solution will break into an unphysical oscillation with a node at every grid point. This problem is discussed further in Sec. IV.
  • 13
    • 84951899727 scopus 로고    scopus 로고
    • The program as written will compute degenerate and nondegenerate eigenvalues and also the eigenfunctions of nondegenerate eigenvalues. At the present, it will not compute the eigenfunctions of degenerate eigenvalues.
  • 24
    • 84951898308 scopus 로고    scopus 로고
    • The truncation error for the [formula omitted] problem is given by Eq. (55) only if one of the grid points, in each calculation at a different value of h, is located at the cusp of the potential.
  • 27
    • 84951880776 scopus 로고    scopus 로고
    • The nodes of the inward solution are counted by counting the number of times the relation [formula omitted] occurs. Multiple nodes between two grid points are handled as explained in Appendix B.

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