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Solution for bound state wavefunctions and matrix elements by the piecewise analytic method
1.R. G. Gordon, J. Chem. Phys. 51, 14 (1969).
2.R. G. Gordon in Methods in Computational Physics, edited by B. Alder, S. Fernbach, and M. Rotenberg (Academic, New York, 1971), Vol. 10, p. 81.
3.A. M. Dunker and R. G. Gordon, J. Chem. Phys. (to be published).
4.A. M. Dunker and R. G. Gordon, J. Chem. Phys. 64, 354 (1976).
5.A. R. W. McKellar and H. L. Welsh, J. Chem. Phys. 55, 595 (1971);
5.A. R. W. McKellar and H. L. Welsh, Can J. Phys. 50, 1458 (1972).
6.W. B. Neilsen and R. G. Gordon, J. Chem. Phys. 58, 4131, 4149 (1973).
7.S. E. Novick, P. Davies, S. J. Harris, and W. Klemperer, J. Chem. Phys. 59, 2273 (1973).
8.M. Abramowitz and I. A. Stegun, Nat. Bur. Stand. Appl. Math. Ser. 55, 446 (1964).
9.The Wronskian is readily shown to be independent of R.
10.J. H. Wilkinson, The Algebraic Eigenvalue Problem (Oxford U.P., Oxford, 1965), p. 233.
11.if is the mth row of then is defined by where q depends on the elements of
12.See, for example, P. Henrici, Elements of Numerical Analysis (Wiley, New York, 1964), p. 198 ff;
12.G. K. Kristiansen, Nord. Tidskr. Informationsbehandlung 3, 205 (1963).
13.G. E. Forsythe and C. B. Moler, Computer Solution of Linear Algebraic Systems (Prentice‐Hall, Englewood Cliffs, NJ, 1967), Chap. 15.
14.Reference 10, p. 619 ff.
15.G. Golub and C. Reinsch, Numer. Math. 14, 403 (1970);
15.G. Golub and W. Kahan, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 2, 205 (1965);
15.P. A. Businger and G. H. Golub, Collected Algorithms from CACM, Algorithm 358.
16.In searching for an eigenvalue it was convenient and trivial to eliminate the effect of the B matrices on detM by dividing the latter by the appropriate detB factors. However, we do not actually remove the B matrices from the M matrix and, therefore, the B matrices must be considered when the wavefunction is determined.
17.The authors acknowledge several conversations with Dr. Moshe Shapiro on this method.
18.B. Numerov, Publ. Obs. Central Astrophys. Russ. 2, 188 (1933);
18.J. W. Cooley, J. Math. Comp. 15, 363 (1961).
19.R. G. Gordon and J. K. Cashion, J. Chem. Phys. 44, 1190 (1966).
20.A. Rosenthal and R. G. Gordon, J. Chem. Phys. 64, 1621 (1976).
21.LeRoy and Van Kranendonk, Ref. 26, also used a least squares technique in their study of these systems, but their procedure was specialized in a different manner to handle the type of potential and eigenvalue algorithm they chose.
22.The best choice is a shifted tangent approximation of the type used in Eq. (2.7).
23.H. Hellmann, Einführung in die Quantenchemie, (Deuticke, Leipzig, 1937);
23.R. P. Feynman, Phys. Rev. 56, 340 (1939).
24.The programs were written for IBM System 360 computers. Most of the calculations are done in standard precision, a maximum of seven digits. However, the matrix multiplications for the propagation of and are performed in double precision, a maximum of 16 digits, since we chose the inward method of obtaining the wavefunction. (See the Appendix).
25.J. E. Rosenthal, Proc. Natl. Acad. Sci. USA 21, 281 (1935);
25.H. S. Heaps and G. Herzberg, Z. Phys. 133, 48 (1952).
26.R. J. Le Roy and J. Van Kranendonk, J. Chem. Phys. 61, 4750 (1974).
27.R. J. Le Roy (private communication). He has kindly supplied the eigenvalues given in Table II.
28.This is analogous to the situation in perturbation theory where knowledge of the wavefunction through kth order determines the eigenvalue to ‐th order.
29.A. C. Allison, J. Comp. Phys. 6, 378 (1970).
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