University of Chicago Laboratory of Molecular Structure and Spectra Technical Report: 1968 Page: 58
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desire value, E(0) )was set as the upper (lower) bound for E and the
V
cycle was repeated. Usually after a few iterations one arrives
at a trial eigenvalue, say E(n), that gives the correct number
of nodes. Then Cooley's correction formula can be used to yield
an improved eigenvalue E(n+l) = E(n) + DE. If E(n) + DE lies
outside the bounds, Q1 and Q2, which may happen if one has still
a poor approximation to the solution, E(n) can be usedl9 to give
a better estimate for the bounds: for positive (negative) DE, E(n)
represents a lower (upper) bound for E and therefore as the
next estimate for Ev one may take E(n+1) = (Q1 + Q2)/2 with Q1
or Q2 equal to E(n). If, however, E (n) + DE is within the bounds
the repeated use of Cooley's formula gives Ev very accurately in
a few iterations. In our computations the process was ended when
-7 -1
E was obtained with an accuracy of 10 a.u. = 0.02 cm i.e.
v
-l
when the last computed DE was below 0.02 cm in absolute value.
The above scheme using the maximum of I"I given by the
inward integration rather than the relative magnitudes of II
and lXI as the criterion for setting the matching point leads
sometimes to a wrong choice. In consequence one of the two
difficulties may arise:
1. Despite refining the upper and lower bounds for E the
integration fails to give the correct number of nodes in the
wavefunction.
2. Even though the number of nodes is correct and the trial58
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University of Chicago. Laboratory of Molecular Structure and Spectra. University of Chicago Laboratory of Molecular Structure and Spectra Technical Report: 1968, report, 1969~; Chicago, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc228352/m1/68/?q=green+energy: accessed July 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.