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319. OSCILL:Matrix Elements of Powers of the
Dimensionless Coordinate for the Non-Degenerate Simple
Harmonic Oscillator and of Powers of the Dimensionless
Radial Coordinate for the 2-Fold or 3-Fold Isotropic
Harmonic Oscillator
by W. H. Shaffer, Department of Physics, Ohio State
University, Columbus, Ohio 43210 and B. J. Krohn, Los
Alamos Scientific Laboratory, University of California,
Los Alamos, New Mexico 97545
Numerical values are computed for (i) matrix elements
of Q ** N for the 1-dimensional simple harmonic
oscillator, with 0 <, N < 12, and (ii) radial matrix
elements of R ** N for the 2-fold or 3-fold isotropic
harmonic oscillator with 0 < N < 7, and the diagonal
element of R ** 8. Simplified closed analytical
formulas for the integrals (ii) have been developed by
the method outlined by Shaffer [Rev. Mod. Phys., 16,
245, (1944)] and expressed in terms of the following
"averaged quantum numbers" by Shaffer and Krohn:
VX = (IV+IW+1)/2.0 for the 1-fold
oscillator
VX = (IV+IW+2)/2.0
for the 2-fold
oscillator
LX = (LV+LW)/2.0
VX = (IV+IW+3)/2.0
for the 3-fold
oscillator
LX = (LV+LW+1)/2.0
The formulas are coded in this program, thus permitting
direct computation of the exact values (to single-
precision accuracy) and rapid construction of large
matrices such as those occurring in some molecular
vibration problems.
FORTRAN IV (CDC 6000/7000)
Lines of Code: 498
Recommended Citation: W. H. Shaffer and B. J. Krohn,
QCPE 11, 319 (1976).
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