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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). |