Two new numerical methods, the log derivative and the renormalized Numerov, are developed and applied to the calculation of bound-state solutions of the one-dimensional Schroedinger equation. They are efficient and stable; no convergence difficulties are encountered with double minimum potentials. A useful interpolation formula for calculating eigenfunctions at nongrid points is also derived. Results of example calculations are presented and discussed.
We have observed narrow, distinct resonances in the NMR spectrum of dilute spinpolarized atomic hydrogen gas (n-10' atoms/cm'). The dependence of the observed spectra on temperature, density, polarization, and magnetic field gradient is consistent with theoretical predictions for spin-wave excitations damped by diffusion. We have measured the parameter p, , which is a measure of the importance of exchange effects in spin-transport processes, and the diffusion coefficient Do, both of which are in reasonable agreement with theory.
The dynamics of the reaction O+H2(v) →OH+H is studied by means of three dimensional classical trajectory calculations on an LEPS potential energy surface. Rate constants are calculated for the two cases in which the H2 molecule is initially in the v=0 and v=1 vibrational state. In the temperature range 298–1000 °K these rates are fit very well by the formulas (cm3 molecule−1 sec−1) k=2.81T×10−14 exp(−4279/T) and k=4.65T×10−14 exp(−1868/T). The calculated value of k at 300 °K is 2.8×10−14 cm3 molecule−1 sec−1 which is below the upper bound established by Birely [J. H. Birely, J.V.V. Kasper, F. Hai, and L. A. Darnton, Chem. Phys. Lett. 31, 220 (1975)]. The branching ratio Γ, defined as the ratio of the rates for populating the v′=1 and v′=0 state of OH when H2 is initially in the v=1 state is also calculated and fit by the expression Γ=2.3 exp(196/T). The value at 300 °K is 4.4.
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