Thus, the quantum mechanical and classical mechanical treatments of nuclear magnetic resonance closely correspond, as has been demonstrated mathematically [ ] [Pg.9]

The name random phase approximation comes from a classical mechanical treatment of the collective properties of the electron gas by Bohm and Pines in the eaxly 1950s. [Pg.709]

A quantum-mechanical treatment has been given for the coherent excitation and detection of excited-state molecular vibrations by optical absorption of ultrashort excitation and probe pulses [66]. Here we present a simplified classical-mechanical treatment that is sufficient to explain the central experimental observations. The excited-state vibrations are described as damped harmonic oscillations [i.e., by Eq. (11) with no driving term but with initial condition Q(0) < 0.] We consider the effects of coherent vibrational oscillations in Si on the optical density OD i at a single wavelength k within the Sq -> Si absorption spectrum. Due to absorption from Sq to Si and stimulated emission from Si and Sq, [Pg.22]

Finally, we note that although all of the discussion in this section has applied to a completely classical mechanical treatment of the reaction, the expression for the cumulative reaction probability can be quantized in the usual ad hoc fasion in statistical theory by replacing the classical flux of equation (21) by the quantum mechanical integral density of states [Pg.278]

The kind of quantum mechanical studies described in the previous sections can be performed only for tri- or at most tetratomics. For larger systems, a classical mechanics treatment is the only alternative beyond statistical approaches. The general aspects of classical dynamics studies and several examples will be discussed in this section. [Pg.205]

Thus, this completely wave mechanical development leads to a picture in which pi is a vector with fixed z component but x and y components that vary sinusoidally, 90° out of phase—i.e., executing a circular motion, as shown in Fig. 2.2. Overall, then, the motion is a precession about the magnetic field axis and is similar to that which would have been obtained from a classical mechanical treatment [Pg.25]

© 2019 chempedia.info