Fourier components harmonic oscillators

As was shown by Bohm and Pines,90 under certain conditions the equations of motion for a Fourier component of the electron density can be reduced to harmonic-oscillation equations with the frequency depending only on the density of electrons ne ... 

The Fourier component of interaction force F(t) on the transition frequency (2-184) characterizes the level of resonance. Matrix elements for harmonic oscillators m y n) are non-zero only for one-quantum transitions, n = m . The W relaxation probability of the one-quantum exchange as a function of translational temperature To can be found by averaging the probability over Maxwelhan distribution ... 

Equations (4.60) and (4.61) are also able to yield the vector recurrence relations for the case of a skew bias field, that is, when vectors h and n are not parallel. In this case one should ascribe to each bi as many as 21+1 components, corresponding to different values of the azimuthal index m. Another problem, involving vector recurrence relations, is a steady-state nonlinear oscillations of bi in a high-AC field. To study the harmonic content of the nonlinear response, one has to expand all the moments b t)l in the Fourier series. Then the Fourier coefficients may be treated as components of a... 

When the amplitude of modulation is small, i.e., A(B/B/ < /s, see Fig. 7 (i)(b), the time dependent change in the resistance SR under photoexcitation at frequency / shown in Fig. 7 (i)(a), reflects mostly the time variation of the magnetic field within a phase factor. This situation changes dramatically, however, when the modulation amplitude matches the period of the radiation induced resistance oscillations, see Fig. 6(c), and Fig. 7(ii)(a) and (b). Here, in Fig. 7(ii)(a), the time response of the specimen, i.e., Sl (t), exhibits a strong harmonic component, which is evident both in the Fourier transform (inset. Fig. 7(ii)) and the harmonic band-pass filtered portion of Si (t) (see Fig. 7(ii)(a)). A further increase in the modulation amplitude such that it corresponds to two periods of the radiation induced resistance oscillations (Figs. 6(d) and 7(iii)), leads to the disappearance of the 3 harmonic component, as a 5 harmonic component takes its place, see inset Fig. 7(iii). 

By Fourier transformation, a signal is decomposed into its sine and cosine components [Angl]. In this way, it is analysed in terms of the amplitude and the phase of harmonic waves. Sine and cosine functions are conveniently combined to form a complex exponential, coscot 4- i sinwt = exp icomplex amplitudes of these exponentials constitute the spectrum F((o) of the signal f(t), where co = In IT is the frequency in units of 2n of an oscillation with time period T. The Fourier transformation and its inverse are defined as... 

---