Oscillators field operators

Another useful realization obtains in terms of the oscillator field operator... 

The most simple way to accomplish this objective is to correct the external field operator post factum, as was repeatedly done in magnetic resonance theory, e.g. in [39]. Unfortunately this method is inapplicable to systems with an unrestricted energy spectrum. Neither can one use the method utilizing the Landau-Teller formula for an equidistant energy spectrum of the harmonic oscillator. In this simplest case one need correct... 

The oscillating field adds a time-dependent term to the Hamiltonian operator for the electron. To an approximation that often proves acceptable, we can write the perturbation as the dot product of E with the dipole operator, p ... 

The same considerations can be expressed in the framework of the SCRF formalism this means reconsidering equations (1) and (2) when an explicit time dependence is introduced. Actually, the introduction of this time dependence can be realized in two different ways. First, we can take into account an external oscillating field which acts as a time-dependent perturbation operator, V (t), to be added to the standard one due to the solvent (Vim). Secondly, the introduction of time may derive from the varying field induced by a solute system which undergoes a chemical reaction, in this case the solute Hamiltonian, and consequently also the solvent perturbator, which depends on time. The effective Hamiltonians corresponding to the two different systems are shown below ... 

An increase in conductance of strong electrolytes is also observed with high-frequency fields operating at frequencies greater than 5 megacycles per second. At such frequencies, a central ion oscillates at a frequency comparable to the relaxation time of the atmosphere. The relaxation effect thus becomes smaller the larger the frequency and the conductance rises. The electrophoretic effect remains unchanged. 

Although use of the density operator does not solve dissipative decay problems, it is still very useful in other areas such as nonlinear spectroscopy [33]. The starting point is very similar to Eq. (9.53), but now the field E(t) is not influenced by the quantum system. It is just an oscillating field that oscillates with the frequency of light... 

The original method employed was to scan eitiier the frequency of the exciting oscillator or to scan the applied magnetic field until resonant absorption occiined. Flowever, compared to simultaneous excitation of a wide range of frequencies by a short RF pulse, the scanned approach is a very time-inefficient way of recording the spectrum. Flence, with the advent of computers that could be dedicated to spectrometers and efficient Fourier transfomi (FT) algoritluns, pulsed FT NMR became the nomial mode of operation. 

Hermitian operators for electric and magnetic field intensities, 561 Herzfeld, C. M., 768 Hessenberg form, 73 Hessenberg method, 75 Heteroperiodic oscillation, 372 Hilbert space abstract, 426... 

It is well known that by inserting an optical amplifier obtained by population inversion in an optical cavity, one can realize sources of coherent radiations, namely lasers. One can operate in the same way with parametric amphfication as shown on Fig. 1. A nonlinear crystal illuminated by an input pump is inserted in an optical cavity. This cavity is represented for convenience as a ring cavity but consists usually of a linear cavity. An important difference with the laser is that there are three different fields, insfead of one, which are presenf in the amplifying medium, all these fields being able to be recycled by the cavity mirrors. One obtain thus different types of "Optical Parametric Oscillators" or OPOs. 

If an electric held of the proper frequency is applied across the quartz crystal, the crystal wiU oscillate in a mechanically resonant mode. These condihons correspond to the creation of a standing acoustic shear wave that has a node midpoint between the two faces of the crystal and two antinodes at both faces of the disk. This is depicted schematically in Eig. 21.20b. In an EQCM experiment the crystals are operated at the fundamental resonant frequency that is a function of the thickness of the crystal. A crystal with a thickness of 330pm has a resonant frequency of 5 MHz. Crystals with these characteristics are commercially available. In an EQCM experiment, an alternating electric field of 5 MHz is applied to excite the quartz crystal into... 

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