Field operator position

BPCS/SIS functions that produce a trend analysis of input and output functions. Graphic video displays set-up to indicate process conditions and valve positions assure that the status of the process conditions is announced to the board operator, who may then verify the conditions with the field operator. 

Emily said to Elizabeth, Thank you so much for taking the time to show me where a pharmacist can aspire to within our company. This really helps me understand our company better, and I would love to work more in the field operator s position. ... 

The relation between the positive frequency part of the electric field operator at a point R RR in the far-field zone of the radiating systems and the dipole moments is given by the well-known expression [4,20]... 

The atoms interact with the quantized three-dimensional vacuum field and are also driven by a single-mode coherent laser field. We express the quantized multimode field in terms of the annihilation and creation operators and a x of field mode kr, which has wavevector k, frequency cd., and polarization ets. Thus, we write the electric field operator at position r in the form... 

The positive-frequency part of the electric field operator 1 has the form... 

Consider first the ligand-field operator, Eq. (60). Owing to the molecular S5nnmetry and to the position of the coordinate system, one has... 

The Furry bound state interaction picture of quantum electrodynamics76 relies on an expansion of the second-quantized electron field operator in terms of single-particle solutions of the Dirac equation for a static external field. This external field may be thought of as some mean atomic or molecular potential, whose single-particle spectrum can be divided into positive- and negative-energy branches. This can always be done for the usual elements of the Periodic Table, although problems arise for super-heavy atomic nuclei. 

Now let us turn to the pair of rods that are maintained at a negative dc voltage. In the absence of the ac field, all positive ions will tend to be drawn to the rods, where they are annihilated. For the lighter ions, how-ever, this movement may be offset by the excursion of the ac voltage. Thus, as shown in Figure 11-8b. the rods in the yz plane operate as a low-pass filter. 

Thereby, d is the material dipole operator. The positive frequency component of the electric field operator is denoted by... 

Field-dependent basis orbitals as vj (r, G, B) — Uj (f) exp(- (BxG)-f) should be used, resulting in a similar transformation of the electron field operators. Such field-dependent orbitals would guarantee gauge origin independence even in a finite basis. In this expression, G is the position of orbital Uj with respect to an arbitrary origin and the electron coordinate r is given in the same coordinate system. Usually the atomic orbitals are centered at the nuclear positions. In such cases, Rg takes the place of G for the orbital Vj f, Rg, By. 

Quantum mechanics taJces many different guises. For instance, one can use a Hilbert space realination in terms of time-dependent wavefunctions ( 1, 2,- of an 7V-particle system, where = (r, C) is a compound configuration space and spin variable for a particle. Operators acting on this Hilbert space are obtained by making the common identifications p —ihV for the momentum and f— fioi position vector of a particle, which can be referred to as first quantization, producing quantum mechanical operators out of classical expressions. One can equally well use time-dependent field operators (so-called second quantization) tp, t) and their adjoints build Hilbert spaces (or rather... 

Here, q is the density operator for the field, and E and E represent the negative- and positive-frequency portions of the electric field operator , respectively. We assume that the final state of the detector is much broader than the bandwidth of the incident radiation, and that a broad band of final states is accessible [7.36, 37]. 

If we specifically consider the mixing of two single-mode, amplitude-stabilized, first-order coherent waves, both of which are well collimated, parallel, plane polarized along a common unit vector, and normally incident onto a photosensitive material, we may write the positive portion of the electric field operator as the superposition of two scalar fields... 

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