Interaction Hamiltonian field

In order to evaluate equation B1.2.6, we will consider the electric field to be in the z-direction, and express the interaction Hamiltonian as... 

Equations (ll-377)-(ll-381) for the field operators entail that under time inversion the interaction hamiltonian transforms like a scalar... 

The basic physics governing the measurement of the EDM in all types of electrically neutral systems is almost the same as discussed in this section. If the system under consideration has a magnetic moment p and is exposed to a magnetic field B, then the interaction Hamiltonian can be written... 

If the system under consideration also possesses an electric dipole moment d and is exposed to an electric field then the interaction Hamiltonian can be written... 

If the transition is of an electric dipole nature, the interaction Hamiltonian can be written as // = p E, where p is the electric dipole moment and E is the electric field of the radiation. The electric dipole moment is given by p =, where r is the... 

Provided that a transition is forbidden by an electric dipole process, it is still possible to observe absorption or emission bands induced by a magnetic dipole transition. In this case, the transition proceeds because of the interaction of the center with the magnetic field of the incident radiation. The interaction Hamiltonian is now written as // = Um B, where is the magnetic dipole moment and B is the magnetic field of the radiation. 

The interaction Hamiltonian contains the operator A, corresponding to the vector potential A of the electromagnetic field.2 Excluding magnetic scattering, the interaction Hamiltonian is given by... 

When the electric field gradient at the nucleus exerted by the electrons is nonzero, the nuclear levels will be split. The eigenvalues of the quadrupolar interaction Hamiltonian are given by... 

This interaction Hamiltonian describes the fe-phonon emission due to a periodical local field. 

As said before, the nonlinear nature of the effective Hamiltonian implies that the Effective Schrodinger Equation (1.107) must be solved by an iterative process. The procedure, which represents the essence of any QM continuum solvation method, terminates when a convergence between the interaction reaction field of the solvent and the charge distribution of the solute is reached. 

The interaction Hamiltonian V(f) of each molecule with the monochromatic electric field of angular frequency go and of strength E° is... 

This operator acts only on the electron-positron and electromagnetic field variables. The normal ordered form of Hm taken in the interaction representation must be added to the interaction Hamiltonian. It gives additional elements to the... 

When the external field frequency is far off-resonant with respect to the optical transition, the field-matter interaction can be described by the effective interaction Hamiltonian given by... 

Except for some quadrupolar effects, all the interactions mentioned are small compared with the Zeeman interaction between the nuclear spin and the applied magnetic field, which was discussed in detail in Chapter 2. Under these circumstances, the interaction may be treated as a perturbation, and the first-order modifications to energy levels then arise only from terms in the Hamiltonian that commute with the Zeeman Hamiltonian. This portion of the interaction Hamiltonian is often called the secular part of the Hamiltonian, and the Hamiltonian is said to be truncated when nonsecular terms are dropped. This secular approximation often simplifies calculations and is an excellent approximation except for large quadrupolar interactions, where second-order terms become important. 

The model Hamiltonian [Eq. (3)] defined on a continuum has some exact solutions [35]. These have culminated in what is now known as the bosonization technique, in which the interacting fermion fields can be expressed in terms of boson field operators. This method is reviewed in Refs. 15, 16, and 31. 

If the molecule in its ground state is subjected to a coupling with a time-dependent field with the interaction hamiltonian ... 

It is expedient to represent this interaction Hamiltonian as a series of terms in which the electromagnetic multipoles are coupled with the external fields and their derivatives taken at the origin of the coordinate system. 

Raab [30] has shown the inadequacies of this procedure, which, in the case of dynamic fields, cannot be extended beyond the quadrupole terms and may lead to inconsistencies with the interaction Hamiltonian (7). Accordingly, we retain here definition (34) within the limits of the quadrupole approximation. To higher order only the set of nontraceless moments (22)-(27) can be properly used. 

This result may be re-expressed in terms of H°, the usual field-free Hamiltonian, and H an interaction Hamiltonian, as... 

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