Hamiltonian description

F. Halbwachs, F. Piperno, and J. P. Vigier, Relativistic Hamiltonian description of the classical photon behaviour A basis to interpret aspect s experiments, Lett. Nuovo Cimento 33(11) (1982). 

NMR pulse sequence without getting tied up in the details of pulse phases and a mountain of sine and cosine terms only the essential elements of the sample net magnetization will be described at each point. Finally, the formal Hamiltonian description of solution-state NMR will be described and applied to explain two related phenomena strong coupling ( leaning of multiplets) and TOCSY mixing (the isotropic mixing sequence). 

The most common approach to the interpretation of EPR and Mossbauer spectra of siderophores is the spin Hamiltonian formalism. The wavefimctions are parameterized in terms of a few coupling constants that arise in the spin Hamiltonian description of the electronic states. In this approach, the crystal field potential is generally described by a series of spherical harmonics. The corresponding operators are tabulated. ... 

In this study we have further elaborated and improved our fully symmetrized vibrational Hamiltonian description of ammonia, which was presented in recent work [13]. Our main objective was to develop the molecular 6-D PES in simple analytical form, as a Taylor series expansion in terms of the conventionally defined symmetrized force... 

This has Important consequences for all such model Hamiltonian descriptions used for explaining the high T. ... 

In this section, we introduce the Hamiltonian description of the motion which is useful for discussing the underlying geometric structure associated to classical mechanics. We can understand the Hamiltonian formulation as a natural description of classical mechanics from several perspectives. First, it is based directly on the... 

A Hamiltonian description of the motion may be formulated in either system of notation. The Hamiltonian formulation with rotation matrices involves variables 9cm,Pern (phase space variables describing the center of mass motion) and O, n, which are 3 X 3 matrices. The Hamiltonian is (for a single rigid body) ... 

The microcanonical ensemble, which we have already gently introduced in a simplified setting in the previous chapter, is defined by constant number of particles N, volume V and total energy E. We assume that all systems of the ensemble evolve independently and are isolated from each other. If a Hamiltonian description is used, the first and third invariances are automatically maintained in a molecular... 

In the spin Hamiltonian description, the presence of double exchange can be described by the introduction of a new parameter ... 

The Hamiltonian description of the magnetic dipole hyperfine interactions is given by,... 

Based on the definition (3.4) let us find the equations enabling to calculate the time profiles of values in a suitable form. Here as a basis is accepted the method of value calculation through the eonjugated functions [14] by using the Hamiltonian description of dynamic systems with marking out target characteristics. 

At this point, we introduce the Hamiltonian description of the system and corresponding form of the optimum theorem. This is done firstly because the Hamiltonian is a concise way to express the state and costate equations. But, more than this conciseness, it turns out that the Hamilton density itself has an interesting and useful property in the optimum system. 

Computer synthesis of EPR spectra from a parametric spin Hamiltonian. Description of programs (MAGNSPEC). 

All phenomena of classical nonrelativistic mechanics are solely based on Newton s laws of motion, which are valid in any inertial frame of reference. The natural symmetry operations of classical mechanics are the Galilean transformations, mediating the transition from one inertial coordinate system to another. The fundamental laws of classical mechanics can equally well be formulated applying the elegant Lagrangian and Hamiltonian descriptions based on Hamilton s action principle. Maxwell s equations for electric and magnetic fields are introduced as the basic laws of classical electrodynamics. 

Fokker-Planck operator, the first term in eqn (13.11). This result is in line with the common sense view that the Hamiltonian description at microscopic level can be replaced by the free energy and entropy description in non-equilibrium statistical dynamics. 

An assembly of nuclei and electrons could be described very accurately within QED. There would still just be a cluster of particles, our molecule, and any structure would have to arise out of the dynamics of the system. For reasons pointed out earlier, QED—if viable at all— would be a very expensive path to calculation of the electronic stracture and chemical properties of molecules. For electrons, we circumvented this problem by going to a many-particle treatment based on the Dirac equation, as discussed in chapter 5, and we could presumably do the same here for our cluster of electrons and nuclei. In doing this, we choose a Hamiltonian description of the system, but alternative approaches based on a Lagrangian formalism are also possible. In this process we draw a formal distinction between the molecule and the electromagnetic field, which leaves us with the normal Coulomb interactions between the particles in the molecule and the radiation field as an entity external to the molecule. 

The characteristic feature of this level of description is to allow for a complete hamiltonian description of the forces ... 

At the Mac-Millan Mayer level we have to introduce solute-solvent interactions in a non hamiltonian description. 

M. Sofer H. Brauchli, Hamiltonian Description of Holonomically Constrained Multibody Systems (submitted for publication). 

By use of the Hamiltonian description established in this subsection, it can be shown that the Hamiltonian equations are equivalent to the more familiar Newton s second law of motion in Newtonian mechanics, adopting a transformation procedure similar to the one used assessing the Lagrangian equations. In this case we set qi = Ti and substitute both the Hamiltonian function H (2.24) and subsequently the Lagrangian function L (2.6) into one of Hamilton s equations of motion (2.29). The preliminary results can be expressed as ... 

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