Kinetic momentum

Further support to the model should be found by examining the values of F], as deduced from AC or DB measurements since p-Ps annihilates in an intrinsic mode, this parameter should reflect directly the average Ps kinetic momentum. However, the data on F, are usually poorly defined [61, 64], so that the correlation with y is more conveniently sought using experimental values of r3, provided that the momentum distribution of the valence electrons participating in the o-Ps pick-off annihilation is reasonably solvent independent. Such a correlation has been effectively found for a variety of solvents at various temperatures [61], leading to ... 

Modern inelastic neutron scattering technique has made it possible to discover free protons in solids [49] that is, free protons have been found in manganese dioxides, coals, graphite nitric acid intercalation compounds, polypyrolles and polyanilines, and fi-alumina. Perhaps the said compounds may be called protonic conductors as well, though in the solids the density of free protons is very small and the distribution of proton kinetic momentum is hidden by the zero-point oscillations of the host matrix [49]. 

Here k = (a>/c)k defines the propagation direction of the laser beam. Employing the relation between the canonical momentum, the principal function S and the kinetic momentum of the electron, i.e. n = VS = p — ([Pg.12]

The energy and the kinetic momentum of the electron derived above are both consistent with the initial conditions. 

This corresponds to the principle of minimal coupling, according to which the interaction with a magnetic field is described by replacing in the Hamiltonian operator the canonical momentum p by the kinetic momentum 11 = p — f A(x). Other types of external-field interactions include scalar or pseudoscalar fields and anomalous magnetic moment interactions. The classification of external fields rests on the behavior of the Dirac equation rmder Lorentz transformations. A brief description of these potential matrices will be given below. 

For the computation of the second derivatives given in Eq. (6.8) for the shielding tensor, it is necessary to specify the molecular (electronic) Hamiltonian H in the presence of a magnetic field. The latter is obtained by replacing the canonical momentum p in the kinetic energy part of H by the kinetic momentum n... 

Which is quite equivalent with the phenomenological deduction in Eq. (1.79) when considering also length-radius connection from (4.150) moreover, with the present approach also the kinetic momentum is found quantified since ... 

However, a more rigorous solution of this problem should account for six conservative variables in a binary system, namely, energy, kinetic momentum (three components), the concentration of the solution, and the total density of the liquid. In the general ca.se, it should be taken into account that the solute flux /involves the diflusional and heat fluxes... 

Rotational mechanics Rotation kinetic L (or o) Angular momentum Also called kinetic momentum ... 

In rotational mechanics, the rotation angle 6 is the basic quantity, the torque (or couple) t is the effort, the angular momentum (or kinetic momentum) L (or angular velocity Q is the flow. All these state variables are vectors. (The angle 0 is a vector perpendicular to the plane of rotation, colinear to the angular velocity.)... 

Angular momentum (vector) (or kinetic momentum) [rotational mechanics] Displacement, position, distance (vector) [translational mechanics]... 

The neutron is a dimensionless particle whose kinetic momentum p is related to the de Broglie wavelength Xn as... 

In the ground state Eq = 0. The wavefunction is a constant, for there is no preferred orientation. In the upper states, the kinetic momentum is nonzero and levels at E j = j B are degenerate, as clockwise and anticlockwise rotations are indistinguishable. 

As the m) state is a linear combination of J,Mj) states characterizing the total kinetic momentum, so called Stevens Equivalent Operators have been introduced to calculate these component. For instance, the first component can be rewritten as... 

From classical mechanics (e.g., Goldstein 1950), we can show that the presence of a vector potential requires that the Hamiltonian function must be constructed using the kinetic momentum (or mechanical momentum), which is the momentum that is given in nonrelativistic theory by m. We must express this momentum in terms of the canonical momentum of Lagrangian mechanics, because it is the canonical momentum to which the quantization rule p —ihV applies. Here (and hereafter) we will use p for the canonical momentum and n for the kinetic momentum. The relation between the two is... 

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