Magnetic field absence

Fig. 7.1 Diamagnetism of a single electron electron rotation creates current i in the magnetic field absence and the additiraial current 8 is induced by the magnetic field H...

Electrons and most other fiindamental particles have two distinct spin wavefunctions that are degenerate in the absence of an external magnetic field. Associated with these are two abstract states which are eigenfiinctions of the intrinsic spin angular momentum operator S... 

By analogy, one is tempted to make the same division in equation (A2.1.7), regarding the first tenn as the work of creating the magnetic field in the absence of the specimen and the second, f dV(Uo dAT), as the... 

Here we shall consider two simple cases one in which the order parameter is a non-conserved scalar variable and another in which it is a conserved scalar variable. The latter is exemplified by the binary mixture phase separation, and is treated here at much greater length. The fonner occurs in a variety of examples, including some order-disorder transitions and antrferromagnets. The example of the para-ferro transition is one in which the magnetization is a conserved quantity in the absence of an external magnetic field, but becomes non-conserved in its presence. 

FIGURE 13 3 (a) In the absence of an external magnetic field the nuclear spins of the protons are randomly oriented (b) In the presence of an external magnetic field Xq the nuclear spins are oriented so that the resulting nuclear magnetic moments are aligned either parallel or antiparallel to Xq The lower energy orientation is the one parallel to Xq and more nuclei have this orientation... 

In the absence of an electric or magnetic field all the functions with f 0 are (2f + l)-fold degenerate, which means that there are (2f + 1) functions, each having one of the (2f + 1) possible values of m, with the same energy. It is a property of degenerate functions that linear combinations of them are also solutions of the Schrddinger equation. For example, just as IJ2p,i solutions, so are... 

The apphcation of microwave power to gaseous plasmas is also of interest (see Plasma technology). The basic microwave engineering procedure is first to calculate the microwave fields internal to the plasma and then calculate the internal power absorption given the externally appHed fields. The constitutive dielectric parameters are useful in such calculations. In the absence of d-c magnetic fields, the dielectric permittivity, S, of a plasma is given by equation 10 ... 

Magnetic fields introduce hydromagnetic waves, which are transverse modes of ion motion and wave propagation that do not exist in the absence of an apphed B field. The first of these are Alfven, A, waves and their frequency depends on B and p, the mass density. Such waves move parallel to the apphed field having the following velocity ... 

No energy difference in nuclear spin states in absence of external magnetic field... 

In the absence of an external magnetic field, the 21 + 1 energy states of a nucleus are of identical energy (they are said to be degenerate) and, therefore, are equally populated at thermal equilibrium in any assemblage of such nuclei. In the presence of an applied steady field Ho, these 21 + states will assume different energy... 

The total electronic wavefunction is the product of a spatial part and a spin part it is it(r) times a(s) or /3(s) for this one-electron molecule. There are thus two different quantum states having the same spatial part i/r(r). In the absence of a magnetic field, these are degenerate. 

Both correspond to the same energy, in the absence of an external magnetic field. In either case, f s) dr ds = 1 and we call s) the density function pi(x)-... 

There are in principle also energy levels associated with nuclear spins. In the absence of an external magnetic field, these are degenerate and consequently contribute a constant term to the partition function. As nuclear spins do not change during chemical reactions, we will ignore this contribution. 

Figure 13.1 (a) Nuclear spins are oriented randomly in the absence of an external magnetic field but (b) have a specific orientation in the presence of an external field, B0. Some of the spins (red) are aligned parallel to the external field while others (blue) are antiparallel. The parallel spin state is slightly lower in energy and therefore favored. 

In the presence of the magnetic field three components are observed, the n component having the same energy as the transition in the absence of the... 

Pauli justified the identification of four quantum numbers with each electron with the following apparently clever argument. He supposed that if a strong magnetic field is applied, the electrons are decoupled and so do not interact, and can be said to be in individual stationary states. Of course, the periodic table arrangement must also apply in the absence of a magnetic field. 

Figure 5-2. In the absence of an applied magnetic field a), the molecular magnetic dipoles are randomly oriented on application of an external field b), the dipoles tend to orientate parallel to the field.

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