Magnetic moment quantization

Some years later a more thorough discussion of the motion of pairs of electrons in a metal was given by Cooper,7 as well as by Abrikosov8 and Gor kov,9 who emphasized that the effective charge in superconductivity is 2e, rather than e. The quantization of flux in units hc/2e in superconducting metals has been verified by direct experimental measurement of the magnetic moments induced in thin films.10 Cooper s discussion of the motion of electron pairs in interaction with phonons led to the development of the Bardeen-Cooper-Schrieffer (BCS) theory, which has introduced great clarification in the field of superconductivity.2... 

When a magnetic field is applied to an electron or nuclear spin, the spin quantization axis is defined by the field direction. Spin magnetic moments... 

In contrast to ESR spectroscopy, which can only be used to study species with unpaired electrons, NMR spectroscopy is applicable to the investigation of all polymer samples. Nuclei with non-zero total nuclear spin (e.g., 1H, l3C, 19F, 14N) will have a magnetic moment which will interact with an external magnetic field resulting in quantized energy levels. Transitions between these energy levels form the basis of NMR spectroscopy. 1H and 13C... 

In addition, a relativistic treatment of the electron introduces a fourth quantum number, the spin, m, with ms = j. This is because every electron has associated with it a magnetic moment which it quantized in one of two possible orientations parallel with or opposite to an applied magnetic field. 

The Point Charge Concept and the Related Divergence Quantized Charged Equilibrium B.4.1. Conditions on Spin and Magnetic Moment... 

The first- and second-order Zeeman effect coefficients in the expansion of equation (62) are defined by the quantum numbers which specify the atomic energy level. They are in general a function of the direction of the magnetic field with respect to the axis of quantization of the wave functions. They are obtained by the use of the magnetic moment operator for the appropriate direction, q = x,y ox z ... 

The presence of magnetic moments /lia, b, of nuclei A,B,... in a molecule are responsible for the two observables of the NMR experiment that are most frequently utilized in chemical applications. They are physically observed in form of quantized energy differences AE that can be measured very precisely. These two observables are the nuclear shielding tensor cr for nucleus A and the so-called indirect reduced coupling tensor KAB for a pair of nuclei A,B. Both crA and Kab are second-rank tensors that are defined via the phenomenological Hamiltonians... 

Apart from the assumed quantization of orbital angular momentum the Bohr model predicted the quantization of electronic energy, radius, velocity and magnetic moment of atoms ... 

Both the orbital and the effective spinning motions of the electron have associated angular moments quantized in units of ii = 1.055 x 10-34 Js. It is an elementary exercise in physics to show that the relationship between the magnetic dipole moment /< and the angular momentum L for a moving particle of mass m and charge Q is... 

The results of the Stern-Gerlach experiment were in complete contradiction to the classical interpretation and its predictions. Silver atoms turned out to possess a magnetic moment, but instead of a single, smeared-out distribution, two spots centered around Mup and Mdown were observed. Thus the magnetic moment of a silver atom is space-quantized by an inhomogeneous magnetic field, and this magnetic moment can adopt only two values, hz Hhl ... 

Let us first consider the normal Zeeman effect, which applies to transitions between electronic states with zero total spin magnetic moment, so-called singlet states. Like the projection Ms of S in the Stern-Gerlach experiment, the projection Ml of the spatial angular momentum L is space quantized in the external magnetic field. We shall describe the quantization of the spatial angular momentum by means of quantum mechanical methods in detail later. Suffice it to say that each state with spatial angular momentum quantum number L splits into 2L + 1 components, i.e., a P state (L = 1) splits into three components with... 

For pulsed n.m.r., the quantum-theoretical concept of 21 + 1 discrete, nuclear energy-levels (I is the spin-quantum number) produced by quantization of individual, nuclear, magnetic moments along the z axis is less useful than for c.w.-n.m.r., and therefore pulsed n.m.r. is usually described, both experimentally and theoretically, in terms of a continuum of extensive, spatial manipulations of the macroscopic magnetization-vector, in a classical, mechanical sense. 

In the majority of heteroaromatic radicals the unpaired electron is in a fully delocalized molecular 7t-orbital. The magnetic moment of the unpaired electron is quantized in an applied magnetic field, which fact gives rise to... 

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