Topic
Spin-½
About: Spin-½ is a research topic. Over the lifetime, 40423 publications have been published within this topic receiving 796639 citations.
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TL;DR: A theoretical analysis of the excitation spectrum of long-chain polyenes is presented in this paper, where one electronic state is localized at the gap center for each soliton or antisoliton present and the soliton's energy of formation, length, mass, activation energy for motion, and electronic properties are calculated.
Abstract: A theoretical analysis of the excitation spectrum of long-chain polyenes is presented. Because of the twofold degeneracy of the ground state of the dimerized chain, elementary excitations corresponding to topological solitons are obtained. The solitons can have three charge states $Q=0$. $\ifmmode\pm\else\textpm\fi{}e$. The neutral soliton has spin one-half while the charged solitons have spin zero. One electronic state is localized at the gap center for each soliton or antisoliton present. The soliton's energy of formation, length, mass, activation energy for motion, and electronic properties are calculated. These results are compared with experiment.
2,276 citations
TL;DR: It is found that the usual measuring procedure for preselected and postselected ensembles of quantum systems gives unusual results and under some natural conditions of weakness of the measurement, its result consistently defines a new kind of value for a quantum variable, which is called the weak value.
Abstract: We have found that the usual measuring procedure for preselected and postselected ensembles of quantum systems gives unusual results. Under some natural conditions of weakness of the measurement, its result consistently defines a new kind of value for a quantum variable, which we call the weak value. A description of the measurement of the weak value of a component of a spin for an ensemble of preselected and postselected spin-(1/2 particles is presented.
2,224 citations
Book•
01 Jan 1971
TL;DR: In this paper, one-body problems without spin are discussed. And the Wentzel-Kramers Brillouin (WKB) approximation of the WKB is used.
Abstract: Part I: One-Body Problems without Spin. One-Dimensional Problems. Problems of Two or Three Degrees of Freedom without Spherical Symmetry. The Angular Momentum. Potentials of Spherical Symmetry. The Wentzel-Kramers Brillouin (WKB) Approximation. The Magnetic Field.- Part II: Particles with Spin. One-Body Problems. Two-and Three-Body Problems. Many-Body Problems. Few Particles. Very Many Particles: Quantum Statistics. Non-Stationary Problems. The Relativistic Dirac Equation. Radiation Theory. Mathematical Appendix.
2,196 citations
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TL;DR: In solid-state materials with strong relativistic spin-orbit coupling, charge currents generate transverse spin currents as discussed by the authors and the associated spin Hall and inverse spin Hall effects distinguish between charge and spin current where electron charge is a conserved quantity but its spin direction is not.
Abstract: In solid-state materials with strong relativistic spin-orbit coupling, charge currents generate transverse spin currents. The associated spin Hall and inverse spin Hall effects distinguish between charge and spin current where electron charge is a conserved quantity but its spin direction is not. This review provides a theoretical and experimental treatment of this subfield of spintronics, beginning with distinct microscopic mechanisms seen in ferromagnets and concluding with a discussion of optical-, transport-, and magnetization-dynamics-based experiments closely linked to the microscopic and phenomenological theories presented.
2,178 citations
TL;DR: In this article, the second moment of the frequency deviation of the absorption line of the electron was calculated and the fourth moment was also computed to examine how good an approximation is the conventional assumption of a Gaussian shape.
Abstract: In regular crystals, the width of the absorption lines arising from the magnetic moment of the electron or nucleus is caused primarily by the interaction between the magnetic dipoles. It is prohibitively difficult to determine the precise shape of the absorption line theoretically, but the invariance of the diagonal sum in quantum mechanics permits the calculation of the second moment of the frequency deviation, and hence the r.m.s. line breadth. The latter agrees excellently with the observations of Pake and Purcell on the magnetic absorption of the F nucleus in Ca${\mathrm{F}}_{2}$, both in absolute magnitude, and in the dependence on the direction between the magnetic field and the principal cubic axes. The fourth moment was also computed to examine how good an approximation is the conventional assumption of a Gaussian shape. As long as no exchange is present (the nuclear case) the Gaussian model is moderately good. For the 100 direction in a cubic crystal, the theoretical ratio of root mean fourth to root mean square breadth is 1.25. Pake and Purcell's measurements yield 1.24. A Gaussian model would require 1.32. The theory is extended to include crystals with two kinds of spin moments (two types of nuclei, or simultaneous nuclear and electronic spin). Coupling between unlike moments is less effective (by a factor ⅔ in the r.m.s. width) than that between like in broadening the lines.In the paramagnetic absorption caused by electronic spin, it is imperative to include the effect of exchange coupling. This interaction does not contribute to the second moment, but greatly increases the fourth. As a result, the lines are peaked much more sharply than one would compute from the second moment with the Gaussian model for line shape. This "exchange narrowing" explains why microwave paramagnetic absorption lines are much narrower than one first conjectures from the amount of dipolar coupling.The theoretical calculations are given in Sections II-IV. The final sections V-VI give the comparison with the experiments of Pake and Purcell, and with the model of Bloembergen, Purcell, and Pound, for r-f absorption in liquids.
2,139 citations