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Journal of Physics B Atomic and Molecular Physics

Generalized bloch equations for any multipole

Peter X. Hammerling

Published Sep 1, 1968• 2 citations
Publisher

Abstract

A generalization of the Bloch equations for a spin ½ particle to those valid for any multipole is obtained by use of tensor operator techniques. As an application of the Bloch-type formalism, we discuss the interaction of coherent and incoherent light with a gas in a magnetic field as contrasted with the description of a Zeeman laser.
DOI
10.1088/0022-3700/1/5/301

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After publishing the derivation from the classical Bloch equation to the quantum von Neumann equation to the Schrdinger-Pauli equation for spin-12\tfrac{1}{2}21​, we proposed renaming the Bloch equation to the Majorana-Bloch equation because Majorana's work predated Bloch's in the presentation of the Bloch equation by 14 years. Here, we first generalize our previous derivation to higher spins or angular momenta in coherent pure states. Using the polynomial representation of the coherent-state projector, we derive an invertible mapping from the Majorana-Bloch equation to the von Neumann equation, establishing a one-to-one correspondence between these two formalisms. Application of the Ehrenfest theorem also shows that expectation values in these states reproduce the classical equation of motion as expected. Then, we obtain arbitrary spin-sss states by symmetrizing tensor products of spin-12\tfrac{1}{2}21​ primitives, in accordance with the Majorana construction or the Schur-Weyl duality.