Kavli Affiliate: Lihong V. Wang
| First 5 Authors: Lihong V. Wang, Lihong V. Wang, , ,
| Summary:
After publishing the derivation from the classical Bloch equation to the
quantum von Neumann equation to the Schr"dinger-Pauli equation for
spin-$tfrac12$, 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-$s$ states by symmetrizing tensor products of
spin-$tfrac12$ primitives, in accordance with the Majorana construction or
the Schur-Weyl duality.
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