Derivation from (classical) Bloch equation to von Neumann equation to Schrödinger–Pauli equation

Lihong V. Wang

doi:10.1117/12.2693007

13 March 2024 Derivation from (classical) Bloch equation to von Neumann equation to Schrödinger–Pauli equation

Lihong V. Wang

Proceedings Volume PC12912, Quantum Sensing, Imaging, and Precision Metrology II; PC129123G (2024) https://doi.org/10.1117/12.2693007
Event: SPIE Quantum West, 2024, San Francisco, California, United States

Abstract

The Schrödinger equation, as a postulate, is a corner stone in quantum mechanics. The transition from classical physics to quantum mechanics, however, remains a mystery. In classical electrodynamics, the motion of the magnetic dipole moment of an electron is governed by the Bloch equation. Majorana stated that both the classical and the quantum-mechanical treatments on spin flip of atoms moving in a magnetic quadrupole field require integration of the same differential equations. Surprisingly, Majorana wrote the “Bloch” equation fourteen years before Bloch published his eponymous equation. Here, the classical Bloch equation for electron spin is mathematically converted to the space-independent von Neumann equation for a pure state of a two-level spin system. Subsequently, the space-independent Schrödinger–Pauli equation is derived in both frameworks of quantum mechanics and recently developed co-quantum dynamics. Therefore, the inverse conversion is shown, and the two-way transitions for a pure state of electron spin between the classical Bloch equation and the space-independent Schrödinger–Pauli equation are established.

Conference Presentation

Citation Download Citation

Lihong V. Wang "Derivation from (classical) Bloch equation to von Neumann equation to Schrödinger–Pauli equation", Proc. SPIE PC12912, Quantum Sensing, Imaging, and Precision Metrology II, PC129123G (13 March 2024); https://doi.org/10.1117/12.2693007

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