Nuclear Spins: From Quantum Mechanics to Classical View
Gonzalo A. Alvarez1,2,3
1Centro Atomico Bariloche, CONICET, CNEA, Bariloche, Argentina, 2Instituto de Nanociencia y Nanotecnologia, CNEA, CONICET, Bariloche, Argentina, 3Instituto Balseiro, CNEA, Universidad Nacional de Cuyo, Bariloche, Argentina

Synopsis

In this talk, I would introduce the basic physics underlying nuclear magnetic resonance. I will present the quantum mechanical description vis-à-vis the classical description of non-interacting spins in static (B0) and time-dependent fields (B1). The spin polarization and its corresponding thermodynamic equilibrium will be introduced based on the density matrix representation. The spin state evolution is dictated by the Liouville–von Neumann equation that gives the laws on how the spin polarization and its coherence evolve as a function of time. This quantum equation of motion arrives at the Bloch equation.

Summary

In this talk, the basic physics underlying nuclear magnetic resonance will be introduced. Nuclear spins are described by quantum mechanics, but typically they are represented by a classical picture in MRI. I will present the quantum mechanical description of non-interacting nuclear spins in presence of magnetic fields, static (B0) and time-dependent (B1). The connection with its classical description will arise naturally. The spin polarization, its observable magnetization and its corresponding thermodynamic equilibrium will be introduced based on the density matrix representation. The spin state is thus described by a density matrix whose evolution is dictated by the Liouville–von Neumann equation. I will show how the spin magnetization moment and its coherence evolve as a function of time based on this equation of motion. This quantum equation of motion arrives at the classical Bloch equation.

Acknowledgements

I acknowledge support by CNEA, CONICET, ANPCyT-FONCyT PICT-2017-3156, PICT-2017-3699, PICT-2018-4333, PIP-CONICET (11220170100486CO), UNCUYO 1705 SIIP Tipo I 2019-C028, and Instituto Balseiro.

References

P. T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy (Oxford University Press, 1993).

Malcolm H. Levitt: Spin Dynamics: Basics of Nuclear Magnetic Resonance (2nd Edition).

McRobbie et al., MRI - From picture to proton, Cambridge.

Weishaupt, Köchli, Marincek - How Does MRI Work? Springer.

Proc. Intl. Soc. Mag. Reson. Med. 30 (2022)