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American Journal of Physics

Dynamical Rotations of Spinors and Other Quantum Systems

Gerald T. Moore

Published Oct 1, 1970• 13 citations
Publisher

Abstract

The adiabatic theorem of quantum mechanics is used to investigate the dynamical rotations of quantum systems which are coupled to an external rotating field. The use of such rotations in combination with interference experiments in principle renders the sign change of spinors under 2π rotations observable. Some practical difficulties of such experiments are mentioned.

DOI
10.1119/1.1975994

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The experimental observation of effects due to Berry's phase in quantum systems is certainly one of the most impressive demonstrations of the correctness of the superposition principle in Quantum Mechanics. Since Berry's original paper in 1984, the spin 1/2 coupled with rotating external magnetic field has been one of the most studied model where those phases appear. We also consider this soluble model. A detailed analysis of the coupled differential equations and comparison with exact results teach us why the usual procedure (of neglecting non-diagonal terms) is mathematically sound.

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Comment on the adiabatic condition

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The experimental observation of effects due to Berry’s phase in quantum systems is certainly one of the most impressive demonstrations of the correctness of the superposition principle in quantum mechanics. Since Berry’s original paper in 1984, the spin 12 coupled with a rotating external magnetic field has been one of the most studied models where those phases appear. We also consider a special case of this soluble model. A detailed analysis of the coupled differential equations and comparison with exact results teach us why the usual procedure (of neglecting nondiagonal terms) is mathematically sound.

arXiv:quant-ph/9912030•American Journal of Physics•Oct 1, 2000•15 citations
The adiabatic theorem of quantum mechanics is used to investigate the dynamical rotations of quantum systems which are coupled to an external rotating field. The use of such rotations in combination with interference experiments in principle renders the sign change of spinors under 2π rotations observable. Some practical difficulties of such experiments are mentioned.
The experimental observation of effects due to Berry's phase in quantum systems is certainly one of the most impressive demonstrations of the correctness of the superposition principle in Quantum Mechanics. Since Berry's original paper in 1984, the spin 1/2 coupled with rotating external magnetic field has been one of the most studied model where those phases appear. We also consider this soluble model. A detailed analysis of the coupled differential equations and comparison with exact results teach us why the usual procedure (of neglecting non-diagonal terms) is mathematically sound.
The experimental observation of effects due to Berry’s phase in quantum systems is certainly one of the most impressive demonstrations of the correctness of the superposition principle in quantum mechanics. Since Berry’s original paper in 1984, the spin 12 coupled with a rotating external magnetic field has been one of the most studied models where those phases appear. We also consider a special case of this soluble model. A detailed analysis of the coupled differential equations and comparison with exact results teach us why the usual procedure (of neglecting nondiagonal terms) is mathematically sound.