By Daniel Greenberger, Klaus Hentschel, Friedel Weinert

With contributions through best quantum physicists, philosophers and historians, this entire A-to-Z of quantum physics presents a lucid realizing of key strategies of quantum conception and scan. It covers technical and interpretational features alike, and comprises either conventional and new options, making it an essential source for concise, updated information regarding the various aspects of quantum physics.

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Wilzcek: Fractional statistics and the quantum Hall effect. Phys. Rev. Lett. 53, 722 (1984). 7. E. Camino, W. J. Goldman: Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics. Phys. Rev. B 72, 075342 (2005). 8. K. F. Gunn: Condensation of composite bosons in a rotating BEC. Phys. Rev. Lett. 84, 6 (2000). 9. G. Wen: Topological orders in rigid states. Int. J. Mod. Phys. B 4, 239 (1990). 10. G. Moore, N. Read: Nonabelions in the fractional quantum Hall effect.

The present case will evidently be approximately realized if we replace these satellites by negative electrons and the attracting centre by a positively charged particle” Atomic Models, Nagaoka’s Saturnian Model 23 the observed atomic spectra should be directly correlated with the electron’s orbit frequency. Radioactivity was interpreted as an occasional breakdown of saturnian rings, with electrons then being ejected from the atoms as β-rays. Consequently, Nagaoka and others tried to correlate spectral series, bands and other data observed in spectroscopy and early research on radioactivity with predictions derived from his model – in vain.

It is a remarkable correction to the quantum adiabatic theorem and to the closely related Born–Oppenheimer approximation [2]. Berry’s elegant and general analysis has found application to such diverse fields as atomic, condensed matter, nuclear and elementary particle physics, and optics. In this brief review, we first derive Berry’s phase in the context of the quantum adiabatic theorem and then in the context of the Born–Oppenheimer approximation. We mention generalizations of Berry’s phase and analyze its relation to the Aharonov–Bohm effect.