Pancharatnam Phase and Berry Phase

Chapter
Part of the UNITEXT for Physics book series (UNITEXTPH)

Abstract

The Indian physicist S. Pancharatnam, working in quantum Optics in 1956, introduced the novel concept of a geometrical phase. Let \(H(\xi )\) denote a Hamiltonian that depends on some parameters \(\xi \), with ground state \(|\psi (\xi )\rangle \). One can define a phase difference \(\varDelta \varphi _{12}\) between two ground states \(|\psi (\xi _{1})\rangle \) and \(|\psi (\xi _{2})\rangle \):
$$ \langle \psi (\xi _{1})|\psi (\xi _{2})\rangle =|\langle \psi (\xi _{1})|\psi (\xi _{2})\rangle | e^{-i \varDelta \varphi _{12} }. $$

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Università di Roma Tor VergataRomeItaly

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