Pancharatnam Phase and Berry Phase

  • Michele Cini
Part of the UNITEXT for Physics book series (UNITEXTPH)


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 \(|\psi (\xi _{2})\rangle \):
$$ \langle \psi (\xi _{1})|\psi (\xi _{2})\rangle =|\langle \psi (\xi _{1})|\psi (\xi _{2})\rangle | e^{-i \varDelta \varphi _{12} }. $$

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Università di Roma Tor VergataRomeItaly

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