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International Journal of Geometric Methods in Modern Physics

ON THE GEOMETRY OF QUANTUM MECHANICS

Elisa Ercolessi, Giuseppe Morandi

Published Mar 1, 2012• 2 citations
Publisher

Abstract

We will present a short review of some work we have done in the last ten years with Giuseppe Marmo, on the attempt to formulate some interesting physical problems — such as the Quantum Inverse Problem, Alternative Structures and Berry Phase — in a geometrical setting.
DOI
10.1142/s0219887812600250

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During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as 'Berry's phase') in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified
Quantum measurement problem is a long-standing problem at the heart of the foundations of modern physics and nascent technology, such as quantum technology. The last forty years brought a renowned interest in this problem with an emphasis on the new foundations of quantum theory and unpredicted formulation of some new quantum disciplines, such as the open quantum systems theory and the quantum information and computation science. A state of the art of the problem of measurement is shortly presented, including a brief historical view, with a review of the authors' original contributions.