Geometry of quantum evolution

J. Anandan*, Y. Aharonov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


For an arbitrary quantum evolution, it is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian used to transport the quantum system along a given curve in the projective Hilbert space. It is the distance along this curve measured by the Fubini-Study metric. This gives a new time-energy uncertainty principle. New geometric meanings to time as measured by a clock and the transition probability during a quantum measurement are also obtained.

Original languageEnglish
Pages (from-to)1697-1700
Number of pages4
JournalPhysical Review Letters
Issue number14
StatePublished - 1990
Externally publishedYes


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