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Geometry of quantum evolution. (English) Zbl 0960.81524
Summary: 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.

MSC:
81Q99 General mathematical topics and methods in quantum theory
81V80 Quantum optics
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