Phys. Rev. A 58, 831–835 (1998)Geometry of the Hilbert space and the quantum Zeno effectReceived 1 December 1997; published in the issue dated August 1998 We show that the quadratic short time behavior of transition probability is a natural consequence of the inner product of the Hilbert space of the quantum system. We provide a relation between the survival probability and the underlying geometric structure such as the Fubini-Study metric defined on the projective Hilbert space of the quantum system. This predicts the quantum Zeno effect even for systems described by nonlinear and nonunitary evolution equations, within the collapse mechanism of the wave function during measurement process. © 1998 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.58.831
DOI:
10.1103/PhysRevA.58.831
PACS:
03.65.Bz
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