zbMATH — the first resource for mathematics

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.

81Q99 General mathematical topics and methods in quantum theory
81V80 Quantum optics
Full Text: DOI
[1] M. V. Berry, Proc. Roy. Soc. London A 392 pp 45– (1984) · Zbl 1113.81306
[2] Y. Aharonov, Phys. Rev. Lett. 58 pp 1593– (1987)
[3] J. Anandan, Phys. Rev. D 38 pp 1863– (1988)
[4] B. Simon, Phys. Rev. Lett. 51 pp 2167– (1983)
[5] D. A. Page, Phys. Rev. A 36 pp 3479– (1987)
[6] J. Anandan, Ann. Inst. Henri Poincare 49 pp 271– (1988)
[7] J. Anandan, Phys. Lett. A 129 pp 201– (1988)
[8] S. Kobayashi, in: Foundations of Differential Geometry (1969) · Zbl 0175.48504
[9] S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 44 pp 247– (1956)
[10] S. Ramaseshan, Curr. Sci. 55 pp 1225– (1986)
[11] M. V. Berry, J. Mod. Opt. 34 pp 1401– (1987) · Zbl 0941.81542
[12] J. Samuel, Phys. Rev. Lett. 60 pp 2339– (1988)
[13] G. Benedict, Phys. Rev. D 39 pp 3194– (1989)
[14] M. V. Berry, in: Geometric Phases in Physics (1989)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.