Time evolution of unstable quantum states and a resolution of Zeno's paradox

Journal Article · Fri Jul 15 00:00:00 EDT 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.16.520· OSTI ID:7090140

Chiu, C B; Sudarshan, E C.G.; Misra, B

The time evolution of quantum states for unstable particles can be conveniently divided into three domains: the very short time where Zeno's paradox is relevant, the intermediate interval where the exponential decay holds more or less, and the very long time where the decay is governed by a power law. In this work, we reexamine several questions relating to the deviations from the simple exponential decay law. On the basis of general considerations, we demonstrate that deviations from exponential decay near t = 0 are inevitable. We formulate general resonance models for the decay. From analytic solutions to specific narrow-width models, we estimate the time parameters T/sub 1/ and T/sub 2/ separating the three domains. The parameter T/sub 1/ is found to be much much less than the lifetime GAMMA/sup -1/, while T/sub 2/ is much greater than the lifetime. For instance, for the charged pion decay, T/sub 1/ approx. 10/sup -14//GAMMA and T/sub 2/ approx. 190/GAMMA. A resolution of Zeno's paradox provided by the present consideration and its limitations are discussed.

• Research Organization: Center for Particle Theory, Department of Physics, The University of Texas, Austin, Texas 78712
• OSTI ID: 7090140
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 16:2; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSONS
DECAY
ELEMENTARY PARTICLES
HADRONS
HAMILTONIANS
LEVEL WIDTHS
LIFETIME
MATHEMATICAL OPERATORS
MECHANICS
MESONS
PERTURBATION THEORY
PIONS
PROBABILITY
PSEUDOSCALAR MESONS
QUANTUM MECHANICS
QUANTUM OPERATORS
RESONANCE