Time evolution of unstable quantum states and a resolution to Zeno'a Paradox
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. Several questions relating to the deviations from the simple exponential decay law are re-examined. On the basis of general considerations, it is demonstrated that deviations from exponential decay near t = 0 are inevitable. General resonance models are formulated for the decay. From analytic solutions to specific narrow width models, one estimates 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/ approximately 10/sup -14//GAMMA and T/sub 2/ approximately 190/GAMMA. A resolution to Zeno's paradox provided by the present consideration and its limitations are discussed.
- Research Organization:
- Texas Univ., Austin (USA). Center for Particle Theory
- OSTI ID:
- 7316669
- Report Number(s):
- ORO-3992-284
- Country of Publication:
- United States
- Language:
- English
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
DECAY
ELEMENTARY PARTICLES
HADRONS
LIFETIME
MECHANICS
MESONS
PIONS
PIONS MINUS
PIONS PLUS
PSEUDOSCALAR MESONS
QUANTUM MECHANICS
RESONANCE PARTICLES
TIME DEPENDENCE