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Quantum Field Theory and Critical Phenomena$
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Jean Zinn-Justin

Print publication date: 2002

Print ISBN-13: 9780198509233

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509233.001.0001

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Instantons In Quantum Mechanics

Instantons In Quantum Mechanics

Chapter:
(p.931) 39 INSTANTONS IN QUANTUM MECHANICS
Source:
Quantum Field Theory and Critical Phenomena
Author(s):

JEAN ZINN-JUSTIN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509233.003.0039

This chapter explains the role of instantons in unstable systems in quantum mechanics. It first discusses the quartic anharmonic oscillator with negative coupling and calculates the contributions of instantons at leading order. In particular, it shows that instantons determine, in the semi-classical limit, the decay rate of metastable states initially confined in a relative minimum of a potential and decaying through barrier penetration. The chapter then generalizes the method to a large class of analytic potentials, and obtains explicit expressions at leading order for one-dimensional systems. The appendix describes how analogous results can be obtained from calculations based on the WKB method, and comments about the average action in path integrals.

Keywords:   instantons, quantum mechanics, quartic anharmonic oscillator, negative coupling, analytic potentials

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