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Particles and Fields
Eur. Phys. J. C 18, 195-201
DOI 10.1007/s100520000514

Classical paths and the WKB approximation

J.C. Martinez - E. Polatdemir

Division of Physics, National Institute of Education, Nanyang Technological University, 469 Bukit Timah Road,
Singapore 259756, Singapore

Received: 6 June 2000 / Published online: 27 October 2000 - © Springer-Verlag 2000

Recently, new connection formulas for the WKB method have been proposed, without justification, for quantum tunneling problems. We show that these formulas can be associated with diagrammatic rules within the complex time framework of the path integral formalism and then we express the relevant Green functions in terms of a sum of contributions coming from (easily interpreted) classical paths. The method is applied to barrier penetration and the double well.

Copyright Società Italiana di Fisica, Springer-Verlag 2000