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Feynman's kernel and the classical path

Published online by Cambridge University Press:  24 October 2008

M. Clutton-Brock
M. Clutton-Brock
Affiliation:
Northampton College of Advanced Technology, London
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Abstract

The quantum mechanical kernel K(q″,t″; q′,t′) in Feynman's form of a sum over paths is evaluated by means of the canonical transformation to the system Q, P for which the Hamiltonian vanishes identically. The kernel is found to be completely determined by the classical paths, and is given by

The sum is over all classical paths leading from q′ at t′ to q″ at t′. S(q″, P, t′; q′, P, t′) is the classical action along the classical path characterized by the constant momentum P.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 201 - 205
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

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