Feynman's kernel and the classical path
- 1 January 1965
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 61 (1) , 201-205
- https://doi.org/10.1017/s0305004100038780
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 byThe 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.Keywords
This publication has 3 references indexed in Scilit:
- Hamiltonian approach to the method of summation over Feynman historiesMathematical Proceedings of the Cambridge Philosophical Society, 1963
- A note on summation over Feynman historiesMathematical Proceedings of the Cambridge Philosophical Society, 1958
- Space-Time Approach to Non-Relativistic Quantum MechanicsReviews of Modern Physics, 1948