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Functional Derivative

Lukong Cornelius Fai

Published Feb 19, 2021• 0 citations

Abstract

As in path integration one deals with classical functions and functionals rather than with operators then fairly simple classical manipulations of path integration can lead to non-trivial quantum mechanical identities. We consider a simple example of the functional derivative that relates some functional, say, Ϝ[ q ] where the function q ( t ) changes by y ( t ) and the transition amplitude Κ remains invariant: 13.1 δ F = F q + y − F q = ∫ δ F s δ q s y s d s ≡ ∫ Α q s y s d s https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003145554/875ff22b-09e9-4373-a808-2051f13516c8/content/eqn13_1.jpg"/> and 13.2 d F = Α d q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003145554/875ff22b-09e9-4373-a808-2051f13516c8/content/eqn13_2.jpg"/>

DOI: 10.1201/9781003145554-13

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