Consider the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

##A## is a functional (some integral operator to be more specific) of a (complex) function ##F##.

We want to minimize ##A[F]## wrt. to a constraint ##B[F]=\int (|F|²)=N##

If I read around online I find that in general such extremization problems are done by minimizing:

##A[F]-µ(B[F]-N) ##

Where ##µ## is a Lagrange multiplier.

My physics book does it slightly differently however, it doesn't include the ##-µN## term in the minimization.

They just say that it's alright to minimize ##A[F]-µB[F]## for a fixed ##µ##.

Why can they use a slightly different way or extremizing a functional under a constraint than the general method I seem to find online?

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# Calc of variations, minimizing functionals question

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