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Proving an operator is hermitian

MB44 · 2010-01-12 15:50:35

I am having troubles proving that an operator is or is not hermitian. How do you go about it. The problem is relating to quantum mechanics but I first need to understand the mathematical theory and the books I have looked at really delve deep in to mathematical analysis. Anyone wanna dumb it down for me? Or are there any…

12-01-2010 3:50pm

#1

MB44

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I am having troubles proving that an operator is or is not hermitian. How do you go about it. The problem is relating to quantum mechanics but I first need to understand the mathematical theory and the books I have looked at really delve deep in to mathematical analysis. Anyone wanna dumb it down for me? Or are there any net books I can have a look at.

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#2 12-01-2010 9:05pm

Fremen

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In the finite dimensional case, a hermetian operator can be represented as a matrix of complex numbers which is equal to its conjugate transpose. The infinite dimensional case is a bit trickier. As far as I remember, Kreyszig's book "introductory functional analysis with applications" covers hermetian operators in Hilbert space in a fairly approachable way. I'm not a physicist, so I can't really help with the QM aspects.

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