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leoflindall
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Homework Statement
Show that the operator O = i [tex]\frac{d2}{ dx2[/tex] (please not 2 a squared term, Latex not working. So i (d2/dx2)) is not hermitian operator for a particle in 1D with periodic boundary conditions.
Homework Equations
The Attempt at a Solution
I know to prove an operator is hermitian that Tnm must equal T mn*.
To show this I would take the intergral [tex]\int \Psi m* T \Psi n[/tex]
What I don't understand is why the operator (in the same conditions) -[tex]\frac{h2}{2m}[/tex] [tex]\frac{d2}{dx2}[/tex] (Please note 2 is a squared term, so h2/2m . d2/dx2) is hermitian and the one above is not?
I assume it is either that the latter is negative, and that if the first operator is positive then it then the when you intergrate by parts it doesn't simplify to Tnm*?
Or that the first operator isn't hermitian as it is complex?
I get the feeling I'm missing something simple here, but any help would be greatly appreciated!
Leo
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