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Let

[tex]\mathcal{L} = \frac{d}{dx} p(x) \frac{d}{dx} + q(x)[/tex]

be a self-adjoint operator on functions [tex]f : [a,b] \rightarrow \mathbb{C}[/tex]. Under what circumstances is the operator Hermitian with

[tex]<u|v> = \int_a^b u^*(x) v(x) dx[/tex]

?

Can someone give me a hint on this one? I know that hermitian operators satisfies

[tex]<u|\mathcal{L}v> = <\mathcal{L}u|v>[/tex]

but I don't really get the question.

[tex]\mathcal{L} = \frac{d}{dx} p(x) \frac{d}{dx} + q(x)[/tex]

be a self-adjoint operator on functions [tex]f : [a,b] \rightarrow \mathbb{C}[/tex]. Under what circumstances is the operator Hermitian with

[tex]<u|v> = \int_a^b u^*(x) v(x) dx[/tex]

?

Can someone give me a hint on this one? I know that hermitian operators satisfies

[tex]<u|\mathcal{L}v> = <\mathcal{L}u|v>[/tex]

but I don't really get the question.

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