What does this notation mean exactly?

[Demon117]

I have been staring at this practically all day. I understand bra-ket notation but this is weird. Possibly a typo?

<f|p, g> = <pf|g>

f and g are functions in Hilbert space and p is the spherical momentum operator. What properties of f and g would make this possible? I guess I just want someone to explain this, and also how do you put this in terms of latex command?

 

[The_Duck]

Is it trying to emphasize that p is http://en.wikipedia.org/wiki/Hermitian_operator#Symmetric_operators"?

 

[Demon117]

Is it trying to emphasize that p is http://en.wikipedia.org/wiki/Hermitian_operator#Symmetric_operators"?

That is kinda what I thought, because if you go through some properties you end up with

<f|p, g> = (<f|p)|g> = <f|(p|g>) = <f|pg> = <pf|g> which is a property of self-adjoint operators.

So maybe that is all it means, but what properties of f and g allow this, do they have to be elements of the specific Hilbert space you are working with?

 

[xepma]

If an operator is self adjoint, then the relation would hold for all elements f and g.

 

[Fredrik]

I have been staring at this practically all day. I understand bra-ket notation but this is weird. Possibly a typo?

<f|p, g> = <pf|g>

f and g are functions in Hilbert space and p is the spherical momentum operator.

Why is there both a | and a comma on the left? It should be \langle f|p|g\rangle or \langle f,pg\rangle