The discussion revolves around the expression < x | f > = f ( x ) in the context of quantum mechanics, specifically relating to the position operator and its eigenvalues and eigenfunctions.
Some participants express confusion regarding the notation and the implications of the inner product, while others provide insights into the use of delta functions and the reasoning behind the notation of eigenvalues in bra-ket notation. There is an ongoing exploration of these concepts without a clear consensus.
Participants are navigating the complexities of quantum mechanical notation and the definitions of eigenstates, with some assumptions about the familiarity with bra-ket notation and the properties of delta functions being evident.
maria clara said:Why is it true that
< x | f > = f ( x )
?
shouldn't it be the result of the integral from minus infinity to infinty on xf(x)?
but then it can't even be a function of x...
maria clara said:detla functions... and it certainly works that way, thanks
but I'm still confused: the definition of the bra-ket is simply the inner product of the functions you put there:
< f | g > = integral from minus infinity to infinity on f*g (f*=the complex conjugate of f).
So the product < x' | f > should be written as follows:
< delta (x-x') | f >...
why do they write the eigenvalue in the bra, and not the function itself?