It always confuse me when we have equation like this
$ \langle \psi|\hat{A} $
What on earth does that mean? Why do we put an operator to the left of the function being applied?
I decided to dig deeper.
According to Wikipedia, a Hermitian Operator in a Hilbert space has this property.
$ \langle \hat{A} x, y \rangle = \langle x, \hat{A} y \rangle $. The angle brackets are NOT bra-ket notation, they represents inner product.
So we can write $ \langle \hat{A} x| \hat{B} y \rangle = \langle x | \hat{A} \hat{B} y \rangle $. This time we indeed mean the bra-ket notation.
$ \langle \psi|\hat{A} $
What on earth does that mean? Why do we put an operator to the left of the function being applied?
I decided to dig deeper.
According to Wikipedia, a Hermitian Operator in a Hilbert space has this property.
$ \langle \hat{A} x, y \rangle = \langle x, \hat{A} y \rangle $. The angle brackets are NOT bra-ket notation, they represents inner product.
So we can write $ \langle \hat{A} x| \hat{B} y \rangle = \langle x | \hat{A} \hat{B} y \rangle $. This time we indeed mean the bra-ket notation.
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