推 realtemper:推～內積的基本定義～ 12/26 01:11
http://en.wikipedia.org/wiki/Hermitian_adjoint
Suppose H is a Hilbert space, with inner product . Consider a continuous
linear operator A : H → H (this is the same as a bounded operator).
Using the Riesz representation theorem, one can show that there exists a
unique continuous linear operator A* : H → H with the following property:
<Ax,y> = <x,A*y>
This operator A* is the adjoint of A. This can be seen as a generalization of
the adjoint matrix of a square matrix which has a similar property involving
the standard complex inner product.
也就是說
<Av|u> = <v|A*u> 這個式子本身就是A*的定義
因此 <u|A|u> = <u|Au> = <u|(A*)*u> = <A*u|u>
※ 引述《chris80634 (紛飛)》之銘言：
: 令波函數為u(x)
: <u|A|u> = <A*u|u>
: 為什麼A拿到bra那邊的時候會變成共軛?
: 我有想過會不會是因為他要對u*(x)作用
: 所以他本身也要是一個共軛的算符?
: 以上
: 感謝解答
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