(adsbygoogle = window.adsbygoogle || []).push({}); ^{Hi!!! First of all I want apologize for my bad english! Second, I'm doing a physical chemystry course about the main concepts of quantum mechanics !! The Professor has given to me this definition of "the adjoint operator": <φ|Aψ> = <A†φ|ψ> My purpose is to verificate this equivalence so i gave some numeric values at <φ|, ψ> and at the matrix A (rappresentative of an operator). Then i calculate the expression <φ|Aψ> multiplicating,at first ,the product |Aψ> = A|ψ> and then doing the scalar product <φ|Aψ>....The bra and ket are 1x3 and 3x1 matrix respectively ,while A is 3x3. Now my problem is to calculate the "other" expression: <A†φ|ψ> Because this expression says to calculate first <A†φ|. BUT i dont' know how to calculate this because according to the linear algebra i can't do the product between A† and <φ| (i.e. <A†φ|=A†<φ|. In fact it would be a product between a 3x3 matrix and a 1x3 vector...I'm not able to do this but only the product 1x3 | 3X3 at most.... So how can i calculate the expression <A†φ|ψ> using the linear algebra?? I have to shift the matrix in order to do that product (where?)or what?? Thanks very much!! :)}

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# Adjoint operator in bra-ket notation

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