Hey everyone! I have a question regarding the matrix representation of a projection operator. Specifically, does the wavefunction have to be normalized before determining the projection operator? For example:(adsbygoogle = window.adsbygoogle || []).push({});

|Ψ1> = 1/3|u1> + i/3|u2> + 1/3|u3>

|Ψ2> = 1/3|u1> + i/3|u3>

Ψ1 is obviously normalized and Ψ2 isnt

Now to calculate the matrix that represents the projection operator, just make row and column matrices and multiply out. For Ψ1:

| 1/3|u1> |

| i/3|u2> | * (| 1/3|u1> i/3|u2> 1/3|u3> |)

| 1/3|u3> |

Which gives a 3x3 Hermitian matrix.

My question is do I have to normalize Ψ2 in order to do the same process? The result is a Hermitian operator either way, I believe, but I just want to know if 'technically' it needs to be normalized first.

thanks for any input!

Timmy

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# Matrix representing projection operators

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