How can I take the inner product between a position eigenstate and a ket?

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The discussion centers on deriving the ket |\phi> corresponding to the wavefunction \phi(x), with the expression |\phi> = \alpha|0> + \beta|2> provided. The user seeks guidance on evaluating this further, specifically on taking the inner product between the position eigenstate and |2>. The response emphasizes the importance of understanding the inner product in quantum mechanics, particularly in the context of position eigenstates.

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rushton_19
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Hi, I have to derive the ket |\phi> that corresponds to the wavefunction \phi(x). I've done this out with the information given to point where I've gotten:

|\phi> = \alpha|0> + \beta|2>

How can I go further in evaluating this?
 
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rushton_19 said:
Hi, I have to derive the ket |\phi> that corresponds to the wavefunction \phi(x).
I've done this out with the information given to point where I've gotten:

<br /> |\phi \rangle ~=~ \alpha |0 \rangle ~+~ \beta |2\rangle<br />

How can I go further in evaluating this?

You might have got more replies if you said what |0> and |2> are.

As it is, I can only suggest this:

<br /> \phi(x) ~=~ \langle x | \phi \rangle<br />

and hope that you know how to take the inner product between
a position eigenstate <x| and |2>, whatever that is.
 

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