Help: question about wavefunction

  • Thread starter Eole
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  • #1
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Here's a derivation of wavefunction of State Ψ in representations of coordinates and momentum
Ψ (x)=<x|Ψ >=<x|∫dp|p><p|Ψ >=∫dp<x|p><p|Ψ>=∫dp exp{ipx/h}Ψ(p)
Ψ (p)=<p|Ψ >=∫dx exp{-ipx/h}Ψ(x)


Ψ (x)=<x|Ψ >=<x|∫dp|p><p|Ψ >=∫dp<x|p><p|Ψ>=∫dp exp{ipx/h}Ψ(p)
i don't understand how ∫dp<x|p><p|Ψ> become ∫dp exp{ipx/h}Ψ(p)
Could you please tell me the drivation of this formula?

and another question is why Ψ (x) could be denoted as <x|Ψ >?
 

Answers and Replies

  • #2
MalleusScientiarum
You can prove (and I challenge you to do so) that [tex] \langle x | p \rangle = \exp \{i p x/ \hbar\}[/tex]

Try doing it by testing the action of [tex] \hat{p} |x \rangle [/tex] and using the completeness relation.
 
  • #3
Tom Mattson
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Eole,

You've got another version of this exact same thread in the Homework Section. Please do not post multiple threads for the same topic.
 

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