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QM, Give an example of a state vector |psi> being represented in a space spanned

  • Thread starter jinksys
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Homework Statement


for discrete basis vectors {{e_n}}, a state vector |psi> is represented by a column vector, with elements being psi_n = <e_n|psi>. When basis vectors correspond to those with continuous eigenvalues, vectors are represented by functions. Give such an example of a state vector |psi> being represented in a space spanned by position eigenvectors {|x>}.


Homework Equations




The Attempt at a Solution



C_n = <x_n | psi>

I'm really taking a shot in the dark with this one. I'm using Griffith's, so I assume my solutions lies somewhere in chapter 3.
 

Answers and Replies

  • #2
dextercioby
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So...[itex] |\psi\rangle [/itex] is a ket which is part of the space spanned by eigenvectors of X, the latter being kets satisfying [itex] X|x\rangle = x |x\rangle [/itex], where the x is a real number, the spectral value of X.

Soo... [itex] |\psi\rangle = \mbox{(something)} ~ |x\rangle [/itex]

What's (something) equal to ?
 
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When you say spectral value, is that the same as the eigenvalue?
 
  • #4
dextercioby
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A generalization of eigenvalue. But you can think of it in a simplified way as an eigenvalue.
 

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