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

  1. Oct 25, 2011 #1
    1. The problem statement, all variables and given/known data
    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>}.


    2. Relevant equations


    3. 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.
     
  2. jcsd
  3. Oct 26, 2011 #2

    dextercioby

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

    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 ?
     
  4. Oct 26, 2011 #3
    Re: QM, Give an example of a state vector |psi> being represented in a space spanned.

    When you say spectral value, is that the same as the eigenvalue?
     
  5. Oct 26, 2011 #4

    dextercioby

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

    A generalization of eigenvalue. But you can think of it in a simplified way as an eigenvalue.
     
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