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Dimensions of a Projection

  1. Sep 22, 2009 #1
    1. The problem statement, all variables and given/known data
    If an arbitrary intial state function for a particle in a box is expanded in the discrete series of eigenstates of the Hamiltonian relevant to the box configuration, one obtains:

    [tex]\psi(x,0) = \Sigma^{\infty}_{n=1}b_{n}(0)\varphi_{n}(x)[/tex]

    If the particle is free, we obtain:

    [tex]\psi(x,0) = \int^{\infty}_{-\infty}b(k)\varphi(k)dk[/tex]

    (a)
    What are the dimensions of:
    abs(b_{n})^2
    and abs(b(k))^2?

    I don't understand what they mean by dimensions! any hints?
     
  2. jcsd
  3. Sep 23, 2009 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    By dimensions they mean, well, dimensions as in dimensional analysis in terms of the standard three, Mass, Length and Time. Start by considering

    [tex]\int \psi^{*}(x)\psi(x)\: dx = 1[/tex]

    What are the dimensions of ψ(x)? Sort it out from there.
     
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