1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]

    What are the dimensions of:
    and abs(b(k))^2?

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


    User Avatar
    Science Advisor
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Dimensions of a Projection
  1. Sensor Project (Replies: 1)

  2. Problem on dimensions (Replies: 0)

  3. Dimension 4 (Replies: 6)

  4. Extra Dimensions (Replies: 3)