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Calculating Average Energy of a quantum state

  1. Apr 19, 2017 #1
    1. The problem statement, all variables and given/known data
    Given a wave function that is the super position of the two lowest energies of a particle in an infinite square well ##\Psi = \frac{\sqrt{2}}{\sqrt{3}}\psi _1 + \frac{1}{\sqrt{3}}\psi _2##, find ##\langle E \rangle##.

    2. Relevant equations


    3. The attempt at a solution
    I'm not sure how to proceed with this problem. I understand that we basically need to find the coefficients ##c_n## from ##\langle H \rangle = \sum |c_n|^2 E_n##, but I'm not sure how to find ##E_n##. The energy of each state is known to be ##E_n = \frac{n^2 \pi ^2 \hbar ^2}{2mL^2}##, but without the problem giving the length of the box, I can't see how we can use this.
     
  2. jcsd
  3. Apr 19, 2017 #2

    BvU

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    Two possibilities:
    1. Continue with ##L## as a parameter that stays in the answer. Same for ##m, \hbar, \pi##, (There is no need for a numerical value in this exercise).
    2. Continue and perhaps some of these divide out (for example because of normalization constants)
    In both cases: continue :smile:

    PS my money definitely isn't on case 2 :biggrin:
     
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