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Allowed Eigenstates for a particle question

  1. Jul 30, 2014 #1
    Screen Shot 2014-07-30 at 15.16.23.png
     
  2. jcsd
  3. Jul 30, 2014 #2

    vanhees71

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    2016 Award

    So? What have you done? What are the relevant equations? You won't get help on this forum by just posting a problem!
     
  4. Aug 5, 2014 #3
    You will have to excuse my ignorance I am very new to Physics Forum and relatively so to QM. Please accept my apologies.

    So inside the box V=0,
    Thus ψ = Ae^ikx +B-ikx = Ccoskx + Dsinkx

    Outside the box V = ∞ therefore ψ = 0
    if ψ is continuous it must be zero at the edges of the box

    → ψ(0) = 0 and ψ(L) = 0
    For ψ(0) = 0 then C = 0 therefore ψ(x) = Dsin(kx)

    These boundry conditions lead to eigen fucntions in the form ψ(x) = Dsin(kx) and quantised values of k=n∏/L leading to quantised values of E given by:
    E = hbar^2n^2/8mL^2

    However if the eigenfunctions must be completely specified we normalize them:

    →∫ψ*ψ dx = D^2sin^2(kx)dx=1 where D=√(2/L)= An and L=W

    →ψn(z) = Ansin(n∏z/w)

    Thanks for your help.
     
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