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Calculating constants in mixed state of first two energy levels (infinite Q Well)

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data
    See attachment


    2. Relevant equations
    for an infinitely deep q well of width L
    [itex]\psi(x)=\sqrt{\frac{2}{L}}Sin\frac{4\pi x}{L}[/itex]
    [itex]<\psi_{n}|\psi_{m}>=0[/itex]
    [itex]<\psi_{n}|\psi_{n}>=1[/itex]


    3. The attempt at a solution
    Taking the inner product;

    [itex]<\psi|\psi>=a<\psi|\psi_{1}>+b<\psi|\psi_{2}>[/itex]

    [itex]<\psi|\psi>=a<\psi_{1}|\psi_{1}>+b<\psi_{2}|\psi_{2}>[/itex]

    [itex]1=a+b[/itex]

    from the second part of the question 3a=b and thus a=.25 b=.75

    I kind of went out on a limb with this and I'm not sure if its correct. It seems very little work for the available marks and I'm just not sure if the second part is ok?
     

    Attached Files:

  2. jcsd
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