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Infinite square well energy

  1. Nov 16, 2012 #1
    Hi

    I have attached my attempt of solving the infinite square well for Energy. The value I get is different from that of the book, also in the attachment,
    Kindly explain if my answer is correct given the fact that I proceeded step by step and used no tricks.
    Thank you.
     

    Attached Files:

  2. jcsd
  3. Nov 16, 2012 #2

    Bill_K

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    Science Advisor

    You assumed the solution is of the form ψ = cos kx. There are also solutions of the form ψ = sin kx.
     
  4. Nov 16, 2012 #3
    yes, but as you see in the excerpt of the book, they have proved that the the given E holds for cos(kx) too
     
  5. Nov 16, 2012 #4
    I think my solution wrong because I have taken k*a/2 = (n+ 0.5)*pi
    For the given situation, for x=a/2 for cos((n+ 0.5)*pi*x)=0 is only possible if n=0, but we are taking n>0.
     
  6. Nov 16, 2012 #5
    If we were taking n>=0 then my solution was right.
     
  7. Nov 16, 2012 #6

    jtbell

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    Staff: Mentor

    The sine and cosine solutions should alternate with n. The ground state is a cosine, the next higher state is a sine, the next one is a cosine, etc.

    If you put the walls of the box at x = 0 and x = a, it's easier because all the solutions are sines.
     
    Last edited: Nov 16, 2012
  8. Nov 16, 2012 #7
    I do not understand what you said jtbell
     
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