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Particle in a box problem please help.

  1. May 3, 2009 #1

    Nio

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    1. The problem statement, all variables and given/known data

    Assume we have an infinitely deep square well of length L, with the left edge of the well at -L/2. Assume U = 0 at the bottom and infinity at the top. A) Using the time independent Schrodinger Equation, derive the wave equation for a particle trapped in this well. Make sure your equation is properly normalized

    2. Relevant equations
    shrodingers equation, the general solution to it which is Asinkx +Bcoskx=psi(0)


    3. The attempt at a solution
    I know that sin is and odd function and cos is even so I am supposed to arrive at two wave functions and have different values of n, even values for cos and odd for sin. I am supposed to get Psi(x)= (2/L)^.5sin(npix/L) where n is odd values and the same thing except cos and even values. I am having trouble deriving this using my boundary conditions, and I am also having trouble normalizing it.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 4, 2009 #2
    I would save normalization for the end. What are your boundary conditions so far?
     
  4. May 4, 2009 #3
    Why is it that you can get sine and cosine solutions? i thought all you needed was the sine solution because it would always satify the boundary conditions of haveing a node at each boundary.
     
  5. May 4, 2009 #4
    Well both satisfy Schrodingers equations. If the boundary conditions were Psi(0) = 0 and Psi(L) = 0, then sine would be your only solution because cos(0) = 1. But now your BC's are Psi(-L/2) = 0 and Psi(L/2) = 0. Therefore both can be solutions. You just need to find the 'k' that satisfies those BC's.
     
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