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Potential well problem

  1. Aug 20, 2009 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m moves in one dimension in the following potential well:

    V(x)=infinity, x<0 , x>L/3
    V(x)=0 , 0<x<L/3

    a)Circle the general functional form of the 1st excited wave function phi_1(x) in the region 0<x<L/3. k is a positive constant; A is constant as well;

    i) A sin(kx)
    ii) A cos(kx)
    iii) A exp(kx)
    iv) A exp(-kx)

    b) use the boundaries conditions to determine k
    c)Find A
    d)Find the 2nd excited state)


    2. Relevant equations



    3. The attempt at a solution

    a) I figured out was iv)
    b) Not sure what to do here but I will give it a try; A*exp(-k*L/3)-A*exp(-k*0)=0 and A*exp(k*infinty)-A*exp(-k*infinity)=infinity)
    c) I would squared phi to get A; (A*exp(-kx))^2=0, x=0...L/3

    d) E=n*h*omega, where n=2?
     
    Last edited: Aug 20, 2009
  2. jcsd
  3. Aug 20, 2009 #2

    George Jones

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    How did you find this?
     
  4. Aug 20, 2009 #3
    For some reason I assumed that L/3 was approaching infinity;
    I think phi =A*sin(kx) since sin(k*x=0)=0 and sin(k*L/3)= 0, assuming L is the value of a unit; This implies k=3pi,9pi,15pi,....

    to find A, I would normilized phi, i.e., A^2*sin^2(3pi*x)=1, not sure what x would be

    E=n*h*omega, n=2
     
    Last edited: Aug 20, 2009
  5. Aug 21, 2009 #4
    Was the second approach I applied wrong as well?
     
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