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Infinite potential well problem

  1. Jan 24, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi,
    Particle of mass m is found in one-dimensional infinite potential well with walls 0<=x<=a.
    In t=0 the normalized wave function is:
    [tex]\psi(x,t=0)=A[1+Cos(\frac{\pi x}{a})]Sin(\frac{2 \pi x}{a})[/tex]

    find psi(x,t)

    2. Relevant equations

    ?

    3. The attempt at a solution

    [tex]\psi(x,t)=\sum C_{n} e^{\frac{-iE_{n}t}{\hbar}}\phi_{n}(x)[/tex]

    [tex]C_{n}=\int^{a}_{0}\phi_{n}(x)\psi(x)dx[/tex]

    [tex]C_{n}=\int^{a}_{0}Sin(\frac{n \pi x}{a})A[1+Cos(\frac{\pi x}{a})]Sin(\frac{2 \pi x}{a})dx[/tex]


    I could do the integral and find Cn coefficients, but it takes time.
    Is there an easier way for findin psi(x,t) ?
     
  2. jcsd
  3. Jan 24, 2008 #2

    malawi_glenn

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    I dont think so, perhaps if you use tables of standard integrals or maple / mathematica.
     
  4. Jan 24, 2008 #3
    Ok, thanks.
    Just wanted to make shure I'm not missing something.
     
  5. Jan 24, 2008 #4

    malawi_glenn

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    there is standard integrals for ortonogal cos and sin integrals, if you want more hints.
     
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