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Infinite square well

  1. Apr 14, 2007 #1
    1. The problem statement, all variables and given/known data
    The eignefunctions for a infinite square well potential are of the form

    [tex] \psi_n} (x) = \sqrt{\frac{2}{a}} \sin \frac{n\pi x}{a}. [/tex]

    Suppose a particle in this potnetial has an initial normalized wavefunction of the form
    [tex]\Psi(x,0)= A\left(\sin \frac{\pi x}{a}\right)^5 [/tex]

    What is the form of [itex] Psi(x,t) [/itex]

    2. The attempt at a solution
    Now the given wavefunction [itex]Psi(x,0)[/itex] can be made to fit the infinite square well by making it a superposition

    [tex] \Psi(x,t) = \sum_{n=1} c_{n} \psi_{n} (x) e^{iE_{n}t/\hbar} [/tex]

    is that it???

    it cnat be that simple...

    thanks for your advice
  2. jcsd
  3. Apr 14, 2007 #2


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    yes. Just use a table of trig identities to write sin to the fifth power as a sum of sine functions of different arguments. That will directly give you the expansion in terms of the eigenstates of the Hamiltonian.

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