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One dimensional infinite potential well problem

  1. Apr 19, 2008 #1
    hi,
    I am not getting idea to solve below problem
    A particle of mass m is in a one-dimensional ,rectangular potential well for which V(x)=0 for 0<x< L and V(x)=infinite elsewhere. The particle is intially prepared in the ground state ψ1 with eigen energy E1. Then , at time t=0, the potential is very rapidly changed so that the original wave function remains the same but V(x)=0 for 0<x<2L and V(x)=infinite elsewhere.Find the probability that the particle is in the first,second,third and fourth excited state of the system when t ≥ 0.
    could you help me please.
     
  2. jcsd
  3. Apr 19, 2008 #2

    Dick

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    When the potential is changed suddenly the original wavefunction stays the same. To compute the amplitudes of being in any other state then just compute the overlap integral <psi1|phi> where phi is the wavefunction of the excited state. To get the probability find the modulus squared of the amplitude.
     
  4. Apr 20, 2008 #3

    the |phi> is the excited states in the new potential, right??
     
  5. Apr 20, 2008 #4

    Dick

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    Sure.
     
  6. Apr 20, 2008 #5
    Two quick questions:

    1. Is this 'overlap integral' the convolution of the wavefunctions in each potential?

    2. Is taking this 'overlap integral' in such a situation generally the way to tackle problems such as this?
     
  7. Apr 20, 2008 #6

    Dick

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    It's not a 'convolution'. That's something else. It's just the integral conjugate(psi1(x))*psi2(x) over the domain of the wavefunctions. And yes, if everything is properly normalized that's all you have to do.
     
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