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Changing size particle in a box

  1. Dec 4, 2012 #1
    1. The problem statement, all variables and given/known data

    there is a infinite quantum well with size L and there is a particle in it with mass m. suddenly the size of the quantum well is doubled. What will be the wave function at a later time t ?

    2. Relevant equations

    ψ= [itex]\sqrt{2/L}[/itex] sin (n pi x / L)

    E = n^2 pi^2 h^2 / 2mL^2

    3. The attempt at a solution

    do we need to find cn again with 2L ?
     
  2. jcsd
  3. Dec 4, 2012 #2

    Simon Bridge

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    Yes.
    I'd normally do this by expressing the initial state of the particle, in the 1L well, in terms of a superposition of states of the final 2L well... then finding the time-evolution of those states.

    I'd have expected the initial state to be a specified n state (i.e. the ground state).

    A lot depends on context - eg.
    If there is a mechanism for decay present, then the question could be answered in terms of the energy lost in the decay from initial to final states. (Otherwise the system remains in a composite state until some measurement of energy is made.)
     
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