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Particle in a box with moving sides

  1. Sep 23, 2008 #1
    1. The problem statement, all variables and given/known data

    a particle is in the ground state of a box with sides x = + or - a. Very suddenly the sides of the box are moved to x = + or - b (b>a). What is the probability the particle will be found in the ground state for the new potential? What is the probability that the particle will be found in the first excited state? In the latter case, the simple answer has a simple explanation. What is it?

    2. Relevant equations and the attempt at a solution

    I believe the probability can be calculated by An2 where

    An = ∫dxψ(x)(2/a)1/2cos(πx/a) for the ground state

    An = ∫dxψ(x)(2/a)1/2sin(2πx/a) for the first excited state

    Is this correct?
    Would the interval be the original or the new walls?
    How can I solve this without knowing ψ(x)?

    Thank you
  2. jcsd
  3. Sep 25, 2008 #2
    I can't really understand some specific aspects of your problem (e.g. bounds), but I understand the general problem statement.

    You are given the initial wave function: the particle is in the ground state within some boundary. Next, the boundary is moved to some new one. Consider this transition to be instantaneous. Now, draw the new potential and its boundaries along with the original ground state wave function; notice that the original wave function does not span the whole range of the new boundary.

    Hint: Since your boundary has changed, so did the general solution to infinite square well potential.
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