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Infinite well linear combo of states

  1. Oct 9, 2013 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.

    3. The attempt at a solution

    I know the process of solving PDE's clear as day, thats not the issue. The problem is that I'm tripping myself out on how to write Ψ(x,t) as a linear combination of its ground state + first excited state.

    My hunch is to approach the problem like this :

    Ψ(x,t)=c1Ψ1(x,t)+c2Ψ2(x,t)

    where 1 and 2 represent the ground state and first state, respectively

    that momentum takes on the largest possible value at t=0 is confusing and not sure what to do.
     
  2. jcsd
  3. Oct 9, 2013 #2

    Simon Bridge

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    Have you tried:

    ##\Psi(x,t)=c_1(t)\psi_1(x)+c_2(t)\psi_2(x)##
     
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