Finding the wave function squared given an integral wave function

  1. 1. The problem statement, all variables and given/known data

    I need to calculate |ψ(x,t)|2 and find how the wave packet moves in time.


    2. Relevant equations

    I am given these three equations:

    (1) ψ(x,0)=∫dp A(p) Exp[ipx/hbar] where A(p) = C Exp[-a(p-p0)/(hbar2 )]
    Integrate from negative infinity to positive infinity

    At a later time the wave function changes to:

    (2) ψ(x,t)=∫dp A(p) Exp[ipx/hbar-ip2t/(2m*hbar)]
    Integrate from negative infinity to positive infinity

    3. The attempt at a solution

    My first step was to normalize the wave function by finding the value of C. I did this by solving:
    ∫|A(p)|2 dp =1
    Integrate from negative infinity to positive infinity

    I found C2=√(2a/(∏*hbar2))

    Once I normalized it, I solved integral (2). I then solved for |ψ(x,t)|2; The answer I got is extremely long and depends on t. I was told that having more than a certain amount of linear combinations for a solution cause the wave function to be dependent on time. Is that correct or am I missing the point entirely? Any help would be greatly appreciated!
     
  2. jcsd
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