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Finding the wave function squared given an integral wave function 
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#1
Jan3112, 12:51 PM

P: 2

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(pp0)/(hbar^{2} )] 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/hbarip^{2}t/(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 C^{2}=√(2a/(∏*hbar^{2})) 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! 


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