# Finding the wave function squared given an integral wave function

by rjop455
Tags: function, integral, squared, wave
 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(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!

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