Is My Approach to the Gaussian Wave Packet Problem Professional?

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Homework Statement
Problem involving normalization and Fourier transform
Relevant Equations
Wave function
hi,

I'm solving this statement,
1721513977862.png

1721513995402.png

We split into parts
1721514094971.png

1721514116323.png

1721514143924.png

Can some expert in Quantum say that my working is professional?
Kind wishes to you
 
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Parts (i) and (ii) are rigorously explained so one may say that they are professionally done. Part (iii) is not "professional", mainly because you make an assertion without justifying it. You say that "the probability density ##~| \Psi(x,t)|^2~## spreads over time indicating that the wave packet disperses as time progresses." To make the argument stick, you need to do the integral in equation (13), find ##~|\Psi(x,t)|^2~##, identify the width and argue that it is time-dependent.
 
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