Is My Approach to the Gaussian Wave Packet Problem Professional?

[BlondEgg]

Homework Statement

Problem involving normalization and Fourier transform

Relevant Equations

Wave function

hi,

I'm solving this statement,

We split into parts

Can some expert in Quantum say that my working is professional?
Kind wishes to you

 

[kuruman]

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.