Quantum Physics: Gaussian Wave Packets

[VVS]

Homework Statement

This is the problem sheet that I am solving at the moment:
View attachment T2SS14-Ex6.pdf


2. The attempt at a solution
I have already solved 17.
Here is my solution to 17:
View attachment Übung 17_3.pdf

Now I am working on 18.
I am trying to show that the probability density function is conserved. I.e the integral of the absolute value of the wavefunction in position space squared is equal to 1 for all t.
But somehow I am not getting 1.
Here is what I have so far:
View attachment Übung 18_3.pdf

 

[dauto]

You just have to plug your expressions for r and θ back in your result and you will get 1.

 

[VVS]

Thanks you're right!