Quantum Physics: Gaussian Wave Packets

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SUMMARY

The forum discussion focuses on the conservation of the probability density function in quantum physics, specifically regarding Gaussian wave packets. The participant is working on problem 18, which requires demonstrating that the integral of the absolute value of the wavefunction squared equals 1 for all time (t). The user has successfully solved problem 17 and is now attempting to apply their expressions for position (r) and angle (θ) to achieve the required result. The discussion highlights the importance of correctly substituting these expressions to confirm the conservation principle.

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  • Understanding of quantum mechanics principles, particularly wavefunctions.
  • Familiarity with Gaussian wave packets and their properties.
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  • Basic skills in calculus, specifically integration techniques.
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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
 
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You just have to plug your expressions for r and θ back in your result and you will get 1.
 
Thanks you're right!
 

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