Hello Colleagues,(adsbygoogle = window.adsbygoogle || []).push({});

I am curious about a problem in Quantum Mechanics that incorporates the evolution of a Gaussian Wave Packet under the Gravitational Potential.

What I am interested in is equation (3) in the following paper:

"On the quantum analogue of Galileo's leaning tower experiment"

(Unfortunately, I can not post a direct link due to forum restrictions...)

I have worked with Gaussian Packets representing a Free Particle before. In that case, I was able to time evolve the function trivially since I had time translation invariance on my side s.t. t ---> (t - t-initial) or (t - t_final).

However, with equation (3), I do not believe that I have time translation invariance. How, then, can I time evolve this function to some later or some earlier time? What Propagator would I use?

Thank you for any effort or time put in to my question. If I can elaborate about what I am asking, please let me know.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Time Evolution Of A 1-D Gaussian Wave Packet Under The Gravitational Potential

**Physics Forums | Science Articles, Homework Help, Discussion**