Hello Colleagues, 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.