I'm having a bit of trouble imagining the time evolution of non-gaussian wavepackets. For a free particle, I usually imagine a diffusing gaussian (in both $x$ and $p$ where $<p>(t)=p_0$) with it's peak having a velocity $p_0/m$. I want to see some more variety of initial wavefunctions and their time evolutions such as a finite sum of these Gaussians with different $<p>$ or infinite superposition of these wavepackets. We can talk similarly for the hydrogen atom. Time evolution for the CoM frame as Gaussian(s) along with non-CoM states. I can only imagine if the overall wavefunction is like (diffusing Gaussian in $R$)$\times$(Superposition of bound states) i.e. separable wavefunction. I haven't seen many books talk about proper time evolution of hydrogen atom as whole (including CoM). Does anyone of you know of any resources such as animations/applets which show time evolution of probability distribution assuming some normalizable initial states? I think this is important to get an intuition for quantum mechanical treatment of particles.
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