The Schrodinger equation (SE), in my opinion, is the most important milestone in quantum mechanics. Before the Schrodinger equation, quantum mechanics was not really "quantum." The methods developed by Einstein, de Broglie, et. al. were more semiclassical.
However, even though it is very powerful, SE was incomplete. It mapped the change of momentum and position of a single particle through time and cannot account for dissipation. But I digress.
Your post is wonderful. I often struggle communicating quantum mechanics to other people and this post gave me insights on how I can help my friends who come from non-physics disciplines appreciate the beauty of quantum mechanics.
Thank you for this!
You are welcome. Thanks for your comment by the way.
I am trying to put things simply enough so that anyone can understand. However, at some point we need to rely on equations and this is where we start to lose people, in general :)
I didn't want to enter few-body systems here... Way off topic for a blog I guess :D