Let’s solve the free particle
At least that works. Not sure I derived it particularly. Or proved it unique.
Whatever. Lagrangian version
Euler Lagrange Equations
How do you get that? By varying the action with fixed endpoints it’s the one that minimizes the path.
Okay. What about the quantum version?
How do I know that? In particular it’s hard to remember where the i goes. Well, I memorized it at some point. It follows that
But what is
Whatever. I’m bored.
Maybe I’ll do the path integral some other day