After GR, it’s time to revisit and dig a little bit deeper on QM – Quantum Mechanics, following prof. Brant Carson.

Skipping the early discovery part about wave characteristics of quantum level matter/particles, we are curious about constructing an equation to describe the wave. it’s exact the same thinking thread Newton conquers the world, connecting force, acceleration and other factors.

This is an PDE, usually hard to solve, one of the tricks mathematicians apply is to try if U can be written as multiplication of function(t) and another function(x).

Schrodinger’s QM wave equation is similar

Or to put it more compact way by introducing Hamilton operator H hat.

Applying the same technique,

The left time part is quite simple to solve: