#The Schrodinger Equation
Consider a particle constrained on the x-axis, with mass , subjected to a force .
- In Classical mechanics, we determined , the position. Then we find the velocity, and momentum . Finally, we determine the kinetic energy ... or any other dynamical quantity of interest.
- From there we find using , for conservative systems.
Luckily, conservative systems are the only ones which occur at microscopic scales. We know that
which, along with initial conditions , we determine .
In Quantum Mechanics, the name of the game is different. We wish to find the particle's *wave function*, , which we do by solving the Schrodinger equation:
-more notes to be written soon.