#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

and thus

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:

(1)

-more notes to be written soon.

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