incomplete
- Every measurable quantity “a” is associated with an operator A^, that is also called an “observable”, that is related through: $$
\hat{A}\varphi(x) = a \varphi(x)
2. Any _measurement_ of $A$ gives a corresponding eigenvalue $a$ and a matching eigenstates $\varphi_{n}$
3. $\Psi_{(x,t)}$ contains all the information of the system
1. $|\Psi|^{2}$ is the probability density, and $<A> = \int \Psi ^* \hat{A} \Psi \, dx$ gives the expectation value of $A$.
4. Time dependent $\Psi(x,t)$ obeys S.E: $$
\frac{\hat{p}^{2}}{2m} \Psi_{(x,t)} + V(x) \Psi_{x,t} = i\hbar \frac{d}{dt}\Psi_{x,t}