# conservation laws and symmetry

### 0.1. rotations (notes that I took after reading feynman lecture)

The rough idea, is that there is an operator, \(R_z(\phi)\) which rotates the system \(\phi\) about the \(z\) axis.

We say that \(R_z(\phi)\) is an observable (?) and that the eigenvalues of this observable are the possible values.

And \(R_z(\phi)\) commutes with \(H\), and if a state is in an eigenstate of \(R_z(\phi)\), then it will remain proportional to that eigenstate. So, we say that the quantity corresponding with the observable, is conserved across time evolution.