As we all know, the magnetic field around a dipole looks like the following: Notice how, directly above and below the magnet, the magnetic fields likes are parallel to the north-south axis. However, to the sides of the magnet, the magnetic field lines are anti parallel. If you've ever played wi...

I am going through Groenewold's theorem and in his book: On The Principles of Elementary Quantum Mechanics, page 8, eq. 1.30: $$[\mathbf{p}, \mathbf{q}]=1\left(\text { i.e. } \mathbf{p q}-\mathbf{q} \mathbf{p}=\frac{\hbar}{i}\right),\tag{1.30} $$ and he wrote: The classical quantities...