[QUE/QFT-06008 QFT-PROBLEM

Consider an electron in a uniform and constant magentic field \(\vec{B}\) along the \(z-\)axis. Obtain the most general four component positive energy eigennfunctions. Show that the energy eigenvalues are given by \[ E= \sqrt{m^2c^4 + c^2p_3^2 + 2ne\hbar c|\vec{B}|}\] with \(n=0,1,2,...\). List all the constants of motion.