The Hamiltonian for an electron in a hydrogen atom subject to a constant magnetic field B is (neglecting spin): p2 e2 = H 2me e -L·B 2me 4T€or where L is the angular momentum operator. Assume the magnetic field points in the z-direction. (a) Write down the values of the first 5 energy levels of such system. (b) Consider the line corresponding to the transition (n = 4,1 = 2) → (n = 2,1 = 0). Find the energy of the possible emitted photons (hw = AE, the energy difference between initial and final state) if the possible transitions are constrained by the selection rule Am = 0, +1.

The Hamiltonian for an electron in a hydrogen atom subject to a constant magnetic field B is (neglecting spin): p2 e2 = H 2me e -L·B 2me 4T€or where L is the angular momentum operator. Assume the magnetic field points in the z-direction. (a) Write down the values of the first 5 energy levels of such system. (b) Consider the line corresponding to the transition (n = 4,1 = 2) → (n = 2,1 = 0). Find the energy of the possible emitted photons (hw = AE, the energy difference between initial and final state) if the possible transitions are constrained by the selection rule Am = 0, +1.