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11. The Hamiltonian for an electron in a hydrogen atom subject to a constant magnetic field B is given by H = e2 p² 2me Απεργ e + (L+2S). B 2me where L and S are the angular momentum and spin operators respectivelyr. Assume the magnetic field points in the z-direction. (a) How many distinct energy levels will the n = : 3 state have? = = 3,1 = 2) → (n = 2,1 = 1). Find the energy of the (b) Consider the line corresponding to the transition (n emitted photons (hw AE, with AE = the energy difference between initial and final state), assuming the possible transitions are constrained by the selection rule Am = 0,±1.

11. The Hamiltonian for an electron in a hydrogen atom subject to a constant magnetic field B is given by H = e2 p² 2me Απεργ e + (L+2S). B 2me where L and S are the angular momentum and spin operators respectivelyr. Assume the magnetic field points in the z-direction. (a) How many distinct energy levels will the n = : 3 state have? = = 3,1 = 2) → (n = 2,1 = 1). Find the energy of the (b) Consider the line corresponding to the transition (n emitted photons (hw AE, with AE = the energy difference between initial and final state), assuming the possible transitions are constrained by the selection rule Am = 0,±1.

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11. The Hamiltonian for an electron in a hydrogen atom subject to a constant magnetic field B is given by H = e2 p² 2me Απεργ e + (L+2S). B 2me where L and S are the angular momentum and spin operators respectivelyr. Assume the magnetic field points in the z-direction. (a) How many distinct energy levels will the n = : 3 state have? = = 3,1 = 2) → (n = 2,1 = 1). Find the energy of the (b) Consider the line corresponding to the transition (n emitted photons (hw AE, with AE = the energy difference between initial and final state), assuming the possible transitions are constrained by the selection rule Am = 0,±1.
Transcribed Image Text:11. The Hamiltonian for an electron in a hydrogen atom subject to a constant magnetic field B is given by H = e2 p² 2me Απεργ e + (L+2S). B 2me where L and S are the angular momentum and spin operators respectivelyr. Assume the magnetic field points in the z-direction. (a) How many distinct energy levels will the n = : 3 state have? = = 3,1 = 2) → (n = 2,1 = 1). Find the energy of the (b) Consider the line corresponding to the transition (n emitted photons (hw AE, with AE = the energy difference between initial and final state), assuming the possible transitions are constrained by the selection rule Am = 0,±1.
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