Angular momentum The rotational motion of a diatomic molecule is described by the Hamiltonian L 21'...

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Angular momentum The rotational motion of a diatomic molecule is described by the Hamiltonian L² 21' Hrot Y(0,0) = (20 marks total) where I is the moment of inertia. The molecule is in the angular momentum state √ni. (0,0) + √er(0,0) + √Ern₁_1(0,0), where Y(0, d) are spherical harmonics. (a) If the rotational energy of the molecule is measured, what are the possible outcomes and associated probabilities? (8 marks) (b) If the z-component of the angular momentum, L₂, is measured in this state, what is the expectation value obtained? (4 marks) (c) If the x-component of the angular momentum, L., is measured in this state, what is the expectation value obtained? (8 marks) Hint: You may find it helpful to express the x-component of the angular momentum operator in terms of the raising and lowering operators. Angular momentum The rotational motion of a diatomic molecule is described by the Hamiltonian L² 21' Hrot Y(0,0) = (20 marks total) where I is the moment of inertia. The molecule is in the angular momentum state √ni. (0,0) + √er(0,0) + √Ern₁_1(0,0), where Y(0, d) are spherical harmonics. (a) If the rotational energy of the molecule is measured, what are the possible outcomes and associated probabilities? (8 marks) (b) If the z-component of the angular momentum, L₂, is measured in this state, what is the expectation value obtained? (4 marks) (c) If the x-component of the angular momentum, L., is measured in this state, what is the expectation value obtained? (8 marks) Hint: You may find it helpful to express the x-component of the angular momentum operator in terms of the raising and lowering operators.

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c The xcomponent of the angular momentum can be written as Lx 4 L L where 4 and I are the ra... View the full answer