For reference, if we choose the eigenstates of Ŝ, as the basis vectors, the components of the spin angular momentum are

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For Reference If We Choose The Eigenstates Of S As The Basis Vectors The Components Of The Spin Angular Momentum Are 1 (59.18 KiB) Viewed 32 times

For reference, if we choose the eigenstates of Ŝ, as the basis vectors, the components of the spin angular momentum are given by: S₂ = ħ/2 ( 1), S = ħ/2 (9), Sy=ħ/2 (7¹). The following identities may be useful: (eie+e-i)/2 = cos(0), (ei-e-i)/(2i) = sin(0) cos² (0) - sin² (0) = cos(20), 2 sin(0) cos(0) = sin(20), cos² (0) + sin² (0) = 1 1. In quantum mechanics, the energy associated with the spin magnetic moment has a corresponding Hamiltonian operator Ĥ for the spin degrees of freedom. If the uniform magnetic field is B = Bok, then Ĥ=-BoŜ₂. Which one of the following is the Ĥ in the matrix form in the chosen basis? (a) - Boħ/2 (1) (b) - Boħ/2 (1) (c) - Boħ/2 (1) (d) -Boħ/2 (¹) 2. If we measured the energy of the above system, which one of the following gives the allowed values of energy E+ and E_? (a) FyBoħ/2 (b) Fħ/2 (c) FyBoħ (d) None of the above