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A spin-1/2 particle has a magnetic moment 𝛍 and is placed in a uniform magnetic field 𝐁, which is aligned with the z-axis, so 𝐁 = B𝓏 𝑧̂ = B𝓏 ẑ. It is known that the Hamiltonian operator for this sytem commutes with the spin component operator in the z direction (z basis?) but not with spin component operators in the x and y directions. The following argument should prove that hypothesis.

The Hamiltonian Ĥ = 
$\mathscr{z}$
$z$
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