The Hamiltonian of a spin \(\frac{1}{2}\) particle in a magnetic field \(\vec B\) is given by H = -μ\(\vec B\).\(\vec σ\), where μ is a real constant and \(\vec σ\) = (σx, σy, σz) are the Pauli spin matrices. If \(\vec B\) = (B0, B0, 0) and the spin state at time t = 0 is an eigenstate of σx, then of the expectation values \(\left\langle\sigma_x\right\rangle,\left\langle\sigma_y\right\rangle \text { and }\left\langle\sigma_z\right\rangle\)
1
only \(\left\langle\sigma_x\right\rangle\) changes with time
2
only \(\left\langle\sigma_y\right\rangle\) changes with time
3
only \(\left\langle\sigma_z\right\rangle\) changes with time
4
all three change with time