=- = . x . 1.[25pt] Effect of measurement on time evolution An electron is subject to the Hamiltonian H, eB H -S. mc (a)

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X 1 25pt Effect Of Measurement On Time Evolution An Electron Is Subject To The Hamiltonian H Eb H S Mc A 1 (90.95 KiB) Viewed 32 times

=- = . x . 1.[25pt] Effect of measurement on time evolution An electron is subject to the Hamiltonian H, eB H -S. mc (a) [10pt] At t=0 the electron is known to be in an eigenstate of Sy with eigenvalue ħ/2. Obtain the probability for finding the electron in the Sc = ħ/2 state at the time t = to. Plot your result as a function of t. for the time interval o sto samc/2eB. (b) [15pt] At t=0 the electron is known to be in an eigenstate of Sy with eigenvalue ħ/2. One measures Sc at t = t. / 2 (0 sto samc/2eB), and regardless of its outcome, one measures Sg again at t = to. Obtain the probability for finding the electron in the Sx = ħ / 2 state at the second S, measurement. Note that the only difference of (b) from (a) is the measurement at the intermediate time t =t, / 2. In which case is the probability at the final time t = to larger? Is it (a) or (b)? t .X = x x = = 0