1. given a mixture of atoms where 20% are in the state | are in the state (a) what is the statistical operator, p, for this mixture expressed as a matrix in the z-basis? (b) if an -stern gerlach measurement is made, what is the probability that the result obtained will be (i deflected up, (ii) deflected down? (c) use these probabilities to compute the expectation value for this measurement (d) check that the result for (b) agrees with that calculated directly using the statistical operator formalism given by tr{s p < s > = | 2. a z-stern gerlach analyser is used as a source preparation device to produce atoms in the +) these atoms are fed into a 2nd analyser oriented in the x-direction. the state atoms are selected and fed into a 3rd analyser oriented in the z-direction. compute the probability that the source atoms are deflected up and down respectively in the final z-measurement note: this is experiment 3, in case you hadn't figured it out!