Abeam of ag atoms, each with spin-1/2, is prepared in a way that 60% of the atoms are in the sz = +ħ/2 eigenstate of sz, and 40% are in the eigenstate sx = -ħ/2 of sc. (a) obtain the density matrix at t = 0, in the basis of eigenstates of sz. (b) admit that the atoms are subjected to a magnetic field b = boû, so that the hamiltonian reads, h = us. b (u is the magnetic moment of an atom). obtain the density matrix at time t, in the basis of eigenstates of sz. (c) calculate (sz) at times t = 0 and t.

While studying chemical reactions and conservation of matter, sarah's class conducted a variety of experiments. sarah and her lab partner found the mass of a wax candle and placed the candle in a flask. the students lit the candle and let it burn to completion. all that was left was wax and charred candle wick. per their teacher's instructions, the students found the mass of the products. their data can be seen in the data table. formulate a hypothesis the students could test to explain why the experiment did not support the law of conservation of matter. a) the students could repeat the experiment using different candles; there might have been a flaw in the candle. b) the experiment should be repeatable. the students should run several trials and then take an average of the after mass in each trial. c) the students should have someone in the class check their measurement skills as they repeat the experiment. they may have made an error using the balance. d) the students should burn the candle in a container that has some type of lid so that any gas that is a product of the reaction can be contained and massed. submit