1. The problem statement, all variables and given/known data The problem is a series of problems all relating to each other. I have gotten most of this done but I will add my answers and continue until the last part which is my main question: We choose a magnetic field in the z direction. Use your knowledge of 2-dimensional representations of 1. Sx, Sy, and Sz to express the Hamiltonian as a matrix: My answer to this: H_z = -γBcosθ1/2[itex]\hbar[/itex] (1 0, 0 -1) H_x = -γBsinθ1/2[itex]\hbar[/itex] (0 1, 1 0 ) H_y= 0 Part 2: Find the eigenvalues and eigenspinors of the Hamiltonian matrix: My answer to this: Eigenvalues of H_z= [itex]\lambda[/itex]=[itex]\pm[/itex]γBcosθ1/2[itex]\hbar[/itex] Eigenvalues of H_x= [itex]\lambda[/itex]=[itex]\pm[/itex]γBsinθ1/2[itex]\hbar[/itex] Eigenvalues of H_y= 0 __________________________ Eigenspinor of Hz using those eigenvalues: [0 1] and [1 0] Eigenspinor of Hx using those eigenvalues: [1 -1] and [1 1] Eigenspinor of Hy using those eigenvalues: [0 0] <---what is up with all my "y" answers?? Part 3: Normalize the eigenspinors My answer: Everything that I am doing is saying that these are already normalized? Is that not correct? Part 4: Get back to experimental measurements. Suppose we collect the atoms that are in the state after going through the region of magnetic field described above. With what probability would a subsequent measurement of the spin in each of the following directions yield ? (The measurements are not consecutive.) a. z-axis b. x-axis c. y-axis MY answer: Here is where I am stuck. 2. Relevant equations I know I have my eigenspinors for my 1/2 spin particles, I have the eigenvalues also. I know the probabilities having read multitude of experiment data on what is going on, and I know Im supposed to measure starting from ONE state, to get the result to the WANTED state. 3. The attempt at a solution I know this is not in line with the forum guidelines but I really do mean it when I say I am dead stuck. I only know that I have to start with one state to get the other, or perhaps I am confused in this sense?