2. A spin-1/2 particle is placed in a magnetic field a (1/2-1/231) B = Bo 2...

Transcribed Image Text:

2. A spin-1/2 particle is placed in a magnetic field a (1/2-1/231) B = Bo 2 (a) Write the Schrodinger equation for this particle. (b) Find the energies and corresponding energy eigenstates. (c) Suppose the initials state is Find (t)). |(0)) = cos 0/2 ) + e sin 0/2) (5) (6) (d) Calculate (Sx) and (Sz) in the state that you found in (c) for arbitrary times t. Find a linear combination of these that is independent of time. 3. Two Stern-Gerlach analyzers, both with magnetic field gradients in the direction, are placed a distance d apart in the direction. In between the two analyzers, there is a uniform magnetic field B B. The lower (spin down) beam of the first apparatus is blocked, while particles in the upper beam exit the apparatus traveling at a velocity voy. What value of Bo should you choose if you want all of the particles to exit the second apparatus in the lower (spin down) beam? 2. A spin-1/2 particle is placed in a magnetic field a (1/2-1/231) B = Bo 2 (a) Write the Schrodinger equation for this particle. (b) Find the energies and corresponding energy eigenstates. (c) Suppose the initials state is Find (t)). |(0)) = cos 0/2 ) + e sin 0/2) (5) (6) (d) Calculate (Sx) and (Sz) in the state that you found in (c) for arbitrary times t. Find a linear combination of these that is independent of time. 3. Two Stern-Gerlach analyzers, both with magnetic field gradients in the direction, are placed a distance d apart in the direction. In between the two analyzers, there is a uniform magnetic field B B. The lower (spin down) beam of the first apparatus is blocked, while particles in the upper beam exit the apparatus traveling at a velocity voy. What value of Bo should you choose if you want all of the particles to exit the second apparatus in the lower (spin down) beam?