Temporary HW

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Problem 1

A researcher in spintronics is investigated two devices in order to generate spin-polarized currents. One of those devices has spins comprising the current described by the density matrix:


,


while the spins comprising the current in the other device are described by the density matrix


, where .


Here and are the eigenstates of the Pauli spin matrix :


.


What is the spin polarization of these two currents? Comment on the physical meaning of the difference between the spin state transported by two currents. (HINT: Compute the x, y, and z components of spin using both of these density matrices to evaluate the quantum-mechanical definition of an average value .)

Problem 2

Problem 3