Temporary HW: Difference between revisions

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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 <math> \langle \sigma_{x,y,z}\rangle =\mathrm{Tr}\, [\hat{\rho} \hat{\sigma}_{x,y,z}] </math>.)
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 the spin polarization vector using both of these density matrices following  the ''quantum-mechanical definition'' of an average value <math> \langle \sigma_{x,y,z}\rangle =\mathrm{Tr}\, [\hat{\rho} \hat{\sigma}_{x,y,z}] </math>.


== Problem 2 ==
== Problem 2 ==


== Problem 3 ==
== Problem 3 ==

Revision as of 14:47, 8 February 2011

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 the spin polarization vector using both of these density matrices following the quantum-mechanical definition of an average value .

Problem 2

Problem 3