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.  
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>.
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 P_{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