Explore BrainMass
Share

Spin 1/2 System: Pure and Mixed Ensembles

Consider a pure ensemble of a spin 1/2 system.
Suppose <Sx>, <Sz> and the sign of <Sy> are known.
Show how we may determine the state vector.
Why is it unnecessary to know the magnitude of <Sy> ?

Consider a mixed ensemble of a spin 1/2 system.
Suppose [Sx], [Sy] and [Sz] are known.
Show how we may construct the 2x2 density matrix which characterizes the ensemble.

© BrainMass Inc. brainmass.com August 20, 2018, 8:19 am ad1c9bdddf

Solution Preview

Please refer to the attached documents.

Consider a PURE ensemble of a spin 1/2 system.

Suppose , and the sign of are known.

Show how we may determine the state vector.

Why is it unnecessary to know the magnitude of ?

Answer.-

The corresponding Eigen states for a ½ spin system are just

In other words the state ...

Solution Summary

This solution provides clarification on pure and mixed ensembles of a spin 1/2 system. It discusses concepts like the state vector, magnitude, and density.

$2.19