I Pauli matrices

Summary
questions about Pauli matrices -

why do they need to be Hermitian, what are they trying to measure and why do they need to

satisfy that those matrices squared equals the identity matrices.
Hi :)
I have several questions about the Pauli matrices,
I have seen them when the lecturer showed us Stern-Gerlach experiment
, and we did some really weird assumptions on what we think they should be.

1- why did we assume that all of those matrices should satisfy
σ2 = I (the identity matrices)

2- why do they have to be Hermitian?

3- what they are trying to measure? (when we insert <-| for example, we get -<-|, why is that? )



thanks for helping !!!
 
530
31
They are a representation of Clifford algebra.

Clifford algebra has operators, abstract objects that have certain properties. Representation is a homomorphism from the operator algebra into matrices. The properties of the matrices reflect the properties of the operators.


By using matrices instead of operators you are losing certain general properties, but at the same time you gain certain simplification and also possibility to do numerical approximations.
 

Want to reply to this thread?

"Pauli matrices" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top