Sigma matrices question Group theory

AI Thread Summary
Every 2x2 Hermitian matrix must satisfy a specific equation due to their properties, such as having real diagonal elements and complex conjugate off-diagonal elements. The discussion highlights that while the reasoning may seem obvious to some, it can be confusing for others, leading to questions about the underlying principles. Participants emphasize that struggling with these concepts is common and does not reflect on one's intelligence. The conversation reflects a supportive atmosphere where clarification and understanding are encouraged. Ultimately, the properties of Hermitian matrices inherently dictate their behavior in relation to the discussed equation.
helpcometk
Messages
71
Reaction score
0

Homework Statement


I have read the following text in a textbook(look the attaxhement) ,and i have a
simple question .WHY every 2x2 hermitian matrix would have to satisfy this Equation.It is not obvious to me why.Does anyone know the answer?
The textbook stops there without giving any answer.Is it something obvious?
Is there any lengthy calculation to show this?


Homework Equations





The Attempt at a Solution

 

Attachments

  • GGGGGGG.PNG
    GGGGGGG.PNG
    19.3 KB · Views: 719
Physics news on Phys.org
helpcometk said:

Homework Statement


I have read the following text in a textbook(look the attaxhement) ,and i have a
simple question .WHY every 2x2 hermitian matrix would have to satisfy this Equation.It is not obvious to me why.Does anyone know the answer?
The textbook stops there without giving any answer.Is it something obvious?
Is there any lengthy calculation to show this?


Homework Equations





The Attempt at a Solution


It's sort of obvious just looking at the expression (5.27). Hermitian matrices have real diagonal elements and the two off-diagonal elements are complex conjugates. By selecting values of x0,x1,x2,x3 you can get any such matrix.
 
Yes its sort of obvious that I am stupid.
Thanks
 
helpcometk said:
Yes its sort of obvious that I am stupid.
Thanks

Hey, I miss the obvious too sometimes. Doesn't make you stupid.
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
View full post »

Similar threads

Noether current in quantum field theory
Replies
1
Views
2K
Finding Cartan Subalgebras for Matrix Algebras
Replies
1
Views
2K
I The SO(3) group in Group Theory
Replies
5
Views
3K
General Irreducible Representation of Lorentz Group
Replies
1
Views
1K
Traceless hermitian matrices form groups?
Replies
5
Views
5K
A Create Hamiltonians in condensed matter with group theory
Replies
6
Views
3K
I Group Theory Appearing in Griffith's Elementary Particles (2nd Ed.)
Replies
20
Views
2K
I What is the proper matrix product?
Replies
9
Views
2K
I Understanding Lorentz Groups and some key subgroups
Replies
3
Views
2K
A In what representation do Dirac adjoint spinors lie?
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top