Hi everyone,
I now able to understand spin matrix (if i am correct in other words Pauli matrix).
For e.g.,
for S=5/2 systems the spin matrix (say for SX) is given by:
Sx= 1/2[a 6X6 matrix]
I hope members will know what is this 6X6 matrix! Since i don't know how to type matrix in this...
Homework Statement
Can anyone tell me why Pauli Matrices remain invariant under a rotation.
Homework Equations
Probably the rotation operator in the form of the exponential of a pauli matrix having an arbitrary unit vector as its input. It may also be written as:
I*Cos(x/2) - i* (pauli...
In the textbook, it uses the pauli matrices to describe the spin and it will also form a vector
\vec{\sigma} = \sigma_1 \hat{x} + \sigma_2\hat{y} + \sigma_3\hat{z}
But each component, \sigma_i, i=1,2,3 is a 2x2 matrix. I am really confuse about the relation between \sigma_i and the...
I have some questions about Pauli matrices:
1. How do we calculate them? Which assumptions are needed?
Are the assumptions related to properties of orbital angular momentum in any way?
2. How do we prove that the Pauli matrices (the operators of spin angular momentum) are the generators...
Hey folks,
I am trying to generate the Pauli matrices and am using the following formula taken from http://en.wikipedia.org/wiki/SU(3 )
"In the adjoint representation the generators are represented by (n^2-1)×(n^2-1) matrices whose elements are defined by the structure constants"...
This has been bugging me for a while, but feel to tell me if it's a nonsensical or silly question..
Suppose there were 4 spatial dimensions instead of 3. How would we go about constructing the Pauli matrices?
Assuming each matrix still only has 2 eigenvectors, we require 4, 2x2 mutually...
I am given the formula (valid for any a)
A ( \vec{ \sigma } \cdot \vec{a} ) A^{-1} = \vec{ \sigma } \cdot R_A \vec{a}
with [itex]A=exp(i \phi \cdot \vec{\sigma} /2) = exp(i \phi \vec{\sigma} \cdot \hat{n} /2)[/tex] R_A the rotation matrix and sigma the Pauli matrices.
And am supposed to...
Ok, I have a stupid question on pauli matrices here but it is bugging me. In a book I'm reading it gives the equation [\sigma_i , \sigma_j] = 2 I \epsilon_{i,j,k} \sigma_k , I understand how it works and everything but I do have a question, when you have k=i/j and i!=j (like 2,1,2) you get a...
Does anyone know of an alternative way of calculating the Pauli spin matrices \mbox{ \sigma_x} and \mbox{ \sigma_y} (already knowing \mbox { \sigma_z} and the (anti)-commutation relations), without using ladder operators \mbox{ \sigma_+} and \mbox{ \sigma_- }?
Thanks!
Ok, I'm working with the Pauli Matrices, and I've already gone through showing a few bits of information. I've got a good idea how to keep going, but I'm not exactly sure about this one--
say M= 1/2(alphaI + a*sigma)
where alpha E C, a=(ax, ay, az) a complex vector, a*sigma=ax sigmax+ay...