Pauli matrices Definition and 60 Threads

  1. R

    Understanding Spin Matrix: Pauli Matrices and 6x6 Matrices

    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...
  2. S

    Why are Pauli Matrices Invariant under Rotation?

    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...
  3. K

    Confuse about the spin and pauli matrices

    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...
  4. L

    Understanding Pauli Matrices and Rotations

    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...
  5. R

    Pauli Matrices and Structure Constants

    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"...
  6. K

    Pauli Matrices in higher dimensions

    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...
  7. W

    How Do Pauli Matrices Relate to Rotation in Quantum Mechanics?

    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...
  8. M

    Pauli Matrices: Troubleshooting a Non-Zero Commutator

    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...
  9. P

    Finding Pauli matrices WITHOUT ladder operators

    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!
  10. C

    Pauli Matrices and orthogonal projections

    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...
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