Read about pauli matrices | 12 Discussions | Page 1

  1. M

    A Diagonalization of 2x2 Hermitian matrices using Wigner D-Matrix

    Motivation: Due to the spectral theorem a complex square matrix ##H\in \mathbb{C}^{n\times n}## is diagonalizable by a unitary matrix iff ##H## is normal (##H^\dagger H=HH^\dagger##). If H is Hermitian (##H^\dagger=H##) it follows that it is also normal and can hence be diagonalized by a...
  2. hamad12a

    I How Peskin & Schroeder simplified this horrible product of bilinears?

    P&S had calculated this expression almost explicitly, except that I didn't find a way to exchange the $$\nu \lambda$$ indices, but I'm sure the below identity is used, $$ \begin{aligned}\left(\overline{u}_{1 L} \overline{\sigma}^{\mu} \sigma^{\nu} \overline{\sigma}^{\lambda} u_{2...
  3. saar321412

    I Pauli 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...
  4. M

    Proving commutation relation

    Homework Statement Prove that the sets ##(S_{\mu\nu})_L## and ##(S_{kl})_R##, where $$ \left( S _ { k \ell } \right) _ { L } = \frac { 1 } { 2 } \varepsilon _ { j k \ell } \sigma _ { j } = \left( S _ { k \ell } \right) _ { R } \quad\text{and}\quad \left( S _ { 0 k } \right) _ { L } = \frac {...
  5. P

    I Why choose traceless matrices as basis?

    While writing down the basis for SU(2), physicists often choose traceless hermitian matrices as such, often the Pauli matrices. Why is this? In particular why traceless, and why hermitian?
  6. AwesomeTrains

    Density matrix for a mixed neutron beam

    Homework Statement A beam of neutrons (moving along the z-direction) consists of an incoherent superposition of two beams that were initially all polarized along the x- and y-direction, respectively. Using the Pauli spin matrices: \sigma_x = \begin{pmatrix} 0 & 1 \\ 1 & 0 \\...
  7. W

    A How spin projector got included in inverse of Matrix?

    The following matrix A is, \begin{equation} A= \begin{bmatrix} a+b-\sigma\cdot p & -x_1 \\ x_2 & a-b-\sigma\cdot p \end{bmatrix} \end{equation} The inversion of matrix A is, \begin{equation} A^{-1}= \frac{\begin{bmatrix} a-b-\sigma\cdot p & x_1 \\ -x_2 & a+b-\sigma\cdot p...
  8. T

    I How is Graphene's Hamiltonian rotationally invariant?

    Graphene's Hamiltonian contains first order derivatives (from the momentum operators) which aren't invariant under simple spatial rotations. So it initially appears to me that it isn't invariant under rotation. From reading around I see that we also have to perform a rotation on the Pauli...
  9. fresh_42

    Insights Representations and Why Precision is Important - Comments

    fresh_42 submitted a new PF Insights post Representations and Why Precision is Important Continue reading the Original PF Insights Post.
  10. M

    A Dirac Spin Exchange Operator

    The spin exchange operator would have the property $$\begin{align*}P\mid \chi_{\uparrow\downarrow} \rangle = \mid\chi_{\downarrow\uparrow} \rangle & &P\mid \chi_{\downarrow\uparrow} \rangle =\mid \chi_{\uparrow\downarrow} \rangle \end{align*}$$ This also implies ##P\mid \chi_{\text{sym.}}...
  11. polyChron

    I Rotations in Bloch Sphere about an arbitrary axis

    Hey, (I have already asked the question at, I am not sure this forum's etiquette allows that!) I am trying to understand the following statement. "Suppose a single qubit has a state represented by the...
  12. HeavyMetal

    Dirac Equation and Pauli Matrices

    I have been reading through Mark Srednicki's QFT book because it seems to be well regarded here at Physics Forums. He discusses the Dirac Equation very early on, and then demonstrates that squaring the Hamiltonian will, in fact, return momentum eigenstates in the form of the momentum-energy...