1. ### 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...

5. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### I Rotations in Bloch Sphere about an arbitrary axis

Hey, (I have already asked the question at http://physics.stackexchange.com/questions/244586/bloch-sphere-interpretation-of-rotations, 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. ### 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...