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...
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,
$$
\begin{aligned}\left(\overline{u}_{1 L} \overline{\sigma}^{\mu} \sigma^{\nu} \overline{\sigma}^{\lambda} u_{2...
Hi :)
I have several questions about the Pauli matrices,
I have seen them when the lecturer showed us Stern-Gerlach experiment
, and we did some really weird assumptions on what we think they should be.
1- why did we assume that all of those matrices should satisfy
σ2 = I (the identity...
While writing down the basis for SU(2), physicists often choose traceless hermitian matrices as such, often the Pauli matrices. Why is this? In particular why traceless, and why hermitian?
Homework Statement
A beam of neutrons (moving along the z-direction) consists of an incoherent superposition of two beams that were initially all polarized along the x- and y-direction, respectively.
Using the Pauli spin matrices:
\sigma_x = \begin{pmatrix}
0 & 1 \\
1 & 0 \\...
The following matrix A is,
\begin{equation}
A=
\begin{bmatrix}
a+b-\sigma\cdot p & -x_1 \\
x_2 & a-b-\sigma\cdot p
\end{bmatrix}
\end{equation}
The inversion of matrix A is,
\begin{equation}
A^{-1}=
\frac{\begin{bmatrix}
a-b-\sigma\cdot p & x_1 \\
-x_2 & a+b-\sigma\cdot p...
Graphene's Hamiltonian contains first order derivatives (from the momentum operators) which aren't invariant under simple spatial rotations. So it initially appears to me that it isn't invariant under rotation. From reading around I see that we also have to perform a rotation on the Pauli...
The spin exchange operator would have the property
$$\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.}}...
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...
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...