I'm probably just complicating things, but I'm a little bit stuck with this problem.
I started with just plugging in the definitions for ##\bar{\Psi}_a^c## and ##\Psi_b^c##. So I get
$$\bar{\Psi}_a^c\gamma^{\mu}\Psi_b^c=-\Psi_a^TC^{-1}\gamma^{\mu}C\bar{\Psi}_b^T$$.
After this I used...
Well, I started with the first equation of motion for the scalar field, but I'm really not sure if I'm doing it the right way.
\begin{equation}
\begin{split}
\frac{\partial \mathcal{L}}{\partial \varphi} &= \frac{\partial}{\partial \varphi} [(\partial_\mu \varphi^* -...
Ahhh, so when they refer to different sources, they are just referring to either electric or magnetic ones?
So just by getting, the equations ##\nabla^2 E=\mu_0 \epsilon_0 \frac{\partial^2 E}{\partial t^2}## and ##\nabla^2 B=\mu_0 \epsilon_0 \frac{\partial^2 B}{\partial t^2}## I'm showing that...
Homework Statement
Use Maxwell's equations to elaborate an coherent explication of why electromagnetic waves propagate independently of the source that produces them.
Homework Equations
Maxwell's equations in vacuum:
##\nabla * E=0##
##\nabla * B=0##
##\nabla \times E = -\frac{\partial...
I thought that, but as the problem states that I have to show that n1 and n2 are the eigenstates of N1 and N2 and after that to determine their eigenvalues, I got really confused.
I suppose I could replace it with ##\sqrt{n_1!}|n_1,0\rangle## to get ##N_1\sqrt{n_1!}|n_1,0\rangle=n_1\sqrt{n_1!}|n_1,0\rangle##.
So that would get me ##N_1|n_1,0\rangle=n_1|n_1,0\rangle##
So, I could apply ##a_1^\dagger## multiple times and using the commutation relationship ##[a_1,(a_1^\dagger)^n]=n(a_1^\dagger)^{n-1}## I would get ##N_1(a_1^\dagger)^{n_1}|0,0\rangle=n_1\sqrt{n_1!}|n_1,0\rangle##
would that be correct?
Well, I stated the problem the exact way they gave it to me. I thought that because of the order they wrote it ##a_1## would be the creation operator. But now that you point it out, revising the books ##a_1## always is the annihilation operator.
then what would ##a_1|0,0\rangle## be? Can I...