Recent content by BobaJ

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...

Maybe you can recommend me a textbook where it is done? Yes, I have seen the wave equation (and how to derive it from Maxwell´s equations).

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...

It is a problem presented by my instructor. I don't know from where he got it

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.

Does it mean that ##n_1## is an eigenstate of ##N_1##?

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?

You are right, I think it should read ##N_1 a_1^\dagger |0,0\rangle = |1,0\rangle##.

Right, now as ##a_1^\dagger## is the creation operator ##a_1^\dagger |0,0\rangle = |1,0\rangle##. And with this ##N_1a_1^\dagger=|1,0\rangle##.

Ok, so then I would just be left with ##N_1a_1^\dagger|0,0\rangle = a_1^\dagger |0,0\rangle##

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...

Yes, as I understand the exercise ##a_1## is the creation operator. But I still don't know how to go on after to solve the problem.