No you didn't scare me away. I do understand what the notation represents too. However, I saw in my notes that they had differentiated quickly the klein gordon lagrangian to get the klein gordon equation.
It is defnitely a notation thing though. I don't really understand the difference between...
I'm just in need of some clearing up of how to differentiate the lagrangian with respect to the covariant derivatives when solving the E-L equation:
Say we have a lagrangian density field
\begin{equation}
\mathcal{L}=\frac{1}{2}(\partial_{\mu}\hat{\phi})(\partial^{\mu}\hat{\phi})
\end{equation}...
Yeh sorry I did mean to put that A is a scalar field. Should be a bit more explicit about the problem I'm having as I wrote that last night after spending almost all my evening on it and I had given up.
Basically the problem is to do with the klein gordon current with an electromagnetic field...
Homework Statement
I really cannot seem to be able to follow the logic of how you would use the product rule when using 4 vector differential operator. ∂μ is the differential operator, Aμ is a scalar field and φ and φ* is it's complex conjugate scalar field. I have the answer, I'd just really...
In magnetic resonance, if we apply a 90 degree pulse in the x direction when we have a magnetisation orientated in the z direction. Why do we get the magnetisation then orientated in the -y direction immediately after the pulse?
I don't understand why it would not be in the +Y direction
I've just come across the spin states of a two electron system. There are 4 states possible and I am a little confused as to why the state below has values of s=1 m_s=0?
[1/√2]{α(1)β(2)+α(2)β(1)}
where α(i) and β(i) tell us if the particle has +ve or -ve z component of spin respectively.
I...
Sorry I understand this now. The expansion was about z=i, but I understand you would just the distance between the place you are expanding around and the closest singularity.
If we have a function:
\begin{equation} f(x,x',y,y',t) \end{equation} and we are trying to minimise this subject to a constraint of
\begin{equation} g(x,x',y,y',t) \end{equation}
Would we simply have a set of two euler lagrange equations for each dependent variable, here we have x and y...
< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >
How would you find the radius of convergence for the taylor expansion of:
\begin{equation} f(z)=\frac{e^z}{(z-1)(z+1)(z-3)(z-2)} \end{equation}
I was thinking that you would just differentiate...
I just read that if we have an antenna, then if the radiation resistance in the antenna is small, then the antenna is an inefficient antenna?
This seems somehow counter intuitive to me. Could anyone help explain?
What does the term αEM mean?
I'm looking at the Coulombic Potential of an alpha particle separating from a daughter nucleus and it is stated that: VC(r)=2ZαEMħc/r
Im not really sure where this term derives from? Does anyone know?
Homework Statement
There are several parts to this question, however I could complete these parts. It is just an equation used in the prior part to the question that is need to solve this:
If we define \begin{equation} \sigma_{n}^{-}=\sigma_{n}^{x}+i\sigma_{n}^{y} \end{equation} and with the...
A charged particle drifts in uniform, constant magnetic and electric fields. The electric field, E, is perpendicular to the magnetic field, B.
Show that the drift velocity is given by vd = (E×B)/B2
Heres where I get to:
F=e(E+vxB)=0 as v is uniform.
Therefore E+vxB=0.
Take vector product...
I've got ∇×(∇×R)=∇(∇.R)-∇2R [call it eq.1]
However I have the identity ∇×(A×B)=A(∇.B)-B(∇⋅A)+ (B⋅∇)A-(A⋅∇)B [call it eq.2]
Substituting in A=∇ and R=B into eq.2 we get ∇×(∇×R)=∇(∇.R)-R(∇⋅∇)+ (R⋅∇)∇-(∇⋅∇)R
which i work out to be ∇×(∇×R)=∇(∇.R)-R(∇⋅∇)+ (R⋅∇)∇-∇2R
Basically I don't understand...
That's exactly it, thank you :). I didn't realize that you could separate the operators out. It's part of the derivation for finding the energy changes in perturbation theory.
Yeh that's part of the proof but that's not what I don't understand. Why do the operations flip the sign of the eigenvalues. I'd have thought <una|VA-AV|unb>=(ana-anb)<una|V|unb>
I'm going through a derivation and it shows: (dirac notation)
<una|VA-AV|unb>=(anb-ana)<una|V|unb>
V and A are operators that are hermition and commute with each other and ana and anb are the eigenvalues of the operator A. I imagine it is trivial and possibly doesn't even matter but why does...