Ok, well in some places I seem to be reading that transposing involves swapping the indices left-right, whereas in other places it seems to imply the indices are completely swapped left-right and top-bottom.
So, assuming we swap left-right only, would you be able to help identify why the...
Thanks for your reply.
Unfortunately I think this just sidetracks the problem. I really need to be able to understand how to deal with the raising and lowering of indices.
For example, I want to be able to understand why the condition Λνμ=(Λ-1)μν doesn't imply that ΛΛT=I. If I just use all...
The Lorentz transformation matrix may be written in index form as Λμ ν. The transpose may be written (ΛT)μ ν=Λν μ.
I want to apply this to convert the defining relation for a Lorentz transformation η=ΛTηΛ into index form. We have
ηρσ=(ΛT)ρ μημνΛν σ
The next step to obtain the correct...
In classical field theory, translational (in space and time) symmetry leads the derivation of the energy-momentum tensor using Noether's theorem.
From this it is possible to derive four conserved charges. The first turns out to be the Hamiltonian, and thus we have energy conservation.
The...
Derive the Fokker-Planck equation by requiring conservation of probability:
∫∂VJ⋅dS=-d/dt∫Vp(r,t)dV
The flux can be written as a sum of convective and diffusive terms
J=p(r,t)v(r,t)-D(r,t)∇p(r,t)
and substitution of this with use of the divergence theorem yields...
Suppose I have an n-doped semiconductor and want to measure the electron concentration in the conduction band as a function of temperature.
How would I go about doing this by measuring the Hall coefficient as a function of temperature, given that I don't know the electron and hole mobilities...
Homework Statement
We have a system of two coupled Langevin equations
dr/dt=kr-yrr+nr(t)
dp/dt=kpr-ypp+np(t)
where the ki,yi are constants and ni(t) are noise terms satisfying <ni(t)>=0 and <ni(t')ni(t'')>=qiδ(t'-t'') (this is zero if the two indices differ).
The physical background of these...
Take the Lorenz equations
x'=σ(y-x)
y'=rx-y-xz
z'=xy-bz
with σ=10, b=8/3 and r=28 as a typical example of chaos (I am using primes to indicate total time derivatives in this post).
A basic property of a chaotic system (where the flow in phase space is a strange attractor) is that if you pick...
Ok - it doesn't surprise me that it's to do with the flow being viscous as opposed to inviscid, as I have used the pressure approach to find say the lift in inviscid flow. So why exactly does pressure give rise to drag and lift in inviscid flow and not viscous flow?
So you can solve the Stokes equation for flow around a sphere to obtain the pressure in the fluid:
p=p0-3nuacosθ/2r2
where n is the viscosity, u is the speed of the fluid (along the z axis) far away from the sphere, a is the radius of the sphere and r,θ are the usual spherical polar coordinates...
Yes it seems to, but that doesn't make sense because we are perturbing the gross structure states which are the set of |n l ml s ms>, so these should be the states used to calculate the expectation value. I've seen degenerate perturbation theory mentioned in a few places but I can't quite see...
So what books seem to use is that (for dimensionless angular momentum operators)
<n l ml s ms|S.L|n l ml s ms>∝<n l ml s ms|J2-S2-L2|n l ml s ms>=j(j+1)-l(l+1)-s(s+1).
However my idea is that we should be writing
|n l ml s ms> as an expansion in the states |n j mj l s> which gives something of...
So we obtain the perturbation Hamiltonian H as something proportional to S.L/r3 and the first order energy shift is then the expectation value of this perturbation Hamiltonian in the state that is being perturbed.
So let a general gross structure state that we are perturbing be |n l ml s ms >...