My notes say that the Resolution of the Aperture(in the Electric field of the wave) is the Fourier transformation of the aperture.
Then gives us the equation of the aperture:
and says that for the circular aperture in particular also:
My attempt at solving this:
We know that the Fourier...
Suppose we have two charged particles A and B released in the center of the Mirror (where the field is minimum). If A's velocity direction is parallel with the Magnetic field of the mirror and B's velocity is perpendicular with the field, then which one is going to get trapped, or escape, or...
It says that since there is homogeneity in the Universe's temperature, all these points must have come from one source (or a source close to each other?) at a certain time.
Then it also calculates the number of these sources and it's ~105. But isn't that very dense mass right before the Big...
You're referring to the fact that I didn't write it like ρr=ao(t)4? I corrected it, so no need to mention it again. I know a is time dependent. Other than pointing it out again, I know the answer is in my op. I just don't understand how it came up.
Thanks. I found out how the redshift zeq came up from the a, but I still don't understand why
(ρm/ ρr)teq = (ρm/ ρr)o * a(teq)/ ao
Anyone has any idea? What's the issue with the densities and the a(teq)/ ao ?
If we say ρm(t)/ ρr(t)= ρom * ao4 / ρor * ao3 then we get
ρm(t)/ ρr(t)= ρom* ao/...
can I say a(t)= a(teq)/ao ? Doing the calculations this is what is missing for the equation mathematically, but not even sure if that's right to say about the expansion rates.
I feel like I'm missing a property of how the different times in the expansion rate work. Like, are there three...
We want to calculate the ao/a(teq) of the equilibrium point between ρm and ρr (ρm= ρr )
My book solves it this way;
ρm(t) / ρr(t)= a(t) ⇒
⇒ (ρm/ ρr)teq =1 =
= (ρm/ ρr)o * a(teq)/ ao
I don't understand the a(teq)/ ao part. If ρm(t)= ρο/αo3 and ρr(t)= ρο/αo4 then it should be
ρm(t)/ ρr(t) =...
I'm talking about the hypothetical models I listed in that url. I know not all of them are true. But also you said we have different fluids at different times. I know that the matter and radiation density ratio change with time. This is what I was asking. Near the Big Bang time, the radiation...
Can we say that a universe with a radiation density (only) exists only in near a Big Bang time, and not a Big Crunch? Since it gets much smaller as time passes.
For example in here:
We have different cosmological...
Does direct radiation increase as the zenith increases? I know the diffuse radiation increases as zenith does, but is it the same for direct
Also is it right to say that when diffuse radiation increase, the direct should decrease and vice versa?
edit: My book says diffuse increases as we...
We are given the wave function with spin, but it doesn't say in which Ylm each spin X± goes. So how do I know?
(1) Ψ = 1/√3 R21(r) ( Y10
Here we have the up Spin X+ to Y10 and the X- to Y11
I notice the X- went to...
I know the eigen value of energy in a Morse potential is
Evib= ħωo(v+ 1/2) - ħωoxe(v+ 1/2)2
but is this the same for every Morse potential, given that the masses μ of the diatomic molecules are the same?
The two potentials are these:
We need to prove that a3(t)= ρo/2Λ [cosh(sqrt(24πGΛ)*t) -1] by changing into a variable of u, where
From Friedmann's second equation we know that Λ= ρm/ 2
Also ρm= ρo/ a3
I begin from Friedmann's equation where (for here), ρtotal= ρm + Λ and k=0;
a'2/a2 = 8πG(ρm +...
No it's not homework question. Don't remove it from this category please, because I think that's the best category for this. It's what I read in my book but I couldn't find where the answers are supposed to be.
The left part of the columns describes the characteristics of the Universe Model...
So I trying solving this by using the formula of dV=... but I couldn't solve the Integral, plus my book says the solution is supposed to be easy. Also we haven't been taught this type of math.
I've searched for a solution on the internet and I found this from a page;
Which is the...
Problem gives these for a chaotic model;
There's a standard method to follow and find the a(t) by using Friedmann's and inflaton equations. I think my mistake is most likely on the math part, because in the physics aspect we always...
The final result must be V=2π2α3
Hint says we must use the dV in the spherical system (dV=r2sin2θdrdθdφ) as well as the equation of the three-dimensional metric ds2= c2dt2 - a2[ dr2/(1-kr2) +r2(dθ2 +sin2θ dφ2) ]
For a closed universe we know k=+1 and with dt=0
My problem is, I don't understand...
According to the Born-Oppenheimer approximation, what does the internuclear distance Req depend on?
Atomic number Z?
Rotational Energy of the nuclei?
Electrons' kinetic energy?
Coulomb interaction between the two nuclei?
Coulomb interaction between the electrons?
Vibrational energy of the...
Suppose we have a surface that scans a cycle, with an S=πR2, when its axis faces the gas' flow vertically.
Now if the gas' flow gets an angle of θ=150ο, what will the S be? My book says it's Scosθ, but with an angle of 150o it gives me a negative number, which doesn't make a lot of sense...
<< Mentor Note -- Two threads on the same question merged into one thread >>
How does the maximum Power equation change if there's an angle to the way the wind falls into the wind turbine's blades?
Example, when it falls vertically to the blades, it's
But if there's for...
I have two questions
(1) If we have two areas, for example one in America and the other on Asia, both with the same latitude φ, which one of the areas will receive more Solar Radiation? Or will it be the same?
(2) If Earth's eccentricity graph for the past 750k years is this...
I've noticed that in the Shell Model of the nucleus, the order of the energy levels is 1s, 1p3/2, 1p1/2, etc. While in the atomic energy levels it goes 1S 2S 2P, ... But they still take the same amount of particles for each level in both the atomic and nucleus.
Am I missing something here? Or...
Why is it that in Grotrian diagram only the 4p->3s is not allowed, but the 4s->3p, 4p-> 3d and 4d-> 3p are allowed ? I'm following the rules of Δl=±1 and Δm=0,±1 and they give the same numbers. I also tried with Δj=0,±1 and still the same.
Grotrian Diagram for Hydrogen for n=[1,4]...
Prove that in an MHD equilibrium state in a pinch with flux and Bθ(r) and Bz(r), the equation for pressure is;
d/dr(P + B2/8π) + Bθ2/4πr - ρ( u2θ/r)= 0
B is the total Magnetic field, uθ(r) the velocity of plasma, ρ= density, and solving in a (r,θ,z) system
When do we use the equations of curvature drift ( ΔΒ⊥Β) V∇B= ±1/2u⊥rL (B x ∇B)/B2 and the general VF= c/q (F x B)/B2?
For particles like muons and protons, do they need different equations to calculate a gas' drift velocity, when the gas is made of protons or muons instead of electrons?
When do we use the Boltzmann equation for density in a Fermi plasma?
n in [cm-3]
and when do we use the ρ=m/V, ρ in [Kg/m3 ]
(this is not an example, I just added the equations to make my question more understandable)
Is the ideal gas only when we have electron and ions? Is the Boltzmann...
Cylinder electron gas with density of ne= 1010 and radius or r=1cm is inside magnetic field of B=104 Gauss.
If we change the electron gas with
(i) muon gas
(ii) proton gas
does the Drift Velocity change?
Boltzmann equation of density...
The Atom of Helium is doubly excited in 2p2 1D
Can someone explain to me how these energy symbols work? I have a problem with what the 1D means specifically. I know 2p2 means two electrons in the 2p state. The 1 in 1D could be referring to electron being in a singleton, but I don't understand...
A system of |1> and |2>, in the beggining has a function |Ψ(0)>= cosa|1> + sina|2>.
The energy of the system is;
a, ε,n are known. Find the |Ψ(t)>
The solution is;
It is known that; |Ψ(t)>= e^(-iHt/ħ) * |Ψ(0)>
but I don't...
So is it wrong if the final frequency becomes f'=[(u+uo)/(u+us)]f, since we consider that the source is moving away from the observer, while the observer moves closer to it (when the velocity of the observer is higher than the source's)
What happens if a source and the observer move at the same direction?
Always hear how only one of them doesnot move, or when they move towards each other.
For example. An ambulance moves towards direction A with Va. A biker moves towards direction A as well, with Vb.
What happens to the...