# Search results

1. ### Fourier transformation for circular apertures

Thanks a lot...! I'm quite desperate over this problem and I couldn't find the solution anywhere over the web. Been searching for it for three days. Now I hope I can solve the rest of it lol
2. ### Fourier transformation for circular apertures

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...
3. ### Magnetic Mirror and particle trap

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...
4. ### B Chemical Potential μ in Solids

There is the equation: μ= Eu +Eg/2 +3/4kβTln(mu/mc) Eg is the band gap, but I don't understand what Eu stands for and how we can calculate it? Could it be the valence band?
5. ### I Horizon Problem

This is what I was looking for. Not sure if I worded "sources" quite right. But it came from calculating the V0(trec)/VH(trec)~1.4x10^5
6. ### I Horizon Problem

My notes from class say it. I didn't provide a source because this was the solution without the inflation correction, and also for the fact that this is not my main question.
7. ### I Horizon Problem

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...
8. ### A Equilibrium point of matter and radiation density

Thank you very much!
9. ### A Equilibrium point of matter and radiation density

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.
10. ### A Equilibrium point of matter and radiation density

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/...
11. ### A Equilibrium point of matter and radiation density

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...
12. ### A Equilibrium point of matter and radiation density

Yes, that's what I mean. The a in time now, just writing as ao instead of a(to) because that's the symbol we also use in class
13. ### A Equilibrium point of matter and radiation density

Ok then ρm(t)= ροm/αo(t)3 and likewise for the ρr(t). Still doesn't explain why the equation turns this way. Also what zeq is.
14. ### A Equilibrium point of matter and radiation density

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) =...
15. ### A Friedmann-Robertson-Walker Models

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...
16. ### A Friedmann-Robertson-Walker Models

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: http://www.nat.vu.nl/~wimu/Varying-Constants-Pictures/Time-Scale-Universe.jpg We have different cosmological...
17. ### Direct polar radiation increases as....

from the sun. Solar
18. ### Direct polar radiation increases as....

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...
19. ### I How to know where the up and down spin go in the wavefunction?

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? Examples; (1) Ψ = 1/√3 R21(r) ( Y10 √2Y11 ) Here we have the up Spin X+ to Y10 and the X- to Y11 I notice the X- went to...
20. ### I Morse Potenials Energy eigenvalues

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:
21. ### Friedmann's equation for a^3 with Λ, ρm

We need to prove that a3(t)= ρo/2Λ [cosh(sqrt(24πGΛ)*t) -1] by changing into a variable of u, where u=2Λa3/ρo From Friedmann's second equation we know that Λ= ρm/ 2 Also ρm= ρo/ a3 [First attempt] I begin from Friedmann's equation where (for here), ρtotal= ρm + Λ and k=0; a'2/a2 = 8πG(ρm +...
22. ### A Different FRW Cosmological Models

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...
23. ### A Different FRW Cosmological Models

ρο/a4 ρο/a3 k Λ Βig Bang Big Crunch Polynomial Expansion Exponential Expansion x 0 x 0 >0 x +1 x +1 x 0 <0 x -1 x -1 >0...
24. ### A Volume of a closed Universe

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...
25. ### Prove that a~t^(8pπ) (inflation)

Problem gives these for a chaotic model; V(Φ)=Voexp(-√(2/p)* Φ/Μp) Φ(t)=√(2p)*Mpln[√(Vo/24πp2) *t/Mp] 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...
26. ### A Volume of a closed Universe

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...
27. ### Born-Oppenheimer approximation & distance

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...
28. ### Solving a trigonometric equation for the angle

Yes you're right. I was just about to edit that
29. ### Solving a trigonometric equation for the angle

Homework Statement The equation; 0.966= -0.354sin(φ+60) + 0.935cos(φ+60) and we're trying to find φ. Homework Equations 3. The Attempt at a Solution [/B] (edited) I tried doing ^2; 0.933= 0.125sin2(φ+60) -2*0.331sin(φ+60)cos(φ+60) + 0.874cos2(φ+60) x=φ+60 0.933= 0.125sin2x - 0.331sin(2x) +...
30. ### Flow (liquid or gas) across a rotating surface's face

So Scos(150o)=πR2cos(150o) is the right choice?
31. ### Flow (liquid or gas) across a rotating surface's face

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...
32. ### Flow (liquid or gas) across a rotating surface's face

<< 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 Pmax= 8/27Sρu13 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...
34. ### I C-G coefficients and Angular momentum

Can someone explain to me how we find it? Examples Y10X-= = |1,0>|1/2,-1/2> = √2/3 |3/2,-1/2> + √1/3|1/2,-1/2> Y11X-= = |1,1>|1/2,-1/2> = √1/3|3/2,1/2> + √2/3|1/2,1/2> Y2-1X- = = √4/5 | 5/2, -3/2> + √1/5 | 3/2, -3/2> I understand it goes like YlmX± = |l,m>|s,ms> = a |jmax, ?> + b |jmin, ?>...
35. ### A Nuclear and Atomic energy levels

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...
36. ### A Grotrian diagram of Hydrogen

Both my physics books and the ones I've seen on the internet have it like this though
37. ### A Grotrian diagram of Hydrogen

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]...
38. ### Plasma Pinch Pressure

Homework Statement 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 Homework...
39. ### I Gas density and plasma

This is what I understood from reading about density in plasma (the n) and the parameters of a gas that make it a plasma. I'm not sure it's true though, that's why I asked.
40. ### I Gas density and plasma

In general, when we say that in a fermionic gas the higher its density, the better we can consider it to be a plasma instead of gas?
41. ### A Velocity Drifts of proton-muon gas

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? Am I...
42. ### Electron Gas (Plasma) to Muon

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...
43. ### Electron Plasma to Muon/Proton

Homework Statement 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? Homework Equations [/B] Boltzmann equation of density...
44. ### A Doubly excited Atom of Helium

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...
45. ### Evolved wave function in Dirac formalism

A system of |1> and |2>, in the beggining has a function |Ψ(0)>= cosa|1> + sina|2>. The energy of the system is; https://i.imgur.com/I0C7BFg.png a, ε,n are known. Find the |Ψ(t)> The solution is; https://i.imgur.com/urWs6XW.png It is known that; |Ψ(t)>= e^(-iHt/ħ) * |Ψ(0)> but I don't...
46. ### B Doppler effect/ both moving same direction

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)
47. ### B Doppler effect/ both moving same direction

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...