Density Definition and 1000 Threads

Can the polarization bound charge density be expressed in vacuum by a wave function?

So PSD is the Fourier transform of the Autocorrelation function. Is there any application of the Fourier transform on PSD in EE? Or it's like in Newtonian dynamics a second derivative wrt time is as far as we can get (more than that it's called a Jerk...).

As you no doubt have heard countless times, GR's prediction that a black hole should collapse to zero size is considered problematic because it would imply infinite density, which isn't physically possible. And yet, over on the other side in QM, electrons seem to be considered pointlike...

Hi all, I am trying to derive a relation (as function of temperature) for the coefficient of linear thermal expansion (CLTE) strating from a correlation for the density. But I'm getting a huge discrepancy from the experimental data. I'll start telling you some reasoning I did to get a relation...

$$u(\nu, T) = \frac{8 \pi \nu^2}{c^3} \cdot \frac{h \nu}{e^{h \nu / k T} - 1}$$ Now using the relation ##c=\nu \lambda##, $$u(\lambda, T)=8 \pi h \frac{1}{\lambda^3} \cdot \frac{1}{e^{hc / (\lambda k T)} - 1}$$ Now this is still per unit frequency. To get it to per unit wavelength, then $$...

The other day, a friend and I had a discussion about black holes, namely how the density of a body affects the process of its transformation into a black hole. My friend and I have too little collective knowledge in the field of theoretical physics regarding black holes, so the discussion has...

I am reading Purcell's Electricity and Magnetism and am getting confused on equation 5.22. It seems to me they are using relativistic velocity addition for u' which is u'=(u-v)/(1-uv/c^2), but aren't we solving for the velocity of the electrons in the test charge's frame of reference, so should...

I could not find an answer by checking the web. Could these perturbations originate from primordial black holes? What else?

Hello, I was thinking 🤔, Einstein's brilliant theory of relativity is an observation of time/space and how it alters with speed. If for example an object were to oscillate at such a speed to produce a very noticeable difference to its progression in time to its surroundings environment, say...

Part a) Is fairly trivial, just multiply both the given numbers to find the total change in momentum per second, which by Newtons II/III law is the thrust produced. Part d) is confusing me a great deal. I agree that pressure/density of air will decrease with altitude, this means that there will...

Liddle (2015, p.67) writes: "From the crude estimates that a typical galaxy weighs about ##10^{11}M\odot## and that galaxies are typically about a megaparsec apart, we know that the Universe cannot be a long way from the critical density." Was this fact (i.e. that the actual density is likely...

Dirac ("GTR" p. 47) makes an interesting observation immediately after obtaining Einstein's field equations with the simple energy-momentum tensor ##T^{\mu\nu}=\rho v^\mu v^\nu##. (##v^\mu## is the four-velocity.) First, the conservation of matter ##\left( \rho v^\mu \sqrt{-g}...

Dirac (GTR, p. 37) shows simply that for a scalar function ##S## $$\int S\sqrt{-g}\,d^4 x = \int S'\sqrt{-g'}\,d^4 x'$$ and this works precisely because ##S=S'## for a scalar. But for a tensor ##T^{\mu\nu}## the same procedure gives $$\int T^{\mu\nu}\sqrt{-g} \, d^4 x = \int x^\mu_{\,\...

This paper aims to resolve the inconsistency between different transformation equations by expressing the electric current created by a moving electric dipole as the sum of polarization and magnetization currents and calculating the resulting magnetic field. Here they take charge density to be...

I cracked an egg into water and it sank implying the egg matter is average more dense than water. If this is the case, a vortex should force the egg (when on the surface) off to the edges via the difference in centripetal force. Why then does the egg stay in the center when the water is swirling?

I'm trying to find how Cavendish got the density of the earth to 5,48 times the density of water. In all of the YouTube videos and webpages I have seen, they mention different formulas where the mass of the earth or the gravitational constant, G, is included. But as far as I understand, these...

For a flat universe, density parameter Ωuniverse=1. How does negative signage of a constituent density parameter, such as that of curvature index Ωk, which can be 0,1,-1 affect the signage of Ωuniverse? If Ωk were to be converted to its energy density, which is much less than the energy density...

Is it correct that: density = [ 0.09 * (density of NaCl) ] + [0.91 * (density of water) ] volume = [ (volume of water) + ( { (volume of NaCl) / 48} * 9) ] Thank you so much for any advice.

We've been talking in another thread about supermassive black holes. That has me thinking about really, really big BH's - so large that the spacetime curvature and evolution of the universe matters. Let's start by defining the density of a black hole as its mass divided by the volume enclosed...

Good evening, I'm running into some trouble with this problem, and I have a hint as to why, but I'm not completely sure. Please see the steps below for context. I've been able to set up the proper equation representing the density as a function of distance from the center which looks like this...

Ok, let's compare two cubes of lead. First lead cube weigh 6078 grams and its area is 3376 cm. The second lead cube is smaller and lighter at 5216 grams and 2713 cm area. The density of the first lead cube which is the bigger and heavier lead (by dividing its weight with the area) is 1.800 g/cm2...

I am not sure if my report is complex enough as it should be at the undergraduate level preferably based on the requirements for it and it feels like it's all over the place as of now.

m * g = mAl * g V * ρ * g = VAl * ρAl * g V * ρ * g = V * ρAl * g ρ = ρAl this does not work at all, because the upper ball must have a density smaller than that of seawater 1200kg/m3 or not?

I'm trying to figure out how describe the mass of air between the piston face and the und of the tube ( position ##o##) in the acompanying diagram. At ##t = 0##, the mass of air in the tube is ##M_o##, and the system is static with tube length ##l##. The ##x## coordinate describes how far...

Can someone please help derive the relations below from first principles? Also does someone please know what happens when ##ρ_{object} = p_{fluid}##? Many thanks!

I want to find the cumulative mass m(r) of a mass disk. I have the mass density in terms of r, it is an exponential function: ρ(r)=ρ0*e^(-r/h) A double integral in polar coordinates should do, but im not sure about the solution I get.

Its form is: (n2-1)/(n2+2)=(4π/3)Nam There is one simple problem with it. Rearrange the left side and you get: (n2+2-3)/(n2+2)=(4π/3)Nam 1-(3/(n2+2))=(4π/3)Nam As you see, the left side cannot reach unity for arbitrarily large n2. But there is no reason why N cannot be arbitrarily large! How...

In the frame of the patch ##-(1/\rho) \nabla p = - \nabla \phi##, and putting ##\nabla p = (\partial p/\partial \rho) \nabla \rho = c_s^2 \nabla \rho## and taking the ##z## component gives\begin{align*} -\frac{c_s^2}{\rho} \frac{\partial \rho}{\partial z} = -c_s^2...

The sphere floats on water so we should have: ##F_b=F_g## The buoyant force is equal to the weight of the displaced fluid, so : ##\rho _wV_wg=\rho _sV_sg## (w: water, s: sphere) From last equation we have : ##V_w=\frac {\rho _s}{\rho _w} V_s \rightarrow V_w=5 V_s ## The volume of displaced...

The starting point is the identity $$\left(\frac{\partial u}{\partial T}\right)_n = T\left(\frac{\partial s}{\partial T}\right)_n.$$ I then try to proceed as follows: Integrating both with respect to ##T## after dividing through by ##T##, we find $$ \int_0^T \left(\frac{\partial s}{\partial...

I need the theoretical energy density of inflation for my story. I seem to recall it as an enormous 1095 ergs per cubic centimeter.

I am studying a 2D material using tight binding. I calculated density of states using this method. Can I also calculate partial density of states using tight binding?

This question is related to equation (1),(3), and (4) in the [paper][1] [1]: https://arxiv.org/abs/2002.12252

Is there a way to independently determine the proportion of dark energy density to total energy density of the universe apart from using 1 -(Ωmatter+Ωdark matter )?

The correct answer to this problem is: ##\sigma = \varepsilon_0E\frac{\varepsilon-1}{\varepsilon}## Here is my attempt to solve it, please tell me what is my mistake? ##E_{in} = E_{out} - E_{ind}## ##E_{ind} = E_{out} - E_{in}## ##E_{in} = \frac{E_{out}}{\varepsilon}## ##E_{ind} = E_{out} -...

Hello everyone! I'm trying to replicate phonon density of states (PHDOS) diagrams for some solids using Quantum Espresso. The usual way I do it is the following one: scf calculation at minima (pw.x) Calculation of dynamical matrix in reciprocal space with nq=1 or 2 (ph.x) Calculation of...

$$n = \sqrt{n_x^2 + n_y^2 +n_z^2}$$ $$E = \frac{n^2 \pi^2 \hbar^2}{2mL^2}$$ $$n = \sqrt{ \frac{2mL^2E}{\pi^2 \hbar^2} }$$ This is all given by the textbook. It's even as friendly as to say $$\text{differential number of states in dE} = \frac{1}{8}4 \pi n^2 dn$$ $$D(E) = \frac{...

For Ω=1, κ=0. Does the value of κ simply follow from the value of Ω, or can its value have an independent existence? So if Ω>1, does κ have to be 1?

Hello, I am going over the derivation for two-electron density. I am having a hard time understanding how the second term in 2.11a seen below is derived. I know this term must eliminate the i=j products but can't seem to understand how. Thanks for the help.

I am confused about how the electric field changes in this problem - is E' = E/Ke=E/2? Is E = V/d a correct usage? When I solve it this way, the answer is incorrect: change in energy density = (1/2)ε(E'2- E2) = (1/2)ε(E2/4 - E2) = (1/2)ε(-3/4)(V/2d)2. What am I doing wrong? Thanks.

Here's my attempt at a solution, but when I plug it in, it gives me a power ten error. I don't really understand what I'm doing wrong here. I think all my variables are in the correct units and it asks for my answer to be in μC/m2. Any help is much appreciated.

Okay so I am a little confused as to where I made a mistake. I couldn't figure out how to program Latex into this website but I attached a file with the work I did and an explanation of my thought process along the way.

Schrodinger’s original interpretation of the wavefunction was that it represented a smeared out charge density however this was replaced with Max Born’s probability interpretation. The issue was from what I understand that a charge density would repel and have self interactions as all the charge...

Hi all, in this question i was asked to find the percentage change in the density, my approach was as following, first i find the change in volume due to putting the gas into the other vessel as: $$ P_{1}V_{1}=P_{2}V_{2}\;\; → \;\;V_{2}=\frac{P_{1}}{P_{2}}V_{1} $$ now i use $$...

If we throw empty but sealed glass bottle in water it will float with 60% of it's volume above the surface of water. What is average density of floating bottle and what is it's volume? Mass of bottle is 0.4 kg(mass of air inside of bottle is irelevant). It's easy problem but I can't get right...

For part a: I know that linear charge density is the amount of charge per unit length, and we are given the volume charge density. Since we are given the volume, we can obtain the length by multiplying the volume by the cross sectional area, so C/m^3 * m^2 = C/m. The cross sectional area of a...

Hello Please help me. I'm not a chemistry student and I don't have a chemistry-related course, so please explain in a very simple way. Thank you. I have a composite composition that I only have the weight percentage of atoms and I need to calculate the density so that I can check the properties...

When arriving at the standard model of cosmology, i.e. the exapnding universe, we assume based on experirmental data that the cosmos is homogenous on large enough scales. But when we go back in time, when the galaxies are beginning to form, we note that because of the growth of density...

Surface acceleration is proportional to density and radius of planet (as 2 powers of R cancel with the volume) g(moon)/g(earth) = density(moon)*radius(moon)/density (earth)*radius(earth) = (1/4)*density(moon)/density(earth)