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I am given a wire with charge density $\lambda$ that is parallel to the $z$ axis and intersects the $xy$ plane at $(d,0,0)$. Space is filled with two different dielectric materials such that in the region $x>0$ the dielectric constant is $\epsilon_1$ and in the region $x<0$ the dielectric constant is $\epsilon_2$. I am... |
In special relativity, one can transform a 4-vector as follows:
$$
x'=\Lambda x
$$
Of course in this case, $\Lambda$ cannot be an arbitrary $4\times 4$ matrix of $\mathbb{M}(4,\mathbb{C})$. For instance, it must invertible. I believe, technically, it must be an element spawned by the basis representation of $O(3,1)$...... |
I know that wavelength is the distance between corresponding points of two consecutive waves. It is the distance over which a wave repeats its motion. But I am unable to understand what is actually wavelength? What does it really mean? Is wavelength the length of medium over which one complete wave is formed?
|
Clearly, if I'm spinning, I'll feel my arms lift away from my torso. But what sets the preferred angular momentum? Is there a preferred angular momentum in a vacuum? In Newtonian mechanics, I imagine one would appeal to the ether, so I suspect the answer lies in general relativity.
|
I read this in Griffith in harmonic oscillator topic(page 45 equation 2.66) . Why when we use creation operator then annihilation operator on w.f of state n it gives wavefunction of state n+1? Isn't the state should remain n as one operator reverse the effect of another which is the case when we use annihilation operat... |
Why some atoms do ionic bonding (electron gain/lose) over covalent bonding (sharing electrons). Are there some rules/theories which explain that?
|
Considering only the secondary steam turbine stage of a thermoelectric plant, if the system is shut down, and the pressure is at equilibrium throughout the system, how is a pressure differential initially created across the vanes to begin rotation? Or is it jump started somehow? Does it have to be decoupled from a load... |
The following is a specific instance of the brachistochrone
problem, which I first encountered in grad school, and I
have occasionally used as hw problem in teaching CM.
A particle is started from rest at the origin and constrained to fall under gravity along a path $y(x)$ which passes through the point $x=5$, $y=-1$ ... |
I was reading this tip on how to cool beers with a gas duster:
https://www.popularmechanics.com/home/how-to/a10535/instant-ice-cold-beer-in-3-easy-steps-16798775/#sidepanel
This made me remember how cold it is when using a gas can to fill a lighter as well.
Pressure drops when gas exits the bottle. Is that enough to ex... |
If cold cannot be achieved without producing heat somewhere else, I was wondering could said heat be sent to outer space using a microwave ray or any other electromagnetic radiation, and thus lowering a planet's temperature?
Note: I am not concerned with engineering questions nor how insignificant such a temp change wo... |
What the characteristic force is
Dimensional analysis has an interesting result in fluid mechanics: the quantity $\chi=\eta^2/\rho$ has the units of force, where $\eta$ is the usual dynamic viscosity. The Reynolds number can then be thought of as
$$\text{Re} = F_\text{Re}/\chi,$$
where the Reynolds force $F_\text{Re}$ ... |
I am trying to prove the invariance of $ds^2$ in any 2 arbitrary inertial frames of reference, and I have reduced the proof to proving that when the relative velocity (of the 2 frames) is along the common $x$-axis, the coordinate transformation does not affect the $y$ and $z$ coordinates.
$$y=y'$$
$$z=z'.$$
This seems ... |
I watched the video: Geometry of scattering amplitudes of lectures by Nima Arkani-Hamed. At 3:00:00, he derived the following equation:
\begin{align}
& \int \frac{dc_1}{c_1} \cdots \frac{dc_5}{c_5}/_{GL(1)} \delta^{4|4} [c_1 Z_1 + \cdots c_5 Z_5] \\
& =\frac{1}{<1234><2345><3451><4512><5123>} \delta^4[ <1234>\eta_5 + \... |
I recently saw an interesting paper: https://arxiv.org/abs/1912.13435, where the author wrote the Feynman propagator of free massless scalar field as
$$
D_F(x-x') = -i\int\limits_{-\infty}^\infty \frac{d\omega}{2\pi} e^{-i\omega (t-t')}\frac{e^{i|\omega||\vec{x}-\vec{x}\,'|}}{4\pi |\vec{x}-\vec{x}\,'|}.
\tag{1}
$$
(Ple... |
The other day I asked a question here. The question concerns two separate, radiating spheres that have constant heat generation and a consequent steady state temperature. Since one sphere has a smaller magnitude heat generation, but is identical to the other in all other respects, it will have a lower temperature. If... |
Free neutrons are unstable (half-life $\sim 10$ min), but bound neutrons are (for many nuclei, including those which are stable) stable.
Question 1: Are there other properties of the neutron / proton which change depending on whether the nucleon is free or bound, or depending on the precise nucleus the nucleon is part ... |
An observer holds a cup of coffee that is filled to the brim at the moment a gravitational wave passes by.
Should the observer be worried about spilling coffee because of the
gravitational wave? If so, could we estimate the maximum height that the observer can fill his cup to avoid spilling the coffee?
|
We have two objects connected over a pulley. If the string is an ideal string most of the times, the acceleration of both the objects will be same. Below are some of the cases. I am trying to think will there be any case, when the objects wont have the same acceleration.? The case that is troubling me is #3 below. In ... |
Recently while going through the chapter calorimetry of class 10 I came across a passage saying "if we add impurities to water such as salt in proper proportion the boiling point of water increases."
How is this happening?
We know when a substance reaches its boiling point it evaporates.
But why does it happen when sal... |
Domain walls have the unusual property that they are gravitationally repulsive (See reviews by Sikivie). Does a similarly strange result hold for monopoles?
|
I'm doing an experiment about the effect of viscosity on water rockets, and was wondering if there are any equations that include viscosity that are significant to rockets/water rockets.
|
I learned from reading nLab (https://ncatlab.org/nlab/show/anti+de+Sitter+spacetime) that the anti-de Sitter Spacetime of dimension $d$, $AdS_d$, is homeomorphic to $\mathbb{R}^{d-1} \times S^1$. I tried to use the first image in this link for inspiration, but still I have a hard time conceptually understanding why the... |
The temperature of deep water is around 3 or 4°C. However, in the Earth's crust, temperature increases with depth (e.g., 66°C in some underground mine). So, why would the water be cold?
If the heat is generated by the soil itself (say, radioactive potassium or whatever), even if such heating would not occur in water, o... |
Is it sure that Milky way and Andromeda will collide or might they just start a rotation around their center of masses?
|
This question is related to this one I asked some time ago: Reason for Symmetry of stress tensors.
The reason behind the symmetry of the Cauchy stress tensor seems to be Cauchy's Lemma. Once you accept that the traction vectors $t^{(n)}=-t^{(-n)}$, one can derive step by step that the tensor must indeed be symmetric. N... |
If we installed an opaque screen in space in the vicinity of Earth blocking all sun rays, how long will it take to cool the planet back to pre-industrial times?
I know global warming is not just about temp, but how heat is unable to dissipate because of greenhouse gases. Yet, I suppose if you turn the incoming heat of... |
I was recently going through question on Simple harmonic motion and came across the example in the photos i could do all the question until the last one which stated to show the time in which the dog would lose contact with the bridge the answer says its at t=0.12 s however at this time the bridge travelling upwards th... |
For starters I may be mistaken bringing this up as a notation problem, maybe for some reason unknown to me this is not about notation at all and I simply do not understand the topic well enough yet, this uncertainty tho is precisely why I am asking this in the first place.
In Modern Quantum Mechanics Sakurai calls the... |
I cannot find in literature an exact expression of the probability of transition of the eigenvectors of the quantum harmonic oscillator Hamiltonian when it is "shaken" in this way:
\begin{equation} H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2(x-x(t))^2\end{equation}
I found only first order approximations with a "forcing" ter... |
Edit:
Thank you all for the explanations, but I think until I fully grok special relativity, Lorentz transformations and relativity of simultaneity, the answers won't make any sense to me. Maybe the question I should be asking is "why do we believe there is no absolute time frame", but that would change this question t... |
I’m working in Peskin and Schroeders book on QFT
These are the Fourier transforms of the field solutions to the Klein-Gordon equation:
I don’t understand how to get from (2.25) to (2.27)
The logical thing seems to me to try the substitution: $p$ becomes $-p$, for each of the components of the momentum in the second te... |
I'm exploring periodic conditions and I'm stuck in a problem. Given that $m\cdot L_1 = n \cdot L_2$, we have two periodic functions $f_1$ and $f_2$ with periods $L_1$ and $L_2$ where we can find, for example that $f_1(x+m\cdot L_1) = f_1(x)$. What can I say about the period of the sum of these two functions? If I use t... |
I am probably going to butcher this questions so don't flame me for it.
If I have an electron and I shoot it at the double slit. Or even better a LOT of electrons and I am shooting them at the double slit. I get the known pattern on the detector after the slits. But doesn't this violate physics? Each electron has a... |
According to my current knowledge, the Cooper-pairs in a closed superconducting circuit should "feel" a centrifugal force. The (-2) charged pairs are therefore accelerated.
Do the Cooper pairs emit photons? Is there some mechanism that prevents it? Even if you look at the complete wavefunction, still there is an electr... |
A force F is continually acting on the end of a solid rod at a pivot point A (see image below). The object causing that continual 'Force F' is attached to pivot point A and constrained to only move in the line of direction shown.
What forces are causing the center of mass (COM) to move in line with the tail end of the... |
In classical physics when a billiard ball hits a stationary one of same mass it transfers all its momentum to it so becoming itself stationary while the other gathers their whole momentum.
But what about relativistic particles? Will a relativistic proton transfer immediately its momentum to a stationary one or the coll... |
Time runs slower near a massive object. I believe this time dilation is due to the gravitational potential present near the surface when compared to a distant point. What about the center of a massive object, how does time run at the center of a massive object compared to its surface?
After all at the center the accele... |
Initial research
I have found many questions and answers about O'Neill cylinders but they are assumed to be rotating. https://en.wikipedia.org/wiki/O%27Neill_cylinder
I am also aware of the Shell Theorem https://en.wikipedia.org/wiki/Shell_theorem
Background
However I would like to understand the nature of the gravita... |
A chimpanzee has just returned to the surface after extended time at 1km depth, breathing trimix air. This brings the possibility of hyperbaric habitation, however how would the basic functions of cooking be affected in hyperbaric conditions?
Specifically, could we have ice cubes or ice cream? Water boils at over 300°... |
Just think of the rotation of the quark inside a proton as the number of times it takes the highest position on an imaginary circle i.e. 90 degrees (up) to the center of mass of the proton. Now, let's push the proton to reach a relativistic speed. The quark must oscillate around the center of the proton and doing so it... |
Did the Big Bang happen at a point? goes through the fact that the Big Bang happened everywhere at the same time. John Rennie's answer explains this as being a consequence of all points in space beings squished into a single point, so technically the Big Bang happened everywhere. But, when we talk about relativity, we ... |
I have grounded one end of my capacitor after charging it but the voltage drops at a steady pace not as if it has lost charge. Is this because the opposing charges on the opposite plate are keeping the charges in place? When both plates are connected we have a voltage drop and V=ED and F=EQ but when one plate is ground... |
If gravity is mediated by particles and you are at a scale where those particles are relatively much larger does that perhaps imply that gravity can't work exactly the same way at very small scales as it does at much larger (like planetary, galactic) scales?
|
What is the relationship between the vibration of the string and the uncertainty of space-time.Not seeing the string, but when doing calculations, some parts of the string are affected by spacetime foam and cannot be expressed
It’s a bit like a dragon with a head and tail but no middle part
|
Why are the directions of frictional forces on the front and rear wheels of a moving car in the opposite direction, when the only the front wheels are accelerated (or only the back wheels)?
When the car accelerates, the direction of the static friction exerted by the front wheels on the surface is directed backward. Bu... |
How does one find solutions to a classical field theory (say, $\phi^4$ theory) when the time dimension is periodic (so in $\mathbb{R}^n \times T^1$ or other compact topology), especially if the initial conditions have some randomness (so we're dealing with statistical physics)? It seems to me that the solutions should ... |
In this video, the following is said between 06:07 to 06:38:
Now one of the interesting questions is how do you get from the
quantum of space and time to Einstein’s theory of general relativity?
It’s because when you add mass and energy, you can distort the shape
of the little volumes. Now that seems like it wouldn’t ... |
Please read this passage, from section I-18-1 of The Feynman Lectures on Physics:
We may consider any object as being made of lots of little particles, the atoms, with various forces among them. Let $i$ represent an index which defines one of the particles. (There are millions of them, so $i$ goes to $10^{23}$, or som... |
I am wondering if it's possible to compute the derivative of the Dirac Delta function using the definition obtained from Fourier transformation: $$\delta(x-x')=\frac{1}{2\pi}\int e^{-ik(x-x')}dk.$$
What I have attempted is the following (all the integrals are from -infinity to +infinity):
$$\frac{d}{dx}\delta(x-x') = \... |
Suppose the object is falling down and surface of conveyer placed on the ground has a co-efficient of kinetic friction $\mu$. After some time of the object travelling, it falls onto the conveyer.
Now in the frame of conveyer, the block is moving towards left, and gets accelerated from a velocity of $ -v$ in direction ... |
Given the following:
The potential is:
$V(x) = 0$ , $x<0$
$V(x) = V_o$ , $0\leq x\leq a$
$V(x) = 0$ , $x > a$
In the three regions the solutions to Schrondinger Eq. are:
$\psi_1 = Ae^{ik_1x} + Be^{-ik_1x}$
$\psi_2 = Ce^{ik_2x} + De^{-ik_2x}$
$\psi_3 = Fe^{ik_3x} + Ge^{-k_3x}$
where
$k_1 = k_3 = \sqrt{\frac{2mE}{\hbar... |
Consider a simple L-R circuit. When I tried to find heat generated in an L-R circuit, I got the result as, mathematically speaking, the work done by the battery, and the heat produced in the resistor are infinite till steady state is reached.
The integral I used for Voltage energy is
$$∫VIdt,$$
where $V$ is the constan... |
The Wigner Function is defined as:
$$W(x,p,t)=\frac{1}{2\pi\hbar}\int dy \rho(x+y/2, x-y/2, t)e^{-ipy/\hbar}\tag{1}$$
Where $\rho(x, y, t)=\langle x|\hat{\rho}|y\rangle$.
I am supposed to find the time evolution of the Wigner function for the Harmonic Oscillator starting from the von Neumann evolution equation given by... |
Intuitively, a wave is something that propagates through an elastic medium (except possibly for ocean waves); is it possible to consider space-time as such a medium? And if so, what would its elastic tensor(s) be, if that is the correct term (it has been many years since I learned the elements of physics)?
And by exten... |
\begin{equation}
\imath q^\mu\mathcal{M}_ \mu(k;q;p)=-\imath\tilde{e}\mathcal{M}_0(p;k-q)+\imath\tilde{e}\mathcal{M}_0(p+q;k)
\end{equation}
This is exactly the Ward-Takahashi identity for two external fermions.
In the case of full-vertex function this equation can be written as
\begin{align}
q^\mu\Gamma_\mu(p,q,p+q)=S... |
I recently started reading about Lagrangian Mechanics. I observed that it uses some basic expressions that are derived by taking Newton's laws of motion as fundamental such as kinetic energy, potential energy, momentum, etc.
So how can Lagrangian even be fundamental if it uses expressions that are based on some other f... |
According to the theory of relativity there is no ultimate preferred frame of reference in our universe. It means that whenever there is motion between object A and object B, whether it is considered that object A is moving or object B is moving or both are moving depends upon your frame of reference.
If we follow this... |
From what i read:
Normal force is the force that prevents objects from passing through eachother,which is the force of the repulsion
from the charge.
The normal force will get as large as required to prevent objects from penetrating each other.
My question is about the scenario of a person inside an elevator:
The... |
pls help me on it. I do not know if it is right but why do we only see black colour while there is no light.
|
I've been attending talks in some condensed matter groups, they always talk about "subbands", but what exactly are they? What's the difference between the "normal" conduction and valence bands? Thank you.
|
In this video, it is explained that it is not necessary that photons obey the laws of reflection and each photon can take any possible path to reach the so-called black hole receiver and all the paths have some certain probabilities as shown in the picture.
But if that's the case why do we see a certain region of the ... |
I need to understand self-adjoint extensions in quantum mechanics to solve some problems of scattering and bound states in Aharonov-Bohm potentials. There are some referencies that present the math concepts in a more friendly way for someone with a physics background as myself? And I would like to see more applications... |
In continuum mechanics, a continuum is defined as a set of points filling a space (or a part of it). This seems a bit confusing to me since in a mathematical sense, points are zero-dimensional but concepts such as stresses (which are defined as force per area) or gravity (which affect masses/volumes) don't really make ... |
I'm 15 and I recently got into electronics and I'm just having trouble understanding what voltage is
I've visited multiple difference websites and they all say different things. Some people say that i'ts the strength of the electric field created between the two poles of the battery. Some people say it's electric p... |
How to calculate the time it would take for a hydrogen atom to collapse if Rutherford's model were correct? I tried using the relation between power (Larmor formula) and energy but I can't seem to get the right answer. I'm new on this site so I apologize if it's not a good question.
|
I'm trying to calculate the magnitude and direction of the force exerted on a wheel when encountering a step. The wheel and the steps are non-deformable.
I found two different approaches:
energy approach, from which I can calculate the difference in speeds before and after, but I have no idea how to continue from ther... |
Consider light as rays interacting with refractive boundaries - no polarization or diffraction, but with scattering - a fixed probability of a ray changing angle per unit time.
First of all, what would be defined as a mode? The trajectory of a ray? Then does a ray that reflects off a surface count as one or two modes? ... |
I was reading a little about electrostatics when i got stuck with a derivation.
Consider an infinitely long conductor exrending to both side . Take two points at distances $a,and b:b>a$ then the potential difference
$v_b-v_a=\int_{a}^{b}-Edr$
=$\frac{\lambda}{2\pi\epsilon}\int_{a}^{b}\frac{dr}{r}$
=$\frac{\lambda}{2\p... |
I'm working through a proof in Griffith's Quantum Mechanics book (Chapter 1.4 - Normalization) and feel like a subtle detail is being omitted. If anyone can supply clarity that would help.
We have $\Psi = \Psi(x,t)$ and the author ends up reaching this point in the proof.
$$\frac{d}{dt}\int^\infty_{-\infty}|\Psi|^2 dx ... |
Deep sea diving and cassion workers are at extreme risk from many hazards such as "bends," nitrogen narcosis, and oxygen poisoning when compressed air is absorbed into their bodies, and then decompressed. However, the cuvier's beaked whale can take in a large volume of regular surface air, dive to a depth of 1 mile in ... |
I have a cart of mass $m_c$ connected to a pole of mass $m_p$ and length $L$ with a frictionless hinge. The cart can slide frictionlessly on a horizontal plane. Let $x_c$ denote the horizontal coordinate of the cart center of mass, and $\theta$ the angle between the vertical direction and the pole, positive if anticloc... |
This is probably an elementary question, but I am trying to help my nephew answer a worry. His question is: given Newton's third law, when a ball is thrown up in the air, we would push the earth a little downward. But whatever acceleration imparted and distance traveled during the throw the earth moved, why don't we ha... |
It is said that:
$$ F = -m\omega^2 x = -kx, $$
so $k=m\omega^2$. Since $k$ is the spring constant it doesn't depend on the mass of the object attached to it, but here $m$ signifies the mass of the object. Then how is $k$ independent of the mass attached?
|
I usually see air conditioners releasing hot air from the inside to the world outside. But since it is warmer than the air outside, I cannot see why this gradient could not do some work and possibly save some energy, like reducing the aircon's electricity consumption.
|
If I refer well (I'm not a physicist) one of the oldest uses/applications of renewable energy is to try to exploit the wind and tides by means of designs of machines: windmills and water wheels. Today this technology has provided us with modern wind turbines and tidal energy (I refer the articles from Wikipedia entitl... |
Given a differential operator $\mathcal{D}$ with adjoint $\mathcal{D}^\dagger$, the analytical index of $\mathcal{D}$ is usually defined by
$$\text{ind }\mathcal{D}=\dim\ker\mathcal{D}-\dim\ker\mathcal{D}^\dagger.$$
Alternatively, we can talk about the superconformal index
$$I(\beta_j) = \mbox{Tr}_{\mathcal{H}}(-1)^F e... |
I‘ve been searching for it on many different websites and they all basically say the same thing. The subatomic particles’ mass is so small that other forces (as the weak force, strong force and electromagnetic force) act on them much more effectively, in such a way that particle physicists may completely ignore gravity... |
My question regards the symmetry properties of the derivatives of diabatic electronic wavefunctions. I think the question goes somewhat beyond the standard group theoretical machinery taught in introductory quantum mechanics classes, so I will try to give some context without reviewing all the details. Consider first t... |
Consider a regular pentagon whose vertices are labelled as $1, 2, 3, 4$ and $5$. Now, let us put a charge +q at each corner. I can understand that the field at the centre $O$ must be zero, from symmetry. Also, by breaking each electric field vector at the centre into two mutually orthogonal components in the plane of t... |
Specific heat capacity depends on temperature.
When heating a substance, energy change = mass of substance $\times$ specific heat capacity $\times$ temperature change.
In school, we may apply this equation over a change in temperature to find the energy put into the system. At the same time, the value for the specific ... |
At some point we are looking for the solution of the Einstein field equation for the Schwarzschild gravitation from
$$ds^2 = A(r)dt^2 +B(r)dr^2+r^2d\theta+r^2\sin^2(\theta)d\phi^2\tag{1}$$
I am reading Wikipedia and the obtained solution is
$$A(r)B(r)=K \quad \mathrm{with} \quad A(r)=(1-\frac{1}{Sr})\tag{2}$$
Then requ... |
The Einstein-Hilbert action on a manifold $M$ with boundary is
$$\frac{-1}{16\pi G}\int_M d^n x \sqrt{-g} R +\frac{1}{8\pi G} \int_{\partial M} d^{n-1}x \sqrt{|h|} K$$
where $K$ is the extrinsic curvature of $\partial M$ in the induced metric $h$. The Gibbons-Hawking boundary term is often justified by the fact that va... |
Every vector space $|\vec{v}\rangle$ over the field $\mathbb{R}$ or $\mathbb{C}$ contains a dual space, and so if we make an identification between elements in the dual space and the original vector space, it seems that every vector space naturally comes equipped with an inner product, called the dual space inner produ... |
I recently read "Atomic Adventures" by James Mahaffey. In the book (Chapter 10) he mentioned a theoretical way of faster-than-light communication. My brain instantly searched for flaws in the proposed system but I couldn't find any, I'm sure there is a reason but I just haven't thought of it yet. It would be very helpf... |
I am trying to work out the Euler equation. However, I find some difficulties of the following step. Am I doing the right things and how could I get into the last step? Thanks a lot.
$$ \nabla (\vec{v} \otimes \vec{v}) $$
$$ = \nabla \left[ \begin{pmatrix} u \\ v \\ w \end{pmatrix} \begin{pmatrix} u & v & w \end{pmatri... |
A bad drawing just so you can see what I mean:
On every derivation I see, at some point it is stated that:
$$ \frac{T_x}{T}=\frac{-x}{L}$$ It is always explained by saying "by the geometry of the problem" or "by triangle similarity" but I fail to see how that follows so easily. This relation implies that as the x comp... |
I am trying to solve Problem 3.21 in Introduction to Electrodynamics, Griffiths where I am asked:
Find the potential outside a charged metal sphere of charge Q and radius R, placed in an otherwise uniform electric field $\mathbf E_0$.
Let us orient our coordinate system such that the electric field acts along the z-a... |
I'm trying to calculate what's known as the Angle of Attack (AOA) for a missile given some missile data. it would be more of a theoretical value for the AOA since I don't have any wind data. I posted a similar question at the aviation stack exchange, but I think my question has evolved into more of a coordinate system ... |
Why am I able to see the top of the pictures even though they aren’t facing the reflexive surface.
The light would have to travel down through the picture
|
The universe has been expanding since the Big Bang. This expansion of the spacetime fabric can be estimated by the Hubble’s constant, and is usually compared (analogously) to a ballon being blown up, where its surface represents the 4 dimensions. One of the flaws in this analogy is that in our classical world a balloo... |
I am a researcher working to develop a hydrogen fuel system for use in a specialized internal combustion engine. The biggest challenge from an engineering standpoint with a project such as this is the inherently volatile nature and small size of the hydrogen molecule. My research has led me in a variety of different di... |
If the most distant galaxies we see in deep space are in proximity of our cosmic event horizon does it mean that if we were on Andromeda galaxy and looking in the same direction we would see objects that are beyond the Earth cosmic event horizon?
|
When considering a one-dimensional monatomic chain of atoms (identical masses $m$ & spring constant $\kappa$), one finds the following dispersion:
$$ \omega(k) = \sqrt\frac{\kappa}{m}\cdot\left|\sin\left(\frac{ka}{2}\right)\right|\, ,$$
which is $\frac{2\mathrm{\pi}}{a}$-periodic. So wavewectors higher than $\mathrm{\p... |
Assume I have a particle $m$ moving in one dimension where function $U(x) = -Ax + Bx^2$ describes the potential energy. I am trying to figure out how I can calculate the frequency of small oscillations around stable equilibrium points.
First off, stable equilibrium occurs when $U'(x) = -A + 2Bx=0$. Hence $x_{eq} = \fra... |
I'm 15 and have recently taken up electronics and I just had a question about batteries.
From what I understand (and according to a video I just watched by "The Engineering Mindest") a battery has a high concentration of electrons on it's negative terminal which creates the potential difference as well as an electric ... |
In the Quantum Mechanics course I took, we defined the operator exponential simply as
$$
\mathrm{e}^{\hat A} = \sum_{n=0}^\infty \frac{1}{n!} \hat A^n \: .
$$
This is probably a good definition for bounded operators $\hat A \in B(\mathcal H)$ over some Hilbert space $\mathcal H$, since the partial sums form a Cauchy ... |
I was rearranging the equation for the energy of a wave in terms of the number of a photons in the wave, and velocity, and found that:
starting with:
$$
nhv=E
$$
$$
E/nh=v
$$
$$
E/nh=fλ
$$
$$
E=nhfλ
$$
$$
hf=nhfλ
$$
$$
hf/hf=1
$$
$$
1=nλ
$$
therefore,
$$
n=λ^{-1} or λ=n^{-1}
$$
is this correct, and why?
|
Is there any fundamental issue to solving electromagnetic problems with the following algorithm? (practicality aside)
i) Set position, velocity, mass and charge for a set of particles.
ii) Compute the electric field at the position of every particle produced by all the other particles with Coulomb law.
iii) Compute the... |
Resolved: Thank you to W H G for the very helpful answer. I couldn't add a comment directly, so I'd like to write it here: your answer was helpful. I now see that I made my calculations in radians as opposed to degrees (the online calculator switched between them regardless of which I clicked on, but I thought it was o... |
Say we have equal masses $M_1$ and $M_2$, traveling at equal but opposite velocities, $v$ and $-v$. Assume elastic collision. The forces are equal and they come to stop, then accelerate away from one another at the same initial speeds.
But what if now we do the same but one velocity is $V$, other is $-2v$. Is the force... |
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