instruction stringlengths 31 24.3k |
|---|
I have encountered a problem with electrostatics potentials. The problem is given as follows:
A sphere of radius $$ has the potential $\Phi(a,\theta, \phi)$ at the boundary. Obtain expressions of the exterior and interior potential.
Solution:
The general solution is given by:
$$\Phi(r,\theta, \phi)=\sum_{l\geq0}\sum_{m... |
Consider complex scalar field Lagrangian
$$\mathcal{L}=(\partial^\mu\psi)^\dagger(\partial_\mu\psi) - m^2\psi^\dagger\psi\tag{1}$$
Which exhibits $U(1)$-invariance, i.e $\psi\mapsto e^{i\alpha}\psi$. On the other hand, to get a locally $U(1)$-invariant Lagrangian, one introduces a gauge field $A_{\mu}$ and promotes the... |
Assume two systems A and B, both are governed by the same physics law, just the sizes are different.
Are their any counter examples or proof to this?
|
The idea of a warp drive is to "expand space behind the ship and contract it in front"- in this way reaching a target destination faster than one could conventionally. However, the actual propagation of that space contraction and expansion would be limited by how fast spacetime distortions propagate in general, which h... |
Say we have an excitonic system with a creation operator operator:
$$ |\Psi_{ex}\rangle=\sum_{\vec{k}} \phi(\vec{k})c^\dagger_{\vec{k}+\vec{Q}}b_{\vec{k}}|GS\rangle$$
And the Hamiltonian of the system reads as:
$$H=\sum_{\vec{k}} E_c(\vec{k})c^\dagger_{\vec{k}}c_{\vec{k}} + \sum_{\vec{k}} E_v(\vec{k})b^\dagger_{\vec{k}... |
I'm confused about what "a Grassmann-odd number" really means and how does it apply to fermions.
In some text, it says that "if $\varepsilon \eta+\eta \varepsilon =0 $, then $\varepsilon $ and $\eta$ are Grassmann-odd numbers.
And in wiki, the Grassmann algebra are those whose generators satisfy $$\theta_1\theta_2+\the... |
We had an experiment in our physics lab where we used two grating materials one with 2500 lpi(say A) and the other with 15000lpi(say B).
Now when we shine white light on both of them we didn't get any spectrum in the transmitted light from A but we did get the pattern from B and my instructor told me that it had to do ... |
Just for the sake of context I'll add a little bit of introductory of the theory we were doing:
Say we are in the context of a bidimensional isotropic harmonic oscillator with an energy found of $2\hbar \omega$ hence $n_x+n_y=1$, which then, we can use separation of variables and suggest a function such that: $$\phi(x,... |
I'm debating about this problem with my friends (they and I majored physics. But I think it's not a trivial question.)
The problem is :
The water in the pot is boiling by the gas stove, and there is a steel ladle in it. When the temperature of the water reaches 100°C, can the temperature of the ladle be higher than 1... |
Since gravity curves space, I wonder how the locally increasing density of matter and energy due to the current galactic mergers with the Milky Way affects our perception of the universe.
Basically, if we have black holes coming closer to us, then the increasing curvature of space should make it look like the universe'... |
I want to show that the wave-function of
$$\Psi(x,0) = \frac{1}{\sqrt{ 5 }}(2\psi_{2}(x)-\psi_{3}(x)) $$
for an infinite potential well of length $a$ is normalized. With the time-independent function of
$$\psi_{n}(x) = \sqrt{ \frac{2}{a} }\sin\left( \frac{n\pi}{a}x \right)$$
where $n = 1,2,3,\ldots$.
My intuition tells... |
While reading Valerio Scarani's book ; Bell Nonlocality I came across section 2.4 where the author tries to represent the set $\mathcal{L}$, of all local behaviours as a polytope. The term behavior is defined (Eqn 2.4 of the book) as the set $$\mathcal{P} = \{P(a,b\ |\ x,y)\}$$ where $P$ represents the probability of ... |
In the two-photon absorption (TPA) process, when there is no intermediate state, it's required that two photons are absorbed either simultaneously or semi-simultaneously, with a relatively short time delay between consecutive absorptions, as observed in experiments. My question is: Is the concept of simultaneous absorp... |
In a circuit with an AV power source $V$ and a zero-resistance ideal coil, the power from the source. $P_{in} = IV$ is equal to the rate of change in the magnetic energy $U_B$ stored in the coil. The source energy goes to the magnetic field: $P_{in}=\dot{U_B}$.
Does the source give energy to the coil? It seems so.
Now... |
Lets say I have 2 capacitors P and Q connected to a 9V supply. Across P there's a resistor connected in parallel with the switch open (off position). When I turn on the battery they both fully charge. When I switch on the battery but also simultaneously switch on the switch to the resistor across P, does P discharge (e... |
I have been working on some results that work for time-independent Lagrangians $L\Big(q,\dot{q}\Big)$ and return a Hamiltonian function
$$
H(q,\dot{q})=\dot{q}^i \frac{\partial L}{\partial \dot{q}^i}-L
$$
and a symplectic form
$$
\Omega=\delta \Big(\frac{\partial L}{\partial \dot{q}^i }\Big)\wedge \delta q^i
$$
where... |
I want to repeat the classic exercise of the 3D jellium model in second quantization framework but in 1D. We know that the hamiltonian of the jellium model is made of three terms as explained in 'Quantum theory of many-particle system' by Fetter:
For example the first term in 3D is
$H_b=\frac{e^2 n^2}{2}\int \int \fra... |
I have a question regarding the dimension of time. We all know that an event in spacetime is defined by a point
$$ {x}^{u} = (ct, x, y, z) .$$
The only component that breaks the symmetry is $ct$, which is why the metric tensor has diagonal components equal to $(-1,1,1,1)$.
Why is it not possible to move in both directi... |
My question seems obvious but nobody is talking about it. The way I understand it, an electromagnetic wave collapses to a particle when observed. This goes for electrons and photons but I imagine the same is true across the EM spectrum.
When I send a wireless transmission and it's observed, some amount of energy within... |
I'm diving into Hartree-Fock methods, and I'm confused on why the Hartree-Fock Hamiltonian reduces into a single particle Hamiltonian.
When applying Wick's theorem to the Fermi Sea vacuum, we use the particle-hole picture which transforms the Hamiltonian into
$$
H = \sum_i h_{ii} + \sum_{ij} \frac{1}{2} \left[ \langle ... |
Using the formula for the volume of a hypersphere, one can easily deduce, using Stirling's aproximation, that the density of states for a system with $N$ particles with hamiltonian $H=\sum_{k=1}^n\left(\frac{\mathbf{p_{k}^2}}{2m}+V(\mathbf{r}_k;L)\right)$ is:
\begin{equation}\Phi=S(E, V, N) = k_B N \ln \left[ V \left( ... |
I wish to find the couple acting on the quadrupole due to q', assuming r>>a. Here is my working:
Force acting on -2q:
$E_{at \ -2q} = \frac{q'}{4\pi\epsilon r^2} \\
F_1 = (-2q) E = \frac{-2qq'}{4\pi\epsilon r^2}$
i.e. $F_1 = \frac{2qq'}{4\pi\epsilon r^2}$ towards q'
Force acting on leftmost q:
distance q to q' $\appr... |
I'm reading Sec. 1.6 of "Condensed Matter Field Theory", 3e, by Altland and Simmons, where the authors derive Noether's theorem. They consider the following mapping of the spacetime coordinates:
$$
x^\mu\rightarrow x'^\mu = x^\mu + \partial_{\omega_a}x^\mu\vert_{\omega=0} \,\omega_a(x)\tag{$\ast$}
$$
where "for a three... |
Here, the expression of the emission spectrum is
$$S(\omega)=\int_{-\infty}^{\infty}\langle A^\dagger(t+\tau)A(t) \rangle e^{-i\omega\tau}\text{d}\tau=2\Re\left\{\int_{0}^{\infty}\langle A^\dagger(t+\tau)A(t) \rangle e^{-i\omega\tau} \text{d}\tau\right\},$$
and the two-time correlation function, i.e. the Fourier invers... |
Why exactly do we need $$ \{q^i,p_j\}=\delta^i_j,$$ where $\delta^i_j$ is Kronecker delta and $\{\cdot,\cdot\}$ is the Poisson bracket? What happens to the phase space structure if these fundamental relations are not satisfied, i.e. if $q$ and $p$ are dependent by some relation? What physical thing do these fundamenta... |
The metric signature of spacetime is usually given as ($3,1$), but spaces can also be ($3,n,1$). Null surfaces include photons and event horizons, which exist, so is $n$ actually $ > 1$ in the signature?
In theory, could an experiment establish the number of null dimensions/directions?
In another answer, someone sai... |
Is the following statement true? "If the overlap integral between two wavefunction is zero, then the two wavefunction are orthogonal."
An example would be two hydrogen atoms located far apart: their s orbitals don't overlap due to spatial separation. Is it valid to claim the two s orbitals are orthogonal?
(So this mean... |
This is a thought experiment and I might be horribly wrong. If we have an electron-positron annihilation a photon pops into existence. This photon is then supposedly moving at speed of light at the exact moment that it pops into existence. How is this possible? Would the photon not have to accelerate to the speed of li... |
I am interested in the BRST quantization of the Hilbert-Palatini gravity theory. In the paper https://arxiv.org/abs/gr-qc/9806001, Alexandrov and Vassilevich write down the BRST procedure for defining the path integral of this gravity theory. I am specifically interested in equation (38) and (41) of this paper. These e... |
The strong CP problem is considered one of the biggest unsolved physics problems. A nonvanishing value of $\theta$ in QCD $\theta$-term violates CP-symmetry. A primary strong CP violating observable is the electric dipole moment of the neutron $d_n$. The current observed upper bound of $d_n$ is extremely small, which i... |
...Because it's Lorentz-invariant.
Different inertial frames observe different distances, durations, and simultaneity. They even report a different time of day on their wristwatch. But everyone in any frame agrees on the interval.
So when I explain stuff to other people, can I refer to "4D absolute distance?"
|
I know that there is both a Cp and Cv value, but here's what I don't understand: are they independent of what the absolute pressure is? They vary with temperature, and tables can be readily found with that information, but I am not sure whether they vary with pressure. i.e. atmosphere vs. 20 bar, either way at room tem... |
For steady state, radial conduction heat transfer through a cylinder, all textbooks show a term $\text{ln}(r_2/r_1)$ in the denominator $[q = (2*\pi*k*L*\delta T)/\text{ln}(r_2/r_1)]$, where $r_2>r_1$. There's always an example where heat is transferring from inside the cylinder (1) to the outside (2). However, if heat... |
Assume a pipe has wall thickness x. If the pressure inside and outside of the pipe bend is the same. Does it result in a non-zero net force on the pipe bend as the inner and outer areas differ?
|
Is $$\frac{Q_c}{Q_h} = \frac{T_c}{T_h}$$ valid for any reversible ideal cycle Or just for the Carnot cycle?
|
I have a confusion when applying the Lagrangian method to calculate the equations of motion of a rigid body. I don't understand at what (physical) point the generalized moments should be calculated, if such a concept exists.
The Lagrangian method can be derived through the method of virtual powers, which dictates the f... |
The orbital period of a satellite is the time it takes to complete an entire orbit around the celestial body around which it orbits. I know that the orbital period using the following formula:
$$T = \frac{T_{\text{tot}}}{n} \tag 1$$
where:
$ T $ is the orbital period,
$ T_{\text{tot}}$ is the total time taken to make ... |
I am studying classical mechanics from Goldstein and I ran into a confusing equation in the textbook. In the third edition of the book, equation (12.92) calcucates the average change of the action variable $J$ over some period of time $\tau$ given that the Hamiltonian depends on some slowly changing variable $a$.
In th... |
New-ish measurements from Hubble + Webb say that the Universe is expanding at different rates everywhere: https://www.livescience.com/space/cosmology/james-webb-telescope-confirms-there-is-something-seriously-wrong-with-our-understanding-of-the-universe
Why is this actually surprising?
According to mainstream GR, there... |
On the wikipedia page "Entropy", entropy is defined as $S=k_B \ln\Omega$, where $\Omega$ is "the number of microstates whose energy equals the system's energy". This is what I had always understood $\Omega$ to mean.
However, on the wikipedia page "Equipartition theorem", entropy is defined as $S=k_B \ln\Omega(E)$ where... |
We know space is expanding at a rate of roughly 432 miles/light-year/year. Since Einstein showed that time was intrinsically linked into the 4 dimensional structure of spacetime one would logically wonder if space expansion is linked to the passage of time. Due to the cosmic microwave background we can infer that the u... |
$\newcommand{\Ket}[1]{\left|#1\right>}$Suppose I have a total Hamiltonian $H = H_0 + V$ given by the usual kinetic term $$H_0 = \frac{\hbar^2}{2m} \sum_{\mathbf{k}, \sigma = \uparrow, \downarrow} \; \mathbf{k}^2 c^{\dagger}_{\mathbf{k} \sigma}c_{\mathbf{k} \sigma}$$ and an interaction $$V = -g \int d^3 \mathbf{x} \; \p... |
I am studying $\phi^4$ theory and so far I understand the mass and coupling constant renormalizations. In these theories, once we expand a diagram in perturbation theory we "cancel" the divergences by demanding the value we get from the diagram equals a measured quantity such as the physical mass or physical coupling.
... |
In the Schroedinger equation the kinetic energy is represented by the operator $T = -\frac {\hbar^2} {2m} \Delta$ which acts on a wavefunction $\Psi$. If we multiply this by the complex conjugate of the wavefunction we get the following density in position space:
$$Schroedinger: K = -\frac {\hbar^2} {2m} \Psi^{*} \Delt... |
From P&S consider the $\phi^4$ bare Lagrangian:
$$\mathcal{L} = \frac12 (\partial_\mu \phi)^2 - \frac12 m_0^2\phi^2 - \frac{\lambda_0}{4!} \phi^4.\tag{p.323}$$
When using renormalized perturbation theory we rewrite this Lagrangian using physical quantities and counterterms:
$$\mathcal{L} = \frac12 (\partial_\mu \phi_r)... |
You have a small globe, which is mounted so that it can spin on the polar axis and can be spun about a horizontal axis (so that the south pole can be on top). Give the globe a quick spin about the polar axis, and then, before it stops, give it a spin about the horizontal axis. Are there any points on the globe that are... |
We are having issues with an experiment with a transformer in Y-YN configuration.
We have a symmetrical three phase system on the primary and experiment with a short circuit (resistive load added) in L1 in the secondary.
The theory for short circuits with symmetrical components states that I0 = I1 = I2 = 1p.u. therefor... |
I would like to know how to derive the explicit form of the GENERATOR of a general two-qubit gate (also here), e.g., controlled-rotation Y.
From the definition: $$\exp(-i\theta G) \ ,$$
I see it is: $$G=\begin{pmatrix}0&0&0&0\\0&0&0&0\\0&0&0&-i\\0&0&i&0\end{pmatrix} \ ,$$
but, I would like to know how to write it in th... |
A uniform electric field has: $$\bar{E} = 2 \times 10^3 \ \hat{i} \ \ \mathrm{N/C}$$.
Find the flux of this field through a square side 20 cm, whose plane is parallel to the $y$-$z$?
I'm fairly new to the realm of electricity and electrostatics, and would appreciate some advice on, how I should think when tackled with... |
If I'm driving and I want clear a roundabout as fast as possible, but I only can take so much G force before dying, do I drive in the inner or outer lane. Assuming that the maximum G force I can take is constant.
|
In David Tong's lectures on the Standard Model I saw that there is a quark condensate, which is just a Vacuum Expectation Value (VEV) of the $\bar{q}_{Li}\, q_{Ri}$ operator,
$$
\left< \bar{q}_{Li}\, q_{Ri} \right> = - A \delta_{ij} \, . \tag{3.47}
$$
Now, this leads me to think that there might also be a VEV for the ... |
I'm having trouble understanding the legitimacy of solving the Schrödinger equation for a particle confined in an infinite square well. Aren't we supposed to solve it for the whole space and not just some region before we claim it to be the state of the particle?
Also what about the energy eigenvalues obtained this way... |
In practice, usually one of the parameters is tuned (for example temperature in 3D Ising model, which is a relevant parameter) so that it coincides with the value of RG fixed point, then RG flow make sure the remaining irrelevant parameter flows to the fixed point.
Now suppose we have a theory where we have solved the ... |
I am relatively new to matrix product states (MPS) and I'm interested in the computational complexity of performing an operation of the form A|a> + B|b> where A, B are scalar coefficients and |a>, |b> are quantum states represented by MPS' with some bond dimension $\chi$ and a site dimension $d=2$.
Is it the case that ... |
I have been surfing for days and still I could not find who wrote the equation $c=λν$ for the first time. Neither I found a name for this equation. A lot about Planck's constant and energy related equations, but nothing on the history of this one in particular. Anyone can help me?
|
I have looked at
Helium Nucleus as boson
How can multiple fermions combine to form a boson?
Why are He-4 nuclei considered bosons, and He-3 nuclei considered fermions?
but I still feel like saying "superfluid helium is a boson" is an oversimplification.
I don't have a problem with the rules of adding fermions to make... |
When two light rays intersect after reflecting from a concave mirror they form a real image.
but what happens if, say, a ray from the head of the object A collide with the reflected ray DA'? It might be a basic question but I'm new in optics.
|
Considering that the covariant derivative $D_{\mu}$ acting on spinors be given by
$$D_{\mu} \eta = \pm \frac{i}{2} \gamma_{\mu} \eta$$
It is claimed that theses spinors lives on a constant curvature spacetime. In fact, a sphere. I was trying to show it, simply by analysing the commutator
$$[D_{\mu},D_{\nu}] \eta =\fra... |
My understanding of leptons and baryons is that leptons are an elementary particle, while baryons are a composite particle. Can someone explain to me what particles fluctuating between lepton and baryon states looks like? What species of lepton are fluctuating into what species of baryon, and by what force?
|
The low-energy effective action of the bosonic string in the critical dimension $D=26$ can be written as:
$$S=\frac{1}{2\kappa_0^2}\int d^{26}x\sqrt{-G} \left[ \phi^2\left( R-\frac{1}{12}H_{\mu\nu\lambda}H^{\mu\nu\lambda} \right) + 4\partial_\mu\phi \partial^\mu \phi\right].$$
which involves the dilaton field $\phi$, t... |
I am reading a "A modern introduction to quantum field theory" by Maggiore and on page 88 it shows the anticommutators of the Dirac field:
$$
\{\psi_a(\vec{x},t),\psi_{b}^{\dagger}(\vec{y},t)\}=\delta(\vec{x}-\vec{y})\delta_{ab}.
$$
So I am trying to calculate it using the anticommutators for creation and destroy opera... |
In general physics courses, we are told that the electric potential a distance $r$ away from a point charge of magnitude $Q$ is given by $$ V = \frac{Q}{4\pi \epsilon r} \tag{1}. $$
Using this definition, it seems that, regardless of the geometrical dimension of our domain (i.e. whether we are looking at some subset of... |
I would like to drop a ball into a test tube containing mixed corn starch and water ( in different ratios) and use Stokes law to get the viscosity for the fixed weight of the ball that I used. Would this be a correct method? Thanks.
|
Consider a two-level atom with a transition at angular frequency $\omega_0$ and $\mu_{12}=2 \times 10^{-29} \text{Cm}$ subjected to a sequence of two resonant pulses. The first pulse has electric field given by $\mathcal{E}(t)=\mathcal{E}_1 \cos \left(\omega_0 t \right)$ and duration $ \tau_1$ while the second has $\ma... |
A train of length 300m observes another train on a parallel track coming towards it at v = √ 3/4c. The other train appears (i.e. is measured by the first train) to have a length of 300 m also. In the reference frame of the second train, how long does it take for the two trains to pass each other (i.e. what is the time... |
“The tennis racket theorem or intermediate axis theorem, is a kinetic phenomenon of classical mechanics which describes the movement of a rigid body with three distinct principal moments of inertia. It has also dubbed the Dzhanibekov effect, after Soviet cosmonaut Vladimir Dzhanibekov, who noticed one of the theorem's ... |
If a drone is designed, such that it applies a constant force equal to it's weight ($mg$) on air, to maintain a constant elevation (say of 10 meters). What will happen when considerable time has passed, taking into account the earth's rotation?
By the FBD of the drone, it's downward force, $mg$, and upward force, $mg$,... |
My question concerns magnetic acceleration due to repulsion. My sketch below shows two Neodymium magnets that I am working with, Magnet A and Magnet B. Thir orientation is fixed so that they cannot twist, and they are confined to travel only in the direction of the arrows. My questions are:
If Magnet A is at rest and ... |
Correlation function of $n$-many scalar fields is given by
$$\langle \Omega |T\{{\mathcal {\psi }}(x_{1})\dots {\mathcal {\psi}}(x_{n})\}|\Omega \rangle = \frac {\int_{\mathcal{F}}{\mathcal {D}}[\psi] \ \psi (x_{1})\dots \psi(x_{n})e^{iS[\psi]}}{\int_{\mathcal{F}}{\mathcal {D}}[\psi] \ e^{iS[\psi]}}\tag{1}$$
Where $|\O... |
I was wondering if there is a result, analogous to the Ehrenfest theorem in quantum field theory (QFT), and in particular if the QFT is on a curved spacetime.
In the last case, I would expect to obtain an equation which resembles the geodesic equation, but I am not able to do the calculation and I have searched online ... |
As I know from Thermodynamics work done by the system is negative and equals to $U=Q-W$. In this picture it clearly describes the process in which when we take some pebbles from the piston the system starts expanding do the work.
In Turbomachinery class my professor first introduced energy balance equation:
$dh+cdc+gd... |
Consider two infinitesimally close, timelike separated but otherwise arbitrary events $P$ and $Q$ with coordinates $(t,\vec{x})$ and $(t+dt,\vec{x}+d\vec{x})$. For example, imagine event $P$ is "a bulb turns on in a room" and the later event $Q$ is "someone sneezes in the room". The invariant spacetime interval between... |
Problem:
Two charges of magnitudes $-2Q$ and $+Q$ are located at points $(a,0)$ and $(4a, 0)$ respectively. What is the electric flux due to these charges through a sphere of radius '$3a$' with its center at the origin?
Solution:
Using Gauss's law,
$Flux(ϕ)=q/ ϵ0$,
Where $q$ is the total charge inside the surface and $... |
Is the dissociation energy of a muonic molecular hydrogen ion the same as an ordinary molecular hydrogen ion? Would the cross-section for dissociation be the same as an ordinary molecular hydrogen ion? I am trying to determine the fusion rate for muon-catalyzed fusion in warm dense plasma, and I need to know the dissoc... |
While studying optics, I came across a problem with solution in which the trajectory of light rays was known—circular paths around a fixed point in space, and the question was that of determining the refraction index as a function of the distance $r$ from that fixed point (given that the refractive index at $r = r_0$ i... |
So I have a vector field defined as $(X(x,y),Y(x,y))$ and I’m trying to make a parametric $(t,t)$ who’s derivative at a point is equal to the vector field at that point.
for example the vector field $(y,-x)$ and the parametric $(sin(t),cos(t))$ would work, but how to I calculate this parametric from any starting point ... |
This question is from K&K's intro book on mechanics. The larger block with the quarter circle missing has mass $M$ and the smaller block has mass $m$. The goal is to find the speed $v$ of the smaller block as it leaves the larger block. There is no friction anywhere. The tricky part here is that there is a recoil of t... |
I asked a question earlier about having a vector field and a starting point, and then making a parametric that starts at the starting point and the derivative at any point in the parametric equals the vector field at that point. Anyway somebody mentioned streamlines and pathlines, what are they?
|
Why, unlike Helmotz resonance's model, does blowing more or less strongly vary the pitch of the note produced in a vessel instrument, like ocarina? Obviously the model is very simplified and approximate, but what are the non-linear effects involved? Is there an intuitive way to explain them?
Thanks in advance.
|
Why is the $F_{\rm net}$ zero when we are standing still?
|
In Special Relativity, we are introduced that any proper orthochronous Lorentz transformation can be given by
\begin{align}
L=e^{u\cdot K+\theta\cdot J}
\end{align}
where $u\cdot K=u_1K_1+u_2K_2+u_3K_3$ and $\theta\cdot J=\theta_1 J_1+\theta_2J_2+ \theta_3J_3$ $\ (K_i, J_i$ are the generators of the Lorentz group).
How... |
Newton's Law of Universal Gravitation is used to approximately model gravitational forces close to Earth. I'm curious as to if there is a weaker-gravity limit to the law's applicability, such as in a void in the Universe. Assuming voids have less of a gravitational wave background, cosmic microwave background, or a low... |
A lot of times, in my materials classes, metal atoms' behavior during deformation is described like a bunch of stacked balls. In my introduction to material class, our professors explained that metals want to form the most packed structure possible. But then why do other structures, like BCC exist? why don't they all f... |
In trying to solve this particular problem:
I have become confused about the conservation of energy and momentum. Specifically for Case A would angular momentum be conserved because there is net torque of zero? I know that the radius of the string is decreasing and that of course there is a tension force. However, wha... |
Many polarization maintaining fibers (for example Corning PM 1550) have a cutoff wavelength specified as a range (for example 1300-1440nm). What is the meaning of this range from the physics point of view and why isn't it a single value like that given for most SM fibers?
https://www.corning.com/microsites/coc/oem/docu... |
If the Feynman rule for the vertex is written as $$-ieQ\gamma^\mu$$ ($e>0$, charge of positron, $Q$ is the charge of the interacting particle in units of $e$), the electron-electron-photon QED interaction vertex will carry a minus sign relative to proton-proton-photon QED vertex because for proton $Q=+1$ and electron, ... |
I can understand the Differential form of Gauss's Law ∇⋅= $\frac{ρ}{ɛ_0}$
as saying that the source of electric field vectors or flow disperse(The divergence of the electric field) is equal to the charge density divided by the permittivity of free space.
However I do not understand how this is equivalent to the integra... |
In non-relativistic quantum mechanics, the canonical momentum of a particle is defined as
$$\tag{1}
p_i = - i \hbar \: \partial_i.
$$
When there's an external magnetic field (suppose for simplicity that it's constant and homogeneous), the observable momentum (or dynamical momentum) isn't $p_i$, but
$$\tag{2}
\pi_i = p_... |
I came across a proof of the chain rule in a book called "Calculus Made Easy" by Silvanus P. Thompson. It said that the rule works because we essentially multiply and divide by another small change in another function (usually represented as du for a change in function u(x)).
I.e.$$\frac {dy}{dx}=\frac {dy}{du}.\frac {... |
Is it accurate to suggest that in chaos theory, information is in practice lost due to the impossibility of characterizing the system's state with infinite precision, making it unfeasible to run the governing equations backwards in time to find previous states?
Or is it an in-principle information loss due to mathemati... |
If our object is in complete contact with the bottom surface of our fluid container let us say water container then why is buoyant force still acting because buoyant force is generated due to the pressure difference in the upper and bottom surface of our submerged object however in the end buoyant force is generated b... |
I would first like to apologize if this is a dumb question.
I understand the physics of color sufficiently well. You have an incoming photon that intercepts an electron on the atom, the electron gets excited to some energy level for a few femtoseconds, and then goes back to the ground state, expelling another photon du... |
Why do we only consider interference of the first two reflected waves when studying thin-film interference (see attached diagram)? Is there a rigorous treatment that considers the infinite number of reflections and refractions that can occur at two interfaces?
I thought that the third and fourth reflected waves and so ... |
Considering a non-rotating and non-charged 2+1 dimensional black hole, known as the BTZ black hole which obtained by adding a negative cosmological constant $\Lambda=-\frac{1}{l^2},l\ne0$ to the Einstein-Hilbert action, resulting the following metric:
$$ds^2=-\left(\frac{r^2}{l^2}-M\right)dt^2+\left(\frac{r^2}{l^2}-M\r... |
I have been reading Introduction to Electrodynamics - Griffiths about solving Laplace equation in cartesian coordinates, and in that book, I saw this statement:
The functions $\sin(n\pi y/a)$ are complete on the interval $0 \leq y \leq a$. It was this fact,
guaranteed by Dirichlet’s theorem, that assured us Eq. $3.31$... |
With the development of relativity it became clear that mass and energy are the same, and therefore that they aren't separately conserved (or balanced). It seems that during the same period when these developments took place, the notion of "matter" also got more and more conceptually separated from mass-energy, and its... |
I was reading into the Oxford solid state basics, by Steven H.Simon and I stumbled upon a confusing interpretation of the Bose Occupation factor: $$n_B (x) = \frac{1}{e^x-1}$$ with: $$x = \beta \hbar \omega \ .$$
This result was interpreted as: the mode $\omega$ is an excitation that is excited up to the $n_B^{th}$ lev... |
Null infinity is the diagonal lines on the edge of a Penrose diagram. It seems to be the place where beams of light go if they never bump into anything, but only light can go there. It appears to be the "other end" of the null cone. This sounds crazy counterintuitive. But is it correct?
Because the upper diagonal li... |
I am messing around with creating small computer simulations to self study. Last time I did physics was in high school.
Consider the setup below. An electric motor (black) is spinning a metal disk (green). The motor is at the end of an arm that can revolve. I would like to set the RPM for the motor and the system react... |
I'm reading this paper [Eqs.(10,11)] and met the following problem. The author states that the following minimization problem
$$
\underset{\tilde{g}\left( \mu \right)}{\min}\,\,\int_a^b{\left| \frac{\mathrm{d}\tilde{g}\left( \mu \right)}{\mathrm{d}\mu} \right|^2d\mu}, \tag{1}
$$
where the function is supported (nonzero... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.