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Let the (normalized) wave function $\Psi(x,y)$ represent a free particle in the XY plane. I know $|\Psi|^2$ gives me the probability density function of the particle's position, which I can then integrate over a given region to calculate the probability of finding the particle in said region. However, how about momentu... |
What does the 'intermediate' part mean? Somehow, I thought an answer would be easy to come across, but I have yet to find one.
|
For the Proca Lagrangian:
$$\mathcal{L}=-\frac{1}{4}F_{\mu \nu}F^{\mu \nu}+\frac{1}{2}m^{2}A_{\mu}A^{\mu}$$
the equation of motion is:
$$\Box A^{\mu}-\partial^{\mu}\partial_{\nu}A^{\nu}+m^{2}A^{\mu}=0$$
The classical plane wave solution is:
\begin{equation}
A^{\mu}=\int \frac{d^{3}p}{(2\pi)^{3}} \sum_{i=1}^{3} \ep... |
I have a question about how the potential for an inflaton field is selected. It is clear that there are limitations associated with number of e-folds, scalar-to-tensor relation and scalar spectral index. But are there any other requirements from quantum field theory? Let's say I want to offer the following potential, w... |
I saw this image and believed this to be the definition of what the relationship between harmonics and overtones to be in strings, closed pipes and open pipes.
That the $n^{th}$ harmonic = $n-1^{th}$ overtone.
But from further research, it seems this is more correct: the $n^{th}$ overtone is the nth possible sound tha... |
Is it possible to create small shape that would be aerodynamic in most directions and not much in one of (kind of fixed sail) ?
Performed some experiments with pyramid like shape in front of bike (simple fairing) and found it can help also a bit in backwind, but remaining angles are unwanted.
Returned to basic simulati... |
When we, for example, scuba dive, we will breathe air at higher pressure, hence the amount of dissolved gas in our blood will be higher (Henry's law) (right?). Now when we come back to normal pressure, the air pressure will be lower, and as a result, the amount of dissolved gas in the blood will decrease and will force... |
This may be a naive question, but today, while reading about the Rutherford experiment in my high school chemistry textbook, I came across the following sentence:
"Calculations by Rutherford showed that the volume occupied by the nucleus is negligibly small as compared to the total volume of the atom.The radius of th... |
I'm trying to understand electric current. I came across an anology of electric current in a lecture note of Oregon State University. But i'm wondering if it is correct or not.
Here is another way to think about current flow; the pipe and ball analogy. A conductor is like a
pipe full of electrons. If an electron is pu... |
I've read in multiple sources (for example, Thorne and Blandford, Modern Classical Physics, pg 83 and Schutz, A First Course on General Relativity pg 92) that the stress components of the stress-energy 4-tensor represent momentum flux across surfaces normal to the space coordinate axes. Simply put, pressure is momentu... |
The size of colloidal nanoparticles in a liquid can be measured from optical reflectance (or absorption) spectra. The smaller the metal (semiconductor) nanoparticle, the more its color shifts to the red (blue) side. Is it possible to simultaneously measure both the size and mass of a nanoparticle (not necessarily by op... |
Does the interposition of the glass slide, which has a refractive index different from that of air, alter the wavelength emitted by the laser? Does this impact young's experiment?
|
Generally, when a solution to a system defined by an equation or set of generalized equations that is generally applicable to a broad range of possible initial conditions, or boundary constraints, is itself applicable only to a narrow subset of that broad range, the more specific constrained solution can be derived fro... |
I wanted to calculated the energy loss of protons traveling through a gas medium such as helium and hydrogen.At energy range of about 10 Gev there should be two effects:1.Coulumb interaction,2.Creation of pions and other particles due to collision with the nucleus.Is it possible to precisely calculate the energy loss?
|
The gravitational redshift equation (for a spherically symmetric gravitational field) is:
Within the Newtonian limit, there is an approximation:
The gravitational time dilation equation (for a spherically symmetric gravitational field) is very similar:
So the question is, like the gravitational redshift equation, is... |
Suppose that we have a system of $L$ qubits and some Hermitian operator $\mathcal{O}$ acting on the system. We can expand $\mathcal{O}$ in Pauli strings $P_{n}$:
$$\mathcal{O} = \sum_{n=0}^{4^{L}}c_{n}P_{n}$$
for some expansion coefficients $c_{n}$. Given a Pauli string $P$, we say it has a size $|P|$ which is equal to... |
Problem statement: an electron is in its fundamental state in an infinite (1-dimensional) potential well, its walls being located at $x=0$ and $x=a$. Suddenly, the right wall moves from $x=a$ to $x=2a$. ¿What is the probability of the electron being in its fundamental state? And what's the probability of it being in i... |
How does a shear layer make vortices? If you have 2 streams of air that are moving at different speeds or opposite directions right beside each other, how does that make a vortex? What causes the rotation, in other words.
|
Consider some dynamical system $\dot{\textbf{X}}(\textbf{x},t)=F(\textbf{X})$ where $\textbf{X}$ is discretized along a 1-dimensional spatial coordinate $\textbf{x}=(x_1,\dots,x_N)^T$. Let $\rho(\textbf{X},t)$ be the probability density function, then the Liouville equation describes the evolution of $\rho(\textbf{X},t... |
I know that mechanical energy is the sum of kinetic energy and potential energy. But there is a sentence in the book like this:
'Our primary goal, however, is to find the energies associated with these states. We know that the total energy of a system is equal to the kinetic energy plus the potential energy.'
However... |
I'm following an introductory lecture on instantons by Hilmar Forkel. In a non-relativistic quantum mechanical setting we have the potential $$ V(x) = \dfrac{\alpha^2 m}{2 x_0^2} (x^2 - x_0^2)^2 \tag{2.42}$$ with the instanton solution
$$
x_I (\tau) = - x_0 \tanh \alpha (\tau - \tau_0) \tag{2.51}.
$$
We also have the o... |
Finding the relationship between scattering and transfer matrix elements is trivial in the case of 2 by 2 matrices when there are two inputs and two outputs. However, how should I approach the task of finding that relationship in the case of arbitrary matrix dimensions? Maybe this derivation is laid out in some literat... |
What resources on numerical relativity/simulation would be suitable for a primarily theoretical computer science background [algorithms analysis, complexity theory, etc.]? Importantly, while I'm planning to take an introductory graduate general relativity class next semester, I don't yet have background on the relevant... |
I was solving a question in my textbook that was under the heading "Solving Problems Related to Objects in a Non-inertial Frame of Reference"
The problem reads
"A teacher suspends a small cork ball from the ceiling of a bus. When the bus accelerates at a constant rate forward, the string suspending the ball makes an a... |
I often create diagrams to illustrate the scenario of an exercise for my students. These are not necessarily free-body diagrams, as creating those may be part of the task or similar or it would be overkill. In such diagrams, I can use straight arrows to indicate that a body is moving in a certain direction and circular... |
Ocean water is flexible enough to allow water from each side of low tide to flow to the sides of high tide.
So for a high tide, there must be a low tide somewhere else from where water is drawn out. But if it's a small inland lake (not connected to any sea at all) that is in the part of earth closest to the moon, it ca... |
As I asked in this question: https://quantumcomputing.stackexchange.com/questions/36998/how-can-i-calculate-the-measuring-probabilities-of-a-two-qubit-state-along-a-cer/37000#37000
From here I know how to calculate the probability of measuring a general state at an arbitrary angle.
I now deal with an exercise with phot... |
Wikipedia defines the psychrometric ratio as the ratio between the convective transfer coefficient $h_c$ and the product of the convective mass transfer coefficient $k_y$ and the humid heat $c_s$:
$$\frac{h_c}{k_yc_s}$$
It claims that this happens to be numerically equal to $1$. However I would assume that both $h_c$ a... |
My concern involves the following lines from Principle of Optics (Born and Wolf 7th ed, 60 year anniverary, Section 1.2 pg 11). I fail to derive these equations 5,6 exactly.
$$
\begin{align}
\nabla^2E -\frac{\varepsilon\mu}{c^2}\partial^2_t E+\nabla(\ln\mu)\times(\nabla \times E)+\nabla(E\cdot\nabla(\ln\varepsilon))&=... |
I've been studying a type of problem wherein we initially have a photon (with (lab frame) energy $E_L$) and atom, both moving in the $+\hat{x}$-direction, with respective speeds $c$ (of course) and $v_i$. The atom and photon then collide, and the atom absorbs the photon. Ignoring any of the specific mechanics of the co... |
Let me explain myself. In my case, I know the wavefunction equation of a infinite-U potential which has the form:
$$V(x)=\begin{cases} V_0,\ \ |x|\leq \frac a2\\ \infty, \ \ |x|>\frac a2\end{cases}$$
And I know that after solving the Schrodinger equation the wavefunction is: $$\psi(x)=\sqrt{\frac 2a}\sin\left(\frac{n\p... |
I want to know if it’s at all possible to calculate the weight distribution (i.e the relative load supported by each foot) using just the location of the human body’s centre of mass and the distance of the COM to each foot.
Thanks in advance for any help
|
Blagoje Oblak in their thesis "BMS particles in three dimensions” says that
"Given a group $G,$ suppose we wish to find all its projective unitary representations. The above considerations [in the thesis] provide an algorithm that allows us, in principle, to solve the problem:
First find the universal cover $\tilde{G... |
I watched this Minute Physics video on how current produces a magnetic force on a moving charge because of relativity. In the video (timestamp is around 2 minutes), he explains that when the charge is moving, in the inertial reference frame of the charge, the protons are contracted and thus increase in density, repelli... |
Can one find the relationship between Quantum complexity and gravity by employing Raichaudhury's equation, utilized by Hawking and Penrose in proving their black hole singularity theorems, to calculate the upper bound of quantum complexity and thereby demonstrate that general relativity would be valid until complexity ... |
The principle of relativity says that all observers see the same laws of physics. It is, to my knowledge, the underlying principle behind General Relativity; put alternatively, General Relativity is what results when one requires the principle of relativity to work for all observers (not just inertial ones).
If this vi... |
In section 2.3.5 of Green, Schwarz, Witten's book on string theory (volume-1) pp. 116-118, the objective is to calculate an Asymptotic Formula for Level Densities $d_n$ for open bosonic string theory. $d_n$ is related to the classical partition function $f(w)$ via the generating function $$G(w)=\sum_{n=0}^\infty d_n w^... |
I am studying rigid body motion in Engineering Mechanics Dynamics by J.L. Meriam, 8th Edition. After he explains about rigid body motion in page 316 at the top of that page the following paragraph:
"Note that the angular motion of a line depends only on its angular position with respect to any arbitrary fixed referenc... |
Let's assume that an electron requires 1eV energy to get excited to the 1st excited state and requires 1.7eV to the 2nd excited state.
What would happen if we supply it with 1.5eV?
Well, in my opinion, I thought that electron will absorb the photon, excite to the 1st excited state and emit a photon of 0.5eV energy back... |
When we put a diode in reverse bias, should not the electrons coming into the p side cross the barrier to the n side. We know that they are minority carriers here but why is their number less in spite of the battery providing electrons in ample to the negative side?
|
In Nastase, Introduction to AdS/CFT, the first chapter talks a little about the star-triangle duality. In fact, it was claimed that the Fourier Transform of a Feynman-like diagram in position space in the form of a Triangle, is the Feynman diagram in momentum space, which seems like a star.
What i mean is: The Fourier ... |
The standard explanation for the observer effect is that a small amount of energy from the observer causes the wave function of lets say an electron to break down and for it to develop determinate characteristics rather than probabilities. However why doesn't this happen anyway baring in mind that until its observed it... |
So, the classical work equation is force * distance. And so holding an apple in your hand so that it doesn't move with respect to the earth would mean you are doing no work, and the apple is not gaining energy, either potential or kinetic.
However, in GR, an object held so that it resists gravity is experiencing accel... |
I am doing a Monte Carlo simulation of protein chains of various lengths.
I change the densities of the simulation box.
In my experiment, I found that density has no effect on relaxation time.
Do you think this is plausible?
If not, what mistake should I look for?
|
The state equation of a van der Waals gas is
$$\left(P+\frac{a}{v^2}\right)(v-b)=RT$$
with $a,b$ and $R$ constant. Find $$\frac{\partial v}{\partial T}\bigg\rvert_P.$$
Finding $\frac{\partial v}{\partial T}\big\rvert_P$ is very tricky and I don't know how to do it. But can I instead find $\frac{\partial T}{\partial v... |
I have doubt in damping oscillations of a pendulum. Let's consider a simple pendulum in a drag medium like air. Suppose if the angular displacement (theta) is larger (say 40°), the oscillations start to occur, that its angular acceleration depends on -g/l.sin(theta). As the time increases the amplitude decreases, due t... |
The Keplerian frequency/ Orbital frequency is the inverse of orbital period and for Schwarzschild black hole it is given by $$\frac{1}{2\pi}\sqrt{\frac{M}{r^3}}.$$ its unit is Hertz. Now To express the frequencies measured by a distant observer in physical units, one must extend the above form by multiplying by the fa... |
I've been studying clustering dark energy when I came across a paper named "A Short Review on clustering dark energy" by Ronaldo Batista. there are 2 equations in this paper (eq.8 and eq.9) which I'm trying to derive:
$$
\begin{gather*}
\delta^{\prime}+3 \mathcal{H}(\delta p / \delta \rho-w) \delta+(1+w)\left(\theta-3 ... |
Treat particle trajectories as embedded submanifolds in the pseudo-Euclidean space, and treat the four-dimensional potential as a 1-form.Is there a statement for the Lienard-Wiechert potentials that does not mention coordinate components?
|
Basically, substances with high specific heat capacity have a greater ability to store heat. Does this go hand in hand with thermal conductivity? Poor conductors do not transfer heat well, trap heat and therefore make things feel warm to touch. Substances with high specific heat capacity resist changes in temperature a... |
I thought that when a system was measured, there could be an interaction between the measurement device or environment and the system but overall energy was conserved. However, I came across these 2 articles which seem to imply this is not the case.
https://link.springer.com/article/10.1140/epjs/s11734-021-00092-2.
htt... |
Which means the formula in general relativity similar to the use of Lienard-Wiechert potentials in electromagnetism.
|
Note: This is a wiki post.
Suppose you are late for a meeting and you have to take an elevator. The floor choice of your fellow passengers influences how late you will reach your destination. If everyone gets off at a later floor, it's perfect. But unfortunately, it doesn't happen like that so often. The most likely s... |
Is it true that a generic operator that is annihilated by the Lindblad superoperator (with both Hamiltonian and dissipative parts of the dynamics) has to be annihilated separately by both the Hamiltonian dynamics and the dissipative dynamics, or are there cases where it is only the sum of the two terms that vanishes, b... |
If we launch an object in some way, and it lands at distance x, if we move forward the launching mechanism y units forward or backwards, will the landing distance also move forwards or backwards y units? Assume the launching force is the same.
Here's an example to make it easier to understand. If we throw a ball one fo... |
I am new to evaluating functional derivatives and I am having difficulty evaluating the following derivative:
$$I = \frac{\delta}{\delta x(t)}\frac{\delta}{\delta x(t')}\int_{u_i}^{u_f}\frac{du}{2}\left(\frac{dx}{du}\right)^2~.$$
I have tried to do it and I obtain the following:
$$I = -\frac{\delta}{\delta x(t)}\frac{d... |
Say you have a system where a weight drops on an air source, which blows on the ball, launching it. Are there any relations or formulas between the forces at work here? For instance, would there be an exponential relation between the distance the ball travels vs the height of the weight? Or would there be a relation be... |
I've been considering an hypotetical situation and it's making me a bit confused. If anyone could give me any insight, I would really appreciate it!
It is as follows:
Let's pretend atmospheric density remains constant with altitude. If I fill up a balloon at sea level and start rising it, would the balloon expand, shr... |
I'm working out of Shankar's principles of quantum mechanics book. And overall, I think I get the gist of how to solve problems with Schrodinger's Equation. I recall in my Modern Physics course, we only worked in the x-space it seems. Basically we limited our Schrodinger Equation to $$ \frac{d^{2} \psi}{dx^{2}} + \frac... |
I've noticed that most of Physics 2 courses highlight the fact that the surface is closed before giving the electric flux formula. Is the following formula only valid for closed surfaces? If yes, are there any general formulas (for both opened and close surfaces).
Note: I read on previous posts that one can use symmmet... |
So the geodesics that point towards the Earth brings space-time towards the Earth and then back out again, but then the moon has its own geodesics so wouldn't it be kind of like geodesics affecting other geodesics because there is no other force in this situation other than gravity? Or do geodesics add? Also how are bl... |
About a month ago, I was presented in my Optics class (classical and electromagnetic optics, to be more precise) the representation of partially polarised light through Stokes' vectors. Now, it occurred to me that instead of representing them with vectors in $\mathbb{R}^4$, perhaps it could be more benefitial to repres... |
These protrusions are sure to create turbulent vortices. But what if these additional vortices can somehow lead to acceleration?
Additional clarification
It is clear that moving protrusions such as fins or wings are useful for accelerating floating and flying bodies. But what about other protrusions (like ears) or depr... |
I'm really wanting to get into physics more and I've had this question for a while. I do know a bit about rocketry as I think it's pretty cool but I'm still struggling to understand how Newton's 3rd law applies on a more microscopic level. In a rocket, propellant is used to produce often very hot gas going very fast. T... |
I have a 1800W induction cooktop.
In my experiment, did the following steps:
I placed a stainless pot on the cooktop, half filled with fridge cold chicken broth.
I heated the pot at 1000W until I could feel the bottom sides of the pot getting too hot to touch.
I set the induction power to the maximum of 1800W.
I waite... |
The NN 2D Ising Model at inverse temperature $\beta$ and external magnetic field $h$ on an $L_1\times L_2$ sized box within $\mathbb{Z}^2$ with periodic boundary conditions $$\sigma_{L_{1}+1,x_{2}} = \sigma_{1,x_{2}}\qquad\left(x_{2}=1,\dots,L_{2}\right)$$
$$\sigma_{x_{1},L_{2}+1} = \sigma_{x_{1},1}\qquad\left(x_{1}=1,... |
When you measure amplitude, does that refer to the electric portion of the electromagnetic field, or does it refer to the magnetic portion? Or is an average of the two?
Another question is, are the amplitudes of the electric and magnetic fields always the same, or can there be a difference? If so, what would happen if ... |
This question pertains a particular example, but I think the answer should be a general statement on a broader misundertanding I must have.
Consider a 3-sphere with metric $g=d\theta^2+\sin^2\theta d\phi^2+\cos^2\theta d\chi^2$. Take the diagonal vielbein $e_1{}^1=1$, $e_2{}^2=\sin\theta$ and $e_3{}^3=\cos\theta$. The ... |
The Doppler shift phenomenon is well understood when the source and observer are in relative constant motion. However, I'm curious to know how the Doppler shift phenomenon is modified when they (i.e., the source and the observer) are in relative accelerating motion (any type of accelerating motion, e.g., linear acceler... |
An alpha particle travels at about half the speed as a beta particle, right? ~5% of light speed versus ~10%?
Therefore, if you doubled its velocity, its energy would roughly quadruple, correct? (Or slightly more than quadruple due to a small Lorentz gamma factor at these slightly relativistic speeds...)
An average 0.... |
Feynman used the following Compton scattering diagram:
Whereas most books use this diagram in their derivation:
Is there a way to relate the two? Feynman's diagram makes more sense to me conceptually, but my professor used the second one in their derivation.
|
A typical derivation of the magnetic mirror force of a charged particle in a magnetic field such as from Nicholson (1983) pg 26 uses the $q \vec{v} \times \vec{B}$ force, conservation of the dipole moment $\mu$, and that $\vec{\nabla} \cdot \vec{B}= 0$ to find the force acting parallel along a magnetic field is $-\mu \... |
Suppose we express the phase space volume occupied by all mechanical states $(\mathbf{q},\mathbf{p})$ with energy equal to or less than mechanical energy $E$ as:
\begin{equation}\Phi(E,\lambda)=\int\frac{d^{n}qd^{n}p}{h^n}\Theta(E-H(\mathbf{q},\mathbf{p}));\lambda)\end{equation}
Where $n$ is the degs of freedom, $H$ is... |
So the escape velocity at Earth is roughly 11.2 km/s, but with the escape velocity of the moon it says that it is 2.38 km/s but since the moon is orbiting the Earth, wouldn't the effective escape velocity at the moon increase if escaping moon away from the Earth, in order to leave the Earth-moon system and so the escap... |
From the Bloch sphere, it is mathematically clear that a $720°$ rotation is necessary to bring a spin $1/2$ particle back to its initial state, as a full rotation changes the sign of the state.
However, what is the physical meaning behind that?
How can we understand the state of the particle after only one full rota... |
I’ve posed the following inquiry on Philosophy Stack Exchange:
Can the idea of continuity make sense in the real world?
A summary of it is presented here:
Continuity in mathematics means no jumps or gaps in functions, akin to the real numbers' property where there's no smallest number after any given number. The questi... |
I have finished quantum field theory and general relativity and want to read about supergravity. I have read about supersymmetry from the demystify series and the supersymmetry part of Wess and Bagger's Supersymmetry and Supergravity. However, I find the supergravity part of Wess's book difficult. I have also try Freed... |
Can one physically distinguish a photon of frequency $\omega$, generated by a stationary laser, from a photon generated by a mechanically moving laser (a different laser from the first one) which, due to the Doppler shift, has the same frequency $\omega$?
Note that the two lasers have different frequencies: The first l... |
In Sakurai's Modern Quantum Mechanics, second edition, $5.6.10$ is
$$\begin{aligned}
\dot{c}_m(t)=-\sum_nc_n(t)e^{i[\theta_n(t)-\theta_m(t)]}\langle m;t|\left[\frac\partial{\partial t}|n;t\rangle\right]
\end{aligned}\tag{5.6.10}$$
where $c_m(t)$ stanstics
$$\begin{aligned}
|\alpha;t\rangle=\sum_nc_n(t)e^{i\theta_n(t)}... |
If the emitting body is blackbody, then the range at which radiation is emitted won't change, because a blackbody is a blackbody whether the temperature is 4000K or 120000K, meaning that, by definition, it emits at ALL wavelengths. However, I am wondering, how things would work for a grey body let's say. My guess is th... |
Given a two-dimensional pressure distribution $p(x,y)$ in a fluid medium, we can perform Fast Fourier transform to obtain the amplitude and phase spectra. The 2D-FFT (and eventually, the IFFT) decomposes the entire pressure distribution into a sum of waves having different combinations of $(k_x,k_y)$.
My question is, f... |
I would like to be able to describe a particles path before collisions with greater precision. We can calculate the "mean" free path of a particle before colliding moving particles, but I can't find anything about the standard deviation of these paths.
Being able to calculate the standard deviation would allow us to an... |
In chapter 5 of Sakurai's Modern Quantum Mechanics (3ed), he considers the dipole approximation for an electron absorbing electromagnetic radiation due to a harmonic electromagnetic potential.
In the end, we obtain an "absorption cross section"
$$\sigma_{\text{abs}} = 4\pi^2\alpha\omega_{ni}\lvert \langle n \lvert x \l... |
The Jacobi's theta functions
$$\theta_1(0,\tau )=0$$
$$\theta_2(\tau)
=\sum_{n\in \mathbb{Z}} q^{(n+\frac{1}{2})^2 /2 }$$
$$\theta_3(\tau)
=\sum_{n\in\mathbb{Z}} q^{n^2/2}$$
$$\theta_4(\tau)
=\sum_{n\in\mathbb{Z}} (-1)^n q^{n^2/2}$$
and the $\eta(\tau)$ functions were used to build the partition functions in the confor... |
Consider a wind speed of $80kmh^{-1}$ towards the west, when this wind comes into contact with another body, it will obviously exert some force. However, what is the magnitude of this force? $F=ma$, as the wind is travelling at a constant velocity there is no resultant force acting on it, so the wind cannot have any fo... |
Once a colleague showed me a sound measurement setup in a reverberation room, meant to measure (unwanted) sound from magnetostriction in ferrite cores. There was a problem creating a true "zero" measurement:
Of course in that case a coil without any ferrite was used as device under test (DUT).
Also the Earth's magneti... |
Can somebody explain how the sinusoidal wave will cross the junction, meaning what will be the intensity and amplitude during and after the crossing?
Assuming constructive interference at the second junction and equal distribution of waves.
I am confused that what should be halved intensity or amplitude, as if we half... |
In a Kubo's classic 1966 paper about the Fluctuation-Dissipation theorem (https://iopscience.iop.org/article/10.1088/0034-4885/29/1/306), I found the following issue which confused me: The author considers an equation of motion with stochastic forcing of the form
$$m\frac{dv}{dt}=-m\gamma v +R(t)$$
Where the second ter... |
When extending general relativity to include electromagnetism, several authors (e.g. Novello, Sabbata ecc.) assume that the traceless part of the torsion tensor vanishes or is deliberately set to zero. Then, either the trace or axial part of the torsion is used in association with the electromagnetic potential (couplin... |
Why do stones in a garden rise to the surface?
I haven't done my own research on the subject, but experienced gardeners seem to suggest that, even if the garden is cleaned from stones, they reappear after some time. Brief internet search confirms this assertion (e.g., this link pops up among the first), however the exp... |
Integrate the general expression
$$\int_{x0}^x \int_{y0}^y \frac{\nabla^{2}\Lambda (\chi ',\psi ')}{\nabla\psi '\nabla\chi '}\nabla\chi '\nabla\psi '$$ in the curve from $(x0,y0)\to(x0,y)\to(x,y)$, working with the function $\Lambda (\chi ',\psi ')$ in the general form and not by replacing it with an arbitrary functio... |
I have some questions about this interesting work (https://iopscience.iop.org/article/10.1086/517603/pdf) where the authors analysed the effects of voids in the CMB radiation (particularly through the Integrated Sachs-Wolfe and the Rees-Sciama effect).
This effect predicts that photons crossing overdensities would be b... |
I'm reading Modern Quantum Mechanics by Jun John Sakurai and in section 2.2 he talks about Base Kets and Transition Amplitudes. He goes to show, that $|a',t\rangle=\mathcal{U}^\dagger|a'\rangle$, (with $\mathcal{U}=e^{-\frac{iHt}{\hbar}}$ being the time evolution operator) and the derivation itself is totally fine, but... |
In a seminal paper, Weinberg has shown that one can relate a $n \to m$ scattering amplitude to the $n \to m + k$ scattering amplitude that involves the same particle content plus $k$ additional outgoing soft photons or gravitons. "Soft" particles are particles with energy below a certain infrared cutoff, that in princi... |
Newton studied a lot about optics and gravitation. Did he realize to some extent that light is a massless particle? How does his theory explain the bending of light due to a gravitational field?
|
I'm curious to understand how the Doppler shift phenomenon occurs and is mathematically expressed for a single photon emitted by a stationary single photon emitter, such as a quantum dot, and observed by a relatively moving observer (of any type). Is the mathematical expression for the Doppler frequency shift of a sing... |
I am trying to calculate the electric susceptibility as temperature changes. From a textbook, [1], the equation is: $$\chi (\omega) = \frac{Ng_2A_{21}\pi c^3}{g_1\omega_0^3}\left\{\frac{1}{\omega_0 -\omega -iA_{21}/2}+\frac{1}{\omega_0 +\omega +iA_{21}/2} \right\}$$
But none of those quantities are dependent on tempera... |
My question is quite general.
I want to make $N$-body simulation, for example galactic dynamics, using $N$ stars.
One possibility is to make these calculations in 2D using an inverse square law and brute force at the beginning.
But I wonder if it is correct to apply these 2D results as if the simulation were done in 3D... |
Many of the sources I find on multipole expansions seem to be about electric potential and involve matrices. However, in my classical mechanics class we have not used matrices for multipole expansions yet, so I have not been able to answer my question with them. We were given this formula for the multipole moments of g... |
I'm currently studying BECs mixtures (with and without the presence of a coupling term between them).
While studying the symmetries of the system I stuck on the following question: does this system posses the Galileian invariance as if not, what are the condition the boost have to satisfy to have it?
The Hamiltonian of... |
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