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Whether it be a YouTube video or book lights rays i.e(the visible specturm,uv rays) are expressed as a sine wave. Why is it so?
What is the plot of its against? Why does it oscillate? Why does it have wavelength? Why does it have frequency ? Does light really travel as a sine wave?
|
If the accretion disk surrounds the black hole but is too far away from the black hole to have its light captured, why do we still see a black shadow? Is the 'shadow' not covered from our perspective by the radiation coming from the accretion disk?
Or does it have to do with the fact that we look at the black hole face... |
I made a simulation that studies the thermalization of massless particles, assuming isotropic and homogeneous spatial distribution, in 3 dimensions. Namely,
I started with $N$ particles having random distribution in energy $E$ and isotropic directions.
Next, I assumed that they meet at one point (so I drop any spatia... |
To quantize the non-Abelien gauge theory. We multiply the path integral by:
$f[A]=\int \mathcal{D}\pi exp[-i\int d^4 x {1\over \xi}(\partial_\mu D_\mu \pi^a)^2]$
then we can shift the argument in the round parentheses by $\partial_\mu A^\mu$ and perform the Stueckelberg trick to eliminate $\pi$s. These are the steps be... |
This might be dumb, but unfortunately I need some urgent help about Cutoff from 2D FFT functions in frequency space.
I am writing my bachelor thesis, near DDL and cannot get a lot of help offline in uni.
The current task is: Get the resolution of image. The instruction is to "transform" raw image to 2D FFT functions in... |
I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they showed a proof of Invariance of Spacetime Interval. You can find the proof Here and Here is the second part of that proof.
They used an apparatus that flies straight "up" 3 meters to a mirror. There it reflects straight back down... |
In my class we were discussing some wave equation for a spherical symmetric wave $u(t,r)$ and my professor investigated the behaviour of the solutions asymptotics $r \rightarrow \infty$. The solution was written as some series
$$u(t,r) \enspace = \enspace u_0(t) + \frac{u_1(t)}{r} + \frac{u_2(t)}{r^2} + \ldots$$
Now my... |
Question: A particle is thrown upwards from the ground. It experiences a constant air resistance which can produce a retardation of $2 \, \text{m/s}^2$ opposite to the direction of velocity of the particle. The ratio of the time of ascent to the time of descent is $\sqrt{\frac{\alpha}{\beta}}$ where $\alpha$ and $\beta... |
An electron in protium can absorb a photon and jump to an orbit of higher energy. Is an analogous procedure possible for the nucleus of protium (a single proton)?
Can this nucleus be in an excited state? Since it consists of a single proton I can imagine that the excitation (if possible) must take place on the level of... |
I heard that the dielectric constant of water is around 78. When we think about the way we get the $\kappa$ of water,
Can we get the $\kappa_{water}$ by putting the water molecules on the $\vec{E}_{free}$ and comparing with the $\vec{E}_\text{net}$? If not, how did the scientist measure the magnitude?
From the equati... |
Unitarity can be verified post hoc by examining the optical theorem. In the context of path integral quantization where formal derivation starting from canonical quantization is unavailable, is it possible to determine if unitarity is guaranteed at the level of the Lagrangian?
I apologize if the question is not very sp... |
Spontaneous symmetry breaking (SSB) occurs when the state of a system possesses less symmetry than the underlying laws governing it. This raises the question: What happens to the entropy of the system during the SSB, from both quantum and classical perspectives? Does the second law of thermodynamics hold during SSB, or... |
In the context of Saturated absorption spectroscopy, I'm having trouble modeling stimulated emission, and getting the result that is written in articles, such as this article. I tried to use a non-relativistic calculation as a start, for an atom with 2-level separated by $\hbar\omega_0$:
A 2 level atom of momentum $p_... |
I am studying how to apply neural networks to the problem of Quantum State Tomography (QST) and I got confused when it comes to decide if this is a supervised or unsupervised learning problem.
At first, I came across the usage of Restricted Boltzmann Machines in the domain of generative models, which are used for unsup... |
This question is based on a problem from JD Jackson's Classical Electrodynamics, which asks for the solution of the inhomogeneous wave equation: $$\frac{1}{c^2} \frac{\partial^2{A^{\nu}}}{\partial t^2}- \nabla^2{A^{\nu}} = \frac{-4\pi}{c}J^{\nu}.$$ I managed to find the solution using the Green's Function method, empl... |
In the thought experiment of Laplace's demon, one talks about an omnipotent being who if he/she knows about all the initial conditions of this world (if the world is considered classical fundamentally) can predict the future and past with absolute determinism. In this hypothetical world, then there is no meaning of fre... |
I'm deriving the results of the Page paper: "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole*" (https://doi.org/10.1103/PhysRevD.13.198). At the appendix he derive the absorption probabilities $\Gamma$ given by equations (13) and (14) in the paper.
To that, he start wit... |
I am trying to calculate the work done on this wheel as it undergoes one full revolution, and is rolling without slipping.
I am aware that work can be calculated either using the integral of force with respect to displacement, or the integral of torque with respect to angle.
Since the speed of the contact point B is z... |
I am working through Introduction to Quantum Mechanics by David J. Griffiths, and part 3.2.2 shows that the standard deviation of an obervable, $Q$, is always $0$ but I do not understand the steps taken:
$$
\sigma^2=\left\langle(Q-\langle Q\rangle)^2\right\rangle=\left\langle\Psi \mid(\hat{Q}-q)^2 \Psi\right\rangle=\la... |
Is it possible to get a really massive osmium planet for its density which has 50 Earth Masses in one Earth radii(Don't want to use more massive objects because it may be harder and require more energy to change its rotation) and make it rotate to the speed of 10% the speed fo light, so the frame dragging will be reall... |
When looking for the derivation of the Kahler potential, generally is assumed the following idendity:
For a Chiral superfield $\Phi$, we have
$$\overline{D}^2 D^2 \Phi = 16 \partial^2 \Phi$$
But before proceed, i can't realize how this is true! I tried to show it by brutal hand, that is, writing all the terms and the d... |
Normally, the Dirac equation for the Green's function reads:
$$(i\gamma^\mu\partial_\mu - m)S_F(x,y) = \delta^{(4)}(x-y)$$
Is it possible to define a Green's function describing the propagation exclusively in one dimension for this 4-dim problem, i.e. something like
$$(i\gamma^\mu\partial_\mu - m)S_F^{(0)}(x^0,y^0) = \... |
In his answer to another post user Albertus Magnus describes the situation of a bullet hitting a rod in free space on its tip in a "purely tangential" way causing the rod to spin in a purely rotational movement. He then elaborates that this case is not realistic and should be rather treated as an external force acting ... |
I have a basic confusion about the two different boundary conditions for a fermion around a compact direction, periodic versus anti-periodic.
We learn in a QM class that a fermion wavefunction picks up a minus sign under a $2\pi$ rotation. I think the statement of this fact is that the fermion is in a projective repres... |
Given the Berry connection
\begin{equation}
\boldsymbol{\mathcal{A}}(\mathbf{R}) = i \langle u(\mathbf{R}) | \nabla_\mathbf{R} | u(\mathbf{R}) \rangle,
\end{equation}
the Berry curvature can be written as its curl,
\begin{equation}
\boldsymbol{\Omega}(\mathbf{R}) = \nabla_\mathbf{R} \times \boldsymbol{\mathcal{A}}(\mat... |
I know there are other questions linking the two subjects. I am not asking about an explanation, rather I am curious whether an experiment would be possible.
To explain the experiment let's start with two entangled particles, one here and one in the Andromeda galaxy. If I measure the direction of the spin here, and som... |
I am trying to create MATLAB code that will simulate a charged particle's path in a magnetic field. I have the user enter vectors for velocity and magnetic field, and then calculate the force vector.
Given these initial conditions, how can I calculate the position vector $[x,y,z]$ of the particle after time t? I'm awar... |
So I am taking my University Electromagnetism course and we are currently learning about gauss's law and gaussian surfaces.
A common question involves point charges inside of a hollow sphere that has a net charge.
When we graph the electric field [there is a mild error in graph with the y axis saying Q however the tre... |
I have been introduced to QM this spring semester. One thing that I couldn't understand is that how do they define the energy of an electron.
For example while solving "Particle in a box" problem my teacher said that note that the energy we are using in Schrodinger's equation is no more equal to the Kinetic plus the po... |
i. What does the power-time graph for a car moving on a horizontal road at constant speed look like? Is it a horizontal line because the car engine is supplying a constant power, or is it zero because there is no change in kinetic energy or gravitational potential energy of the car (so no work is done and therefore pow... |
The Schwarzschild metric is the metric calculated from the field equation outside of the black hole. This condition of region (outside of the matter) was the reason why we could use $T_{\mu\nu}=0$.
But we can tell some properties of the singularity of the black hole, which is at $r=0$, from the schwarzschild metric. Fo... |
I am reading Sec. 2.5 of Weinberg's Quantum Theory of Fields, Volume I. There he talks about the classification of relativistic one-particle states according to their transformation under the Poincare group.
In Eq. 2.5.2, Weinberg derives that the action of an arbitrary proper, orthochronous Lorentz transformation, $\L... |
I am trying to understand how gyroscopes can maintain rotation in different "impossible" orientations when spinning.
I saw that the behaviour in zero-g is slightly different. On Earth, the gyroscope rotates but with the same rotation axis, however, in space, the gyro seems to maintain fixed to a direction. Can someone ... |
I was solving a question, in which, a particle has travelled a distance $s$, with initial velocity $0$ and constant acceleration.
So the equation of motion becomes,
$$ v = a t \tag{1} $$
and
$$ v = \sqrt{2 a s} \tag{2} $$
So, both represent velocities and by definition both their averages must represent the same thing.... |
I'm into an article wich describes "short-term dynamics" ( it's a ping pong ball falling with water from a height H.)
What does that term mean, I find nothing in internet...
Does it mean that we study the phenomenon during a time dt ?
Does it mean something else wich has implications (approximations or others..) ?
Rega... |
E.g. CO2 absorbs and emits electromagnetic radiation at some frequencies.
If the CO2 molecule is in a continuous electromagentic field, it will absorb and emit. What is the time between absorption and emission of a photon ?
How can this time be calculated?
In a classical calculation the emitted field from a dipole will... |
Consider a bicyle on a bank.
The weight of the bicycle acts downwards, we can resolve this vector to the normal force and a component down the bank. Hence the normal force is less than this weight force. However, now when we resolve the normal force vector to a vertical component and a horizontal component that produce... |
I am working on a problem (the 12th problem in the third chapter of the third edition of Goldstein's Classical Mechanics) that asks the reader to consider certain long-range interactions between atoms in a gas in the form of central forces derivable from a potential
\begin{equation*}
U(r) = \frac{k}{r^{m}}
\end{equatio... |
I am reading Sec. 2.5 of Weinberg's Quantum Theory of Fields, Volume I. It talks about the classification of relativistic one-particle states according to their transformation under the Poincare group. Since the states of a particle of a specific type are assumed to be components of irreducible representations of the P... |
It is a well-known fact that rotating planets have a flattened spheroidal shape. However, the NASA site says about Haumea:
The fast spin distorts Haumea's shape, making this dwarf planet look like a football.
Haumea rotates especially quickly, and its shape is an ellipsoid with 3 different axes. Does one in fact caus... |
Consider we have been provided a RGE
$$
\mu^2\frac{d}{d\mu^2}\ln Z=\frac{\epsilon}{2}+\beta
$$
where $\beta=-\beta_0\alpha_s^2$, upto the $\mathcal{O}(\alpha_s^2)$ and $Z$ is the renormalization constant for $\alpha_s$. I want to solve the RGE to find out $Z$ in terms of $\beta_0$ and $\alpha_s$. I am trying to solve t... |
Consider this diagram in which the ring of mass $M$ is at rest initially and the bead of mass $m$ has velocity $u$ as shown.
Why isn't the force of interaction (normal force) between the bead and ring $mu^2/r$?. I know the ring will start moving after $t>0$ but initial if we calculate normal reaction shouldn't it be... |
If a fermionic Slater determinant state is represented as
\begin{equation}|\Psi\rangle=|\phi_v\phi_{v_1}...\rangle\tag{1}\end{equation}
\begin{equation}\implies|\Psi\rangle= c^\dagger_v|\phi_{v_1}...\rangle\tag{2}\end{equation}
Then,
$$\langle\Psi|=\langle\phi_{v_1}...|(c^\dagger_v)^\dagger$$
After using $\langle\Psi|\... |
I'm watching a video about Bell's inequality and how there can be no local hidden variables. They explain it using photons and whether they pass through a polarizer or not when they're oriented at different angles. I know there have been multiple attempts to disproof Bell's theorem over many years so I'm sure I'm missi... |
I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they said, and I quote,
In what follows we find that momenergy is indeed a four-dimensional
arrow in spacetime, the momenergy 4-vector (Box 7-1). Its three "space
parts" represent the momentum of the object in the three chosen space
... |
I had a couple of questions about cosmic filaments in the context of the cosmic web structure formation:
In this thesis (https://www.imprs-hd.mpg.de/51939/thesis\_cpenzo.pdf), the author indicates in section 2.2.2 that as voids expand and merge with other bigger voids, the matter that they contain is forced into high d... |
Given a Dirac fermion $\psi$
$$\mathcal{L} = \bar{\psi} \gamma^\mu \partial_\mu \psi - m \bar{\psi}\psi \ ,$$
which can be written in terms of chiral left and right handed fields as
$$\mathcal{L} = \bar{\psi}_L \gamma^\mu \partial_\mu \psi_L + \bar{\psi}_R \gamma^\mu \partial_\mu \psi_R - m \left(\bar{\psi}_L\psi_R + \... |
For a conical pendulum at an angle $\alpha$ from the vertical,
$$ cos \alpha = \frac{g}{\omega ^2 l} $$
When $\omega = \sqrt{\frac{g}{l}}$ , $cos \alpha= 1$
That is straight forward.
But How can $cos \alpha $ still be 1 when $\omega > \sqrt{\frac{g}{l}}$ ?
Atleast that is what Kleppner and Kolenkow says:
|
A fairly well-known puzzle asks for the resistance between two adjacent nodes of
an infinite square resistor grid, like the points A and B in the drawing.
If the resistors are all $1\Omega$, the answer is $\frac12\Omega$, which can be
seen by superposition of the two situations where you inject a current in node A,
or ... |
Consider a number of chiral superfield $\Phi_i$ with components $A_i$, $\psi_i$, $F_i$, respectively a complex scalar, a 2-component Weyl fermion and an auxiliary complex scalar. The most general supersymmetric renormalizable Lagrangian involving only chiral superfields is given by the $\Phi_i^\dagger \Phi_i$, $\lambda... |
I have been studying quantum mechanics and I came across Planck's relation which describes the energy $E$ of a photon as being directly proportional to its frequency $f$, with Planck's constant $h$ as the proportionality constant, i.e. $E=hf$.
My question arises from the observation that this linear relationship betwee... |
In weinberg's book, the author has calculated the power series of$$
H(\nabla S(\mathbf{x})-i \hbar \nabla, \mathbf{x}) N(\mathbf{x})=E N(\mathbf{x}) .
$$
and mentioned that the function $H(\nabla S(\mathbf{x})-i \hbar \nabla, \mathbf{x})$ is defined by its power-series expansion. In this expansion, it should be underst... |
Below I have attached a solution to a problem from a quantum mechanics textbook, and I'd simply like someone to explain why the boundary terms vanish in Hilbert Space for the functions $f(x)$ and $g(x)$, all I know is that a Hilbert space is a vector space where an inner product is defined, and that wavefunctions live ... |
In their famous paper in 1985 (link), Damour&Deruelle describe the orbital motion for a binary system taking into account first-order post-Newtonian corrections (1PN). The solution is given in their eqs. (7.1-7.2), according to which the binary separation $a_R$ (just to make an example) is:
\begin{equation}\tag{1}
a_R=... |
Anyone has (even a "pictorial") way of visualize what the group $U(1)$ does on the fields in the QFT framework?
I know that $U(1)$ can be seen as a circle and the operation of the groups is basically a rotation of a certain angle along of the cirle.
But I don't know how to relate QFT with this visualization.
I also kno... |
In Goldsteins' Mechanics, page 371 (relevant part appears below), it follows from what he states in the first yellow part that the equations of transformation:
$$Q = Q(q, p,t), \quad P = P(q, p,t)\tag{9.4}$$
are known, since he says that we can express $F$ as a function of either coordinate because we know eqs. (9.4) a... |
I was watching a lecture about circular motion and how angular velocity and angular acceleration differ if origin changes.The teacher at 9:10 says that we cannot apply the formula $a=rα$ as position vector $r$ changes about $O$. But at the starting while calculating angular velocity , he used $v=rω$. $r$ changes in th... |
Consider ideal MHD: infinite conductivity, frozen-in magnetic field lines etc. Clearly total energy of the system is conserved (magnetic field energy + plasma internal energy + kinetic energy = const). This suggests that the energy can be redistributed between these components, for example kinetic energy can be convert... |
I struggled a bit to understand the proof of the relation $C\overline\psi\psi C=\overline\psi\psi$ in Peskin's and Schroeder's book An Introduction to Quantum Field Theory (page 70, formula 3.147):
$$C\overline\psi\psi C=\ldots=-(\gamma^0)_{ab}(\gamma^2)_{bc}\psi_c\overline\psi_d(\gamma^0)_{de}(\gamma^2)_{ea}=\overline... |
I have an uncertainty about the proof of Noether's Theorem. Many books/notes that I have consulted and also my professor used the following proof:
Let's consider a transformations such as
$$Q_h=q_h+s$$
where $q$ is one of our lagrangian coordinates. We want to demonstrate that:
$$\frac{\partial\mathcal{L}}{\partial s}=... |
I'm trying to calculate the one loop correction to the quark-gluon vertex of QCD using euclidean formalism ($x^0 \rightarrow -ix^4$) and I'm having trouble to compute the integral in the picture below.
where$$ V_{\mu \nu \rho}(k, q, r) = (r − q)_\mu \delta_{\nu \rho} + (k − r)_\nu \delta_{\mu \rho} + (q − k)_\rho \del... |
I know that masses on their own don't produce Unruh radiation outside of black holes which produce a similar effect known as Hawking radiation. However, what if some observer hovers above the Earth and fires the rocket engines to prevent from going closer to the surface?Does that create Unruh radiation or no or would t... |
Consider a laser line position estimation by fitting using the Least Square Method (LSM) and prove (or disprove) that it can be considered as a convolution with some function and finding the center by looking for the maximum (zero‐crossing by the derivative). What is the smoothing function?
The Least Square Method (LSM... |
What do cosmologists actually mean by Anthropic Principle? What are the differences between weak and strong Anthropic Principle?
|
I have derived a formula for the coefficient of restitution, $e$, between two smooth particles, A and B, of fixed masses. I would like to confirm that it is generally true. Because it gave me the wrong answer to a question and now I am not so sure it is always true.
Deriving my Formula for the Coefficient of Restitutio... |
I understand that if there exists a charged particle, then there is an electric field.
In a wire (or a conductor), there are electrons (a billions of them) which are seperated from protons (i.e. there is a non-null distance between the charged particles). Supposed that the wire is not connected to any source/battery. D... |
Most ordinary surfaces are near Lambertian diffuse reflector, i.e. a small local radiates most strongly at norm then attenuates by cosine law when one gets to the tangentials. However this seems hard to square with the fact that it's simply an incoherent reflector. When we consider only a single wavelength, the surface... |
My understand is that GR says that mass curves space but it does not say why or how this occurs. Is the idea of gravitons that they are the entities that actually affect space?
|
Consider the above diagram.
Apparantely the vertical component of the normal force should balance $mg$.
However, this cannot be the case. The normal force is equal to the component of $mg$ perpendicular to the bank. As it is a component of $mg$, its magnitude must be less than the magnitude of $mg$. Again when we reso... |
The question says it all. I believe a hypothetical perfect reflector is what's referred to as a "white body", but I might be wrong. From what I understand such a hypothetical perfect reflector should still emit thermal radiation based on its own temperature (as long as it's above 0 K, of course), just not absorb any th... |
So my old microwave (which worked fine) heated a cup of coffee in about a minute to a good temperature. I would pull it out and could hold the mug handle with no issue.
That microwave recently broke, and I replaced it was a slightly smaller microwave (both in wattage and in cubic feet). Now I need to heat my coffee for... |
In mathematics, you can show that some problems are unprovable or have no solution at all and you also have the tool of proof by contradiciton, and similar. But is any of this also applied in physics to find out whether GR and QFT can be unified at all?
Are there people/papers dealing with the question about whether a ... |
I watched a YouTube video of Derek from Veritasium in which at 13:20, he claims that the lightbulb will turn on even if the circuit is broken, which astonishes me.
How can it be possible while when I cut the wire from the source to my lightbulb in my house, the light goes away immediately? Is there any special conditio... |
I'm trying to teach myself general relativity, and I came across the subject of covariant and contravariant components of a vector. Suppose your basis is $e_1, e_2$, and they are separated by 45°. Let the magnitude of $e_1$ be 2, and let the magnitude of $e_2$ be 1. My question is how do you find the dual basis $e^1... |
I'm doing a small experiment about kinetic gas theory where I have to check if the density of my gas corresponds to the barometric formula. My experimental setup is like this one Experimental setup where I got my gas density with a photoelectric detector. When I take logarithms and fit it to a linear regression all, it... |
Can any one give me a TRUE VALUE for the anomalistic periods of Earth and Mercury?
I note the previous question on the following.
I more or less implemented the method suggested above using elliptic integrals, but the results I got seems a little off. For Earth, I get 365.30 days.
|
Is there a way to find the object and image distances from the object height, image height, and focal length? I understand that the magnification is equal to $-\frac{d_i}{d_o}$ or $\frac{h_i}{h_o}$, but how does that relate to the mirror equation, $\frac{1}{f} = \frac{1}{d_i} + \frac{1}{d_o}$?
|
I'm currently studying the quantization of the EM field in a dielectric medium and trying to understand the quantization scheme of Huttner and Barnett (1992, see Phys. Rev. A 46, 4306). The system consists of a field part $H_{em}$, a matter part $H_{mat}$ (includes polarization and reservoir for losses), and an interac... |
Can anyone explain the relationship between the refractive index, the speed, wavelength and angle of a wave?
in my book is states that $$n = \frac{v_1}{v_2} = \frac{\sin θ_1}{\sin θ_2} = \frac{λ_1}{λ_2}$$ but it doesn’t state any explanation for the relationship.
|
I'm reading Birkhoff, George David (1942), "What is the ergodic theorem?", doi:10.2307/2303229, and I'm stuck on his 2nd example:
the line segment is divided into the infinite set of intervals, [0,1/2), [1/2,3/4], (3/4,7/8]..., and then the second interval is interchanged with the first, the fourth with the third, etc... |
I'm asking this here rather than on (Home Improvement)[diy.stackexchange.com] because I believe a more purely physics based answer is appropriate.
I am in the process of building a DIY exhausted spray booth for air brushing indoors. I'm a bit hung up on what the overall effect of decresing the opening of the front will... |
Why are cylinders more aerodynamic than spheres? Say you have a cylinder falling vertical that has rounded ends. Now remove the cylinder part. Now you’re left with a sphere but without the skin friction of the cylinder.
Where am I going wrong?
(This is also one of the reasons bullets are cylinders, not spheres)
|
I am reading An Modern Introduction to Quantum Field Theory by Maggiore. I have difficulty following the calculation of $\delta ( d^4 x)$ and $\delta (\partial_\mu \phi_i)$. Also, wonder whether the infinitesimal parameter $\epsilon^a$ depends on $x$.
On section 3.2 Nother's Theorem, given the transformation
$$
\begin{... |
Consider a system of $n$ particles, such as isolated atoms, molecules, nuclei, and the solar system, with $3n$ degrees of freedom; why does translational invariance eliminate three degrees of freedom and rotational invariance eliminate two degrees of freedom for this system?
|
There is a famous "derivation" or "demonstration" that is often presented in introductory classes in quantum mechanics. I find it deeply unsettling and I feel like key information are being left out.
It starts by assuming that a photon is somehow represented by a plane wave:
$$\psi = \exp{(i(kx-\omega t))}$$
where $\om... |
It has been established that light or other forms of electromagnetic radiation needs electric and magnetic fields in order to propagate. What would happen if it were possible to shield an area from both electric and magnetic fields and also to create a vacuum in the given space. Theoretically it should be possible to s... |
I stumbled upon this research article, where they define a digital organism as an abstract minimal model of an evolving predator-prey system as follows:
An organism is defined via its genome of fixed length 2048, consisting of upper- and lowercase letters, i.e. 52 possible letters. All but eight letters are inactive an... |
Let’s consider electromagnetic Lagrangian
$$\mathcal L=-{1\over 4}F_{\mu\nu}F^{\mu\nu}\tag{1}$$
Is charge conservation derived as a consequence of $U(1)$-invariance of this Lagrangian?
|
In my EM class we went over $$\nabla\times \frac{\vec{d}\times \vec{r}}{r^3}$$ which apparently can be breaken down to $$r(d\cdot \nabla)\frac{1}{r^3}-d(r\cdot\nabla)\frac{1}{r^3}+\frac{\nabla\times(d\times r)}{r^3}.$$ From now on the solution is clear, but how did the two first terms emerge? I see that there is a simi... |
I want to know if convection occurs, and contributes significantly to evaporation, in a puddle of water at room temperature, on a level floor. Do currents develop in the water as evaporation takes place? And what if the water was initially at a higher temperature? Would there be convection, and would it contribute sign... |
A catenary is the ideal shape for an arch whose job is to support its own weight. First, would this be true for a surface of revolution about a vertical axis through the lowest point, i.e. would a catenary describe the radial cross-section for a dome as well? Second, would the catenary describe the ideal radial cross-s... |
Physicists and Physics enthusiasts . I am new to this platform. And I wanted to post a question . Since I have nothing in my mind. I wanted to ask , Why is the earth a sphere and not other shape?
Moreover please provide me some books where I can learn physics. I am in my senior year in high school i.e 12th Standard
|
In the context of low-energy scattering, as the potential becomes more and more attractive, the scattering length varies from negative, diverging then to positive values. It corresponds to wavefunction undergoing effective interaction from attractive ones to repulsive ones. I am confused by why deep attractive potentia... |
The defining equation for simple harmonic motion is such
$$a=-ω^2x$$
When we find the centripetal acceleration of an object in orbit we use the formula
$$a=ω^2r$$
As a consequence of the accleration being $\frac{v^2}{r}$
The two formulas for acceleration look extremely similiar, and displacement $x$ is essentially the ... |
Assume a full cylinder starts slipping without rolling on the floor with initial velocity $v_0$ and the floor has kinetic and static friction coefficient $\mu$. Find the distance it will travel until it rolls without slipping.
My idea was to use the work-energy theorem:
$E_{k,final}-E_{k,initial}=W_{friction}$, but the... |
In the book by S. Pal Arya "Introduction to Micrometeorology" there is a chapter about Laminar Ekman Layers.
I refer to the following example:
Variables are:
U, V wind velocity in x, y direction
G Geostrophic wind magnitude
Ug, Vg geostrophic wind in x, y
f Coriolis Parameter
$h_s$ a reference height at which Us is g... |
there we have the EOM:
\begin{align*}
\alpha q_{2} + \lambda - \ddot{q}_1=0 \\
\alpha q_{1} + \lambda - \ddot{q}_2=0
\end{align*}
and $q_{i}$ is the canonical coordinates. Can I use the Fourier transform to solve it? and how?
I want to solve the EOM like the coupled Hamonic oscillators by using Fourier transform like
$... |
Would I still see the specimen but completely blurry? or wouldn't I see it at all? For example, let's say the wavelength of the light used is 600nm and the diameter of the specimen is 550nm.
|
Given $G = (V,E)$, with the set of vertices $V$ and the set of edges $E$, the corresponding graph state is defined as
$$|G\rangle = \prod_{(a,b)\in E} U^{\{a,b\}} |+\rangle ^{\otimes V}$$
where the operator $U^{\{a,b\}}$ is the controlled-$Z$ interaction between the two vertices $a$ and $b$. Further, we define an opera... |
It is well known that the open quantum dynamics is governed by the Lindblad master equation
$$\partial_t{\rho}=\mathbb{L}(\rho)=-\frac{i}{\hbar}[H, \rho]+\sum_i \gamma_i\left(L_i \rho L_i^{\dagger}-\frac{1}{2}\left\{L_i^{\dagger} L_i, \rho\right\}\right),$$
where the solution is given by $e^{\mathbb{L}}(\rho)$, which i... |
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