instruction stringlengths 31 24.3k |
|---|
First of all, I will ask the patience of community because this is a "need-an-explicit-calculation answer". Pure abstract considerations will not, I think, help me very much.
So, I would like some sort of step-by-step rule to calculate tetrad coefficients. I will explain (please consider the metric tensor signature as ... |
Some time ago I read that without knowing more about quantum gravity
the assumption that Black Holes continue to collapse is valid.
That mystifies me somewhat but for the purpose of this question I’m going to say we found a Black Hole that is fully mature and the singularity is as small as it’s going to get.
I would li... |
I have a question about Constructuion of Chern-Simon Action.
In its paper "Non-commutative geometry and string field theory", Witten construct the Action of the String Field Theory inspiring on the Chern-Simon theory one.
In the paper, there are few objects, with analogy with gauge field objects (I will not define prec... |
If I am standing $10$ feet away from an explosion, what would hit me first? Shock wave, sound, shrapnel, etc (besides light!)
If the shock wave was powerful enough, is it possible to be thrown out of the blast radius and not get hit by shrapnel.
If my question(s) are missing something technically, please help develop ... |
Suppose we have got some operator $A$ which does not commute with the Hamiltonian, for example $\hat{p}_{x}$ and $\hat{H}$, where $\hat{p}_{x}$ does not commute with the $\hat{H}$ and we make the first measurement and we get $p_{x}^{\prime}$ and immediately after the first measurement the system's momentum is in the ei... |
If 2 spaceships are travelling in the same direction with the same speed, one after the other. Do their clocks show different times to a stationary observer?
|
The Chandrasekhar limit assumes the white dwarf is made of carbon, but hydrogen has a much lower ratio of mass to electrons, so the limit should be different in that case. And electron degeneracy pressure might not even be the limiting factor, if neutronization or cosmic ray initiated fusion chain reactions are possibl... |
In the chapter of energy of the Kleppner's book, Introduction to Mechanics, he explain diagrams of energy and the concept of bounded motion. There is an example which explains that if a motion is bounded or not can depend on the total mechanical energy, that is the case of the motion of an atom which experiment the rep... |
In Section 37 (The spin of the electron), Dirac writes,
"The eigenvalues of $m_z$ are $\hbar/2$ and $-\hbar/2$, so the eigenvalues of $\sigma_z$ are 1 and -1, and $\sigma_z^2$ has just the one eigenvalue 1. It follows that $\sigma_z^2$ must be 1, and similarly for $\sigma_x^2$ and $\sigma_y^2$..."
I understand why $\... |
Is it possible to calculate the flux of some electromagnetic radiation (say, a radio wave) using other parameters?
|
I have read in Brian Greene's book "The Elegant Universe" that so far physicists don't know the exact equations of string theory, and they have to use approximations of those equations and get approximate solutions. But how come? Surely, although the solutions may be approximate, we should be able to get the exact equa... |
I have a perplexity regarding Feynman's famous "little arrows" approach.
To summarize and paraphrase Feynman as I understand him, he is claiming that we model the probability that an event will happen by squaring the length of the arrow we get by adding up all the arrows belonging to the various different ways the even... |
How do experimental physicists measure the angular momentum for the spin of an electron? A paper about an experiment would be helpful. Alternatively, how was the electron spin value of $\hbar/2$ determined?
|
I was trying to prove that during reflection from a concave mirror, all rays parallel to the principal axis will meet the principal axis at a point (focus) that is equidistant from the centre of curvature and the pole.
I thought of proving this using coordinate geometry (and some trigonometry). I thought of proving it ... |
Suppose that one could "flip" a coin, and that it settled onto a platform.
For simplicity, let the coin processed with the nonzero angular momentum on $y$ axis only.
To further simplify the question, suppose that the platform was in vacuum, and the "falling" of the coin onto the platform was created by some "fictional ... |
When the lid is not kept on and a hole is created about an inch or two from the bottom the water bottle, I observed that the water flows out the bottle in a parabolic manner. What is the reasoning behind this mechanism?
|
My current understanding is that materials found in nature attenuate light as a function of some fixed constant, according to this equation: $ I(x) = I_0 e^{-\kappa_v \rho x} $, where $ I_0 $ is the initial intensity, x is distance inside the material, $ \kappa_v $ is 'opacity', and $ \rho$ is mass density. I am assumi... |
I have seen several questions about this on this site and quora and there seems to be no definite, unanimously agreed upon answer. Does static friction do work on an accelerating car.
Heres what i think:
Ignoring the affects of air resistance, since the chemical energy of the car is being converted into kinetic energy,... |
I was wondering, as my question suggests, that which kind of waves are more efficient in transporting energy, considering longitudinal and transverse waves. I checked out this post here, but didn't get a satisfactory answer.
What I think is that because for longitudinal waves, because the motion of particles is along t... |
Given is the page of a book which I was studying. I was trying to study the derivation of the wave equation in a lossy medium. As I have underlined a sentence that says, "most of the case in which wave is propagating does not contain the charges". Why is it so?
|
On chapter 7 of their book on QFT, Peskin and Schroeder derive the vacuum polarization correction to the photon propagator in bare renormalization theory. On page 247, they state that to leading order in $\alpha$, $\Pi(p)=\Pi_2(p)$. This is obviously simply the definition of $\Pi_2(p)$, the one loop correction to the t... |
As we know that quantum many-body systems can be roughly classified into two classes --- gapped phases and gapless phases --- depending on whether there is a nonzero energy gap above the ground state(s) in the thermodynamic limit.
Within the gapless phase, there are a subclass of systems called critical phase, which ar... |
The question that I have is how should I calculate the total capacity of the capacitor described in the picture below:
I tried taking Air, $C_1$,$C_2$ as parallel capacitors (They should have the same potential difference) with their effective being $C_{eq1}$ and taking $C_4$ and $C_5$ in series and adding up their ef... |
We know that $$\frac{dv}{d t}=\frac{d\left(v^{i} e_i\right)}{d t}=\partial_{j} v^{i} v^{j} e_{i}+v^{i} v^{j} \partial_{j} e_{i}$$
As $\partial_{j} e_{i}$ is another vector we can expand it in the same basis $$\partial_{j} e_{i}=C_{i j}^{k} e_{k}$$
then we obtain the condition for constant vector as
$$\nabla_{j} v^{k}=... |
I'm wondering why correlation function is a more fundamental object in conformal field theory than the notion of particle. By conformal symmetry, I think we can still discuss about massless particle.
I'm wondering if there will be bound state and scattering state, those exists in quantum mechanics scattering theory,... |
I'm wondering if one could use conformal field theory to predict any facts in (experimental) particle physics?
I think CFT shares some similarities with QCD, but I'm not sure if one could use CFT to predict any effects in QCD.
|
Given the de Sitter metric for spacetime
$$ds^2 = \left( 1 - \frac{\Lambda}{3}r^2\right) dt^2 - \frac{1}{\left( 1 - \frac{\Lambda}{3}r^2 \right)}dr^2 - r^2d\Omega^2 $$
we understand this is a solution to Einstein's field equations in vacuum with the addition of a cosmological constant which is maximally symmetric. In t... |
Given the gauge-fixing term $\mathcal{L}_\mathrm{gf}=-\frac{1}{2\xi}(\partial_\mu A^\mu)^2$ and the gauge transformation $A_\mu\mapsto A_\mu+\partial_\mu\alpha$, how does the term break gauge invariance?
Under this gauge transformation we have $\partial_\mu A^\mu\mapsto \partial_\mu A^\mu+\Box\alpha$. But in Lorenz gau... |
How to derive the Zeeman energy density $E=\mu_0 \mathbf{M}\cdot \mathbf{H}$ from the general expression $E=\int \mathbf{H}\cdot d\mathbf{B}$?
My try for a 1D case:
The Zeeman energy can be seen as the energy difference between the case when there is no magnetization $M=0$ and no field $H=0$ and the case where there is... |
I was deriving the expressions for capacitance for spherical capacitors and i am completely confused now.please help!
Outer sphere is B with radius b and inner sphere is A with radius a.
CaseI- sphere B is earthed( +Q given to sphere A)
(i) outer surface earthed:
Potential on B is just due to -Q (induced charge) as pot... |
Imagine you have a ventilator that is spinning madly an creating strong air up force upwards. Then you put in the middle with a holder a paper ball. Then some-have detach the paper from holder. Sure it will fly up. The question is - would it have a instant and constant up velocity or would it accelerate (from slower to... |
Here is a sketch of a system
It is a homogeneous chain on a prism. It needs to find an equilibrium.
length of the chain is $l$
length of a horizontal part of the prism is $a$
angles of the prism are $\alpha$ and $\beta$
My thoughts are that we should take a length of a left part of the chain as a generalized coordinat... |
I read that the fluctuation in energy is given by $$ \delta E = E - \langle E\rangle $$
But I don't quite get this. Is this only over one particle? So is E the definite energy of the particle? The last term is of course the average energy so I suppose this is indeed the fluctuation in energy, but how would you gener... |
Just something I can't wrap my mind around. If light is oscillating EM field, and the strength of EM field weakens proportionally to distance squared, then why light doesn't lose energy as it travels further from the source? Why wouldn't oscillating EM field weaken over distance same as non-oscillating field does?
P.S.... |
I read about Kepler's Laws and in one of them he mentions that the path of a planet is an ellipse, with the sun as one of its foci (I'm narrowing down this to only our solar system).
However though I'm not experienced in this subject, I had a doubt.
I read in places that the Sun is not stationary. Please correct me if ... |
At normal incidence the plane of incidence is not defined! So how do we will understand that whether the reflection coefficient is positive or negative; because according to frensel equation for E perpendicular to the plane of incidence and for E parallel to the plane of incidence have different singns(i.e. positive o... |
I stumbled on a problem in a textbook, where I was asked to describe the change in ammeter's indication due to change in resistance in circuit: rheostat's slider is moved or key is locked as indicated in the pictures, how ammeter's indication will change? (the generator's resistance is negligible)
It is clear, that in... |
Let a box be divided into two parts by a partition. Let each part be filled in by the same gas in equal concentrations but different temperatures. Let the gases start diffusing through a hole in the partition.
Assume also that the temperature is each part is maintained constant.
Is it true that the concentration of ga... |
(Note: I am crossposting this from https://math.stackexchange.com/q/3740738/)
Let us work with these definitions $L=\sqrt{dAdB}$ and $S[A,B]=\int_{\Delta \lambda}\sqrt{\frac{\partial A[\lambda]}{\partial \lambda} \frac{\partial B[\lambda]}{\partial \lambda}} d\lambda$. Here I consider $A$ and $B$ to be general commutat... |
Suppose we have two different QFTs with the same set of quantum fields which differ in their Lagrangians by a relevant operator. Assume both QFTs approach a CFT fixed point in the UV. Suppose at time $t=t_0$, both QFTs have the same wavefunction in the Schroedinger picture. According to the AdS/QFT conjecture, both QFT... |
For two-dimensional conformal field theories it is usually assumed that the cental charge is fixed (for simplicity let's assume that $c=\bar c$).
Is there a generalization or a concept that uses the concept of changing central charge within one theory? Is there any useful interpretation for this scenario?
|
I'm not studying physics. I only worked with basic dynamics and have no idea how to calculate this. It's likely that the answer to the question I'm asking is nonsensical, but, from my point of view, it's still worth asking, since I have no idea if that's the case:
How can I find out if there's a minimum to how many Tr... |
Assume you have an action $S=\int \sqrt{-g}(R+p(X,\phi)) d^4x$.
I want to calculate the perturbations for $\phi(t,x)=\phi_0(t)+\delta \phi(t,x)$ and the standard perturbed metric $ds^2=(1+2\Phi)dt^2-(1-2\Phi)a^2(t)\gamma_{ik}dx^idx^k$.
I can't seem to figure how to calculate $\delta X$, where $X=\frac{1}{2}g^{\mu\nu} \... |
In the Sachs-Wolfe effect (the one at last scattering, not the ISW), the standard result is
$$
\frac{\Delta T}{T} = \left( 1 - \frac{2}{3} \right) \Delta \Phi = \frac{1}{3} \Delta \Phi .
$$
To calculate this in full one might do integrals, but there is a standard simple argument to justify the factor $2/3$ in the first... |
I found it really intresting to read about the surface tension phenomena, and I was thinking about that if there is any relation between the percent of of liquids in a mixture. I mean if I know that $\gamma_1= A$ and $\gamma_2 = B$ (while $1$ and $2$ are some liquids) so $\gamma_1$ and $\gamma_2$ is the values of $1... |
I need to find a transition dipole moment of Rhodamine 6G molecule, however they provide ground state and excited state dipole moment. Are they similar or can I somehow obtain transition dipole moment from the given ones?
|
I have the following quadratic Hamiltonian (of boson type):
$$\hat{H}=\epsilon b^\dagger b -v(b^\dagger b^\dagger + b b )$$, where both $\epsilon$ and $v$ are real parameters. The operators $(b,b^\dagger)$ Are the bosonic operators and they obey the usual commutation relations (specific for the bosonic case).
My task i... |
At the outset I'll state that I understand completely why, physically speaking, there's no preferred frame - that's not what I'm asking in the question.
I'm not sure why we don't give spacetime a vector space structure though. I realize that doing so forces us to identify a certain unique point in spacetime as the "uni... |
I was going through this lecture, where Leonard Susskind explains that these two Feynman diagrams are considered to be equivalent in QFT:
One diagram explains the same phenomena in one possible way and the other describes the same thing in a different way. But, when I look at it, it seems an awful lot that if you take... |
I have a fairly longstanding confusion over several different equations involving energy in special relativity and I struggle to see how they relate to each other.
$E=mc^2$
$E=\gamma mc^2$
$E=mc^2+\frac{1}{2}mv^2$
$E^2=m^2c^4+p^2c^2$
$P^0=E/c^2$ (the $0-$component of the four momentum)
Could someone explain in w... |
I am looking for insight on quantum field theory, and more precisely, I am interested in having a low-detailed idea of what a quantum field theory is about; moreover, I should say hat I am a mathematician with little physical background.
I found this question: What are quantum fields mathematically? but am not fully sa... |
I noticed, reading the solid state physics book by Ibach & Lüth, that the majority of elements crystallize in a handful of space groups:
I highlighted face-centered cubic (FCC) structures in blue and hexagonal closely-packed (HCP) structures in green.
As I understand it, directed covalent bonds give rise to the more ... |
Let's consider a wave which propagates on 2 or three directions, like for instance an electromagnetic wave inside a rectangular waveguide totally closed on two ideal conductor surfaces:
The walls of the guide force the wave to assume an integer number of half-wavelenghts along x,y,z:
$$l_{x,y,z} = m_{x,y,z} \cdot \fra... |
I'm trying to figure out a detail on the calculation of correlation functions in the $\phi^3$ theory. So, I know we can calculate a 2-point correlation function as:
$$G(x_1, x_2)=\frac{\langle0|\mathcal{T}\phi_{1I}(x_1)\phi_{2I}(x_2)e^{-i\int dz\phi³}|0\rangle}{\langle0|\mathcal{T}e^{-i\int dz\phi³}|0\rangle}$$
Now, I ... |
Let's say a torpedo moved under the water. Water is virtually in-compressible right? So what happens to the water in front of the torpedo as it pushes forward? It has to somehow move out of the way, so where does it go?
Does it get pushed up? How can it get pushed if there is feet of water above it. Does it get push u... |
Matter-antimatter destruction is 'decay', correct? And since antimatter particles are considered the opposite of matter ones in every way, not just in terms of EM charge, does that mean they are decaying via all three quantum forces simultaneously?
|
this problem is often presented as a simple demonstration of relationship between the heat capacity at constant volume $C_V$ and entropy $S$.
Let's say the heat capacity $C_V$ is equal to $a T + b T^3$ where $a$ and $b$ are constants. We then have
$$
\mathrm{d} S = \frac{C_V (T)}{T} \mathrm{d} T \quad \implies \quad S ... |
I don't understand why reaction force would decrease at the start of a countermovement jump. I've tried looking at this diagram and considering moments and how lowering the position of the center of gravity may affect them, but I don't seem to understand why this would be. I'm still in high school,so a simple explanati... |
I'm doing some adiabatic and super adiabatic evolution using python but without success, the super adiabatic to be more precise. The problem is the way I've manage to write the super adiabatic Hamiltonian, it can be written in function of the eigenvalues and eigenvectors of the Adiabatic Hamiltonian as:
$$ H_{SAD} = \s... |
Can computation be accomplished using any physical process? For simplicity let me restrict myself to the computation of performing addition. I am aware that mechanical calculators just use Newtonian mechanics to perform computation. As far as I can see, it seems that it is possible to perform computation using any phys... |
I'm wondering in experiment, how can one measure the lifetime of a particle, because it is a very short time.
Also, I'm wondering how experimentalists measure the mass of the particle, which is also very small
|
Please try to provide a sufficient answer, and when it is just „because it satisfies Newton‘s equations“, please try to give an example or explain it. If you know it, I would be very happy if you could tell me how Lagrange himself came up with this.
|
Take the formula for Coloumb's law. It does not show in any case as to how the static field propagates. What I can feel is that the field of a static charge is ever prevading from the time the charge was created and other charges interact with it.
But consider a static charge kept in your room. Now another charge in An... |
I've made an experiment with resonance frequency of a LC circuit. One part was to place a metal (I think iron) in the middle of the induktivity of LC circuit.
I measured a higher resonance frequncy as without the metal. How is this possible? I thought cause of the permeability of the metal the induktivity would increas... |
Let us suppose there is a solenoid which has $n$ turns per unit length the current is varying with time as $I =kt$ where k is a constant if the current is flowing then there must be induced electric field inside and outside the solenoid since $$\oint E_{induced}.dl= -\frac{d\phi}{dt}$$. now my question is if I place a ... |
In CFT ($d>2$), 2-point functions (between two scalar primary operators, for example) vanish unless the operators have same scaling dimension. This leads me to wonder whether a CFT can have two operators with same scaling dimension. Extending to the possibility of spin-ful primaries, is it possible that they have same ... |
This document https://arxiv.org/abs/1601.03547 refers to the “single pulse radiometer equation”. Apparently, it’s used to calculate the flux of radio transients. What is the “single pulse radiometer equation”?
|
I have rolling shutters, e.g.:
I am trying to determine how much time it takes to raise/lower the shutters a specific amount. (Because of the physics involved, the time is non-linear relative to the amount of shutter movement.)
This is very similar in concept to a winch raising/lowering a weight.
I found an excellent ... |
I'm trying to develop a more intuitive understanding of the states of matter..specifically the difference between solid and liquid. To this end, I'd like to consider the most basic system in which the concept "state of matter" still applies. Obviously a system with a single atom doesn't qualify, as a state describes th... |
I need to know the total cross section for the process $H \rightarrow W^{+}W^{-}$, but cannot find it anywhere. Decay widths for Higgs decays are mentioned in Peskin and Schroeder (page 776), but I gather that one cannot compute cross sections directly from decay widths.
Edit: looks as if the answer is on page 6 ofthi... |
Every major theory in physics - from classical dynamics, to quantum mechanics, to general relativity - makes assumptions about the structure of spacetime. Among the most common assumptions are that spacetime is:
uncountable (in the sense that the set of points that we identify as "spacetime" has cardinality greater th... |
What I have understood from the concept of reducing a Bloch wave $\psi_{n,k}(x)=e^{ikx}u_{n,k}(x)$ to the first Brillouin zone is the following:
$$\psi_{n,k+\frac{2 \pi}{a}m}(x)=\psi_{n-m,k}(x),\tag1$$ with $m$ and $n$ integers and lattice period $a$. I can see this easily mathematically by repeating the argument in th... |
Unlike speed which is capped for anything with rest mass at speed of light in a vacuum, what would prevent an object to undergo infinite acceleration in an instant? I assume in theory if we can apply infinite amount of force on the object at a particular moment, it must undergo an infinite acceleration right? What laws... |
Reading this article I ran into a doubt.
It derives the Polyakov action for a general $p$-brane
$$S(X,g)=-\frac{T}{2}\int\text{d}^{p+1}\xi\,\sqrt{-g}\left(g^{ab}h_{ab}-(p-1)\right)\tag{7}$$
by integrating out the Lagrange multiplier from the action
$$S(X,g,\Lambda)=-T\int\text{d}^{p+1}\xi\,\left(\sqrt{-g}+\Lambda^{ab}(... |
I read about [Nordström's Theory of Gravitation][1]
[1]: https://en.wikipedia.org/wiki/Nordstr%C3%B6m%27s_theory_of_gravitation and how it was proposed before General Relativity. There were two Nordström Theories of Gravitation, but I will be asking specifically about the second. The field Equations for Nordström's T... |
I was studying about what does it mean canonical quantization treatment. But now I have the next question.
Why if we establish canonical the commutation relations $$\left[q,p\right]=i\hbar,\quad \left[q,q\right]=\left[p,p\right]=0, $$
we can say that the system is quantized?
I mean, what does imply these relations in t... |
In what form and by what way is energy converted when i, say lift a block to a height h above the earth's surface. If the said energy, say 5 Joules, is spent in lifting a block, is the whole of the energy converted into potential energy, as given by the formula, mgh or is part of the energy lost as heat due to the laws... |
I have read a number of textbooks (e.g. Sakurai), and they all seem to say that the unperturbed Hamiltonian of hydrogen is:
$$
H_0 = \frac{p^2 }{2m_e} - \frac{e^2}{r} \tag{1}
$$
and the relativistic correction is given by:
$$
T = \sqrt{p^2c^2 + m_e^2c^4} - m_e c^2 \approx \frac{p^2}{2m_e} - \frac{p^4}{8m_ec^3}
$$
and h... |
One can show that there are no unitary finite-dimensional irreducible representations of the Poincaré group. The reason is that the generators for boosts are antihermitian.
Since boosts are basically time-space rotations, this led to me wondering whether for Euclidean space, where we don't have minus signs in the metri... |
The path intgral formalism of quantum mechanics states that the amplitude to go from $\left(x_i,t_i\right)$ to $\left(x_f,t_f\right)$ is $$K\left(x_f,t_f,x_i,t_i\right) = \int \mathcal{D}x\quad e^{i\frac{S\left[\gamma(x)\right]}{\hbar}}\tag{1}$$
where $\gamma$ is a possible trajectory and the integral is the sum on all... |
I was reading about the experiment that confirms the wave particle duality as we see a sudden rise in galvanometer which was explained as a phenomenon of constructive interference.
Is it possible that the galvanometer shows zero deflection even if electron reaches the collector plate i.e. a phenomenon of destructive in... |
Let's say we have a massless body connected to 2 strings. Now lets pull the body with a force $F$. As the body is massless tension in both strings will be equal. Let that be $T$. Now we know that $$F-2T=Ma$$
But as $M=0$, we get $F=2T$. Now although the forces are equal the body still has an non zero acceleration $a$. ... |
I'm going to ask about if there is some effect/interaction of the magnetic bubbles that are explained in [1] from YouTube and the Earth's magnetic field. I know these subjects from an informative point of view. I refer (as reference for all users) the existence of such magnetic bubbles at Solar System's edge, as [1], a... |
I have some questions regarding the physical meaning of the units.
The unit of Planck's constant $h$ is J$\cdot$s= kg$\cdot$m$^2\cdot$s$^{-1}$ in the SI system. My question is: When multiplying by m$^2$ what is the meaning of kg$\cdot$m$^2$? As $\frac{kg}{m^2}$ is kilogram per square meter. So, can we write J$\cdot$s=... |
Take the Langevin equation for the position of a particle in Brownian motion.
$$
m\frac{d^2x}{dt^2} = -\gamma\frac{dx}{dt} + \eta(t)
$$
My professor wrote this as the following in the class:
$$
\lim_{\Delta t\to 0} \frac{x(t+\Delta t) + x(t-\Delta t)-2x(t)}{(\Delta t)^2} = \lim_{\Delta t\to 0} \frac{-\gamma}{m} \frac{... |
What is the material or metamaterial that is a very good dielectric and has a very high refractive index at least in frequencies below $500\ MHz$?
|
I wonder why the dielectric strength is higher the thinner the material is:
"Dielectric films tend to exhibit greater dielectric strength than
thicker samples of the same material."
Source
In the german article there is also an equation given: $ E = U / d $.
Given that, I can simply understand it. But I wonder about ... |
Recently I was solving some boundary value problems in Electrostatics. I stumbled upon a problem with an infinitely long cylinder (axis along the $z$-direction and radius $a$) with a plate inside it (centered at $z=0$). The plate is perpendicular to the axis of the cylinder and has the same radius as the cylinder. The ... |
Will magnets lose strength over time when coupled to another magnet ?
Im designing a part (c. 200g) which needs to be held in place, but also be removable, so looking into a pair of magnets (neodymium or other) to do this, the magnets will for >99% of their life be coupled to one another, but wondered if over time the ... |
I was solving an example of 1D wave equation with given BC and IC by separation of variables and Fourier series.
$$\frac{\partial^2u}{\partial t^2}=c^2\frac{\partial^2u}{\partial x^2} $$ $$BC: u(0,t)=u(l,t)=0$$ $$IC:u(x,0)=\sin\left(\frac{\pi}{l} x\right) $$$$\partial_tu(x,0)=0$$
By separating the variables and solving... |
In the literature of Open Quantum System, one often comes across the following ($t_2>t_1,>0$):
Semi-group property of a map: $A(t_1+t_2,0) = A(t_2,0) A(t_1,0)$.
What does this mean physically, and why the name semi-group?
|
My question is about how to properly compute the projection of a tensor in a given direction using inner product product in a pseudo-riemannian manifold, since inner product isn't defined positive.
For simplicity, suppose we have a 2-dimensional curved manifold with signature $ (-, +) $ and a generic metric tensor $ g_... |
I have learned that uranium atom can be split in two different ways in a fission reaction. In one case it produces two neutron while in the other it produces three.
\begin{align}
^1n + {}^{235}\mathrm{U} & \longrightarrow {}^{94}\mathrm{Sr} + {}^{140}\mathrm{Xe} + 2 \, {}^1n \\
^1n + {}^{235}\mathrm{U} & \longrightarro... |
I have been reading a Daniel Schroeder's book called "An introduction to Thermal physics", and after having completed first couple of paragraphs of "Free energy as available work" (chapter 5) I got this question.
I the book a $Pb$ based battery is considered with the discharge reaction that goes as follows:
$$Pb + PbO_... |
So I'm trying to understand velocity time dilation, even still after brushing it multiple times throughout university. I am doing so with the example of a spaceship travelling to Alpha Centauri [AC].
Lets approximate both the Earth and AC to be stationary, the distance between Earth and AC to be be 4ly, the speed of ou... |
According to wikipedia, then the Noether current for
$$
L= \eta^{\mu\nu} \partial_\mu \phi^* \partial_\nu \phi - m^2\phi^*\phi
$$
with invariant transformations:
$$
\phi\to e^{i \theta}\phi\\
\phi^*\to e^{-i\theta}\phi^*
$$
gives the probability current:
$$
j^\nu=i\left( \frac{\partial \phi}{\partial x^\mu} \phi^* - \f... |
Why meson conservation doesn't exist?
|
Proof of the Piola Transform. As I understand it, the relationship between the second order tensor $\bf T$ over a reference configuration and the same tensor in a deformed configuration $\bf T^\prime$ is given defined as follows:
$
{\bf T} := {\bf T^\prime} \, \textrm{cof} \, {\bf F}
$
Where $\bf F$ is the deformatio... |
First of all, I know that any math (or computation) a classical computer can do, we human can do with pen and paper at same type of efficiency. Obviously, that is because we tell a classical computer what to do steps by steps, and we are capable of completing each step.
My question is whether it is true with quantum co... |
I wonder eta and pion could exist containing up quark (anti up quark)?
Isn't there pair annihilation in this meson?
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.