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This is a fairly popular problem.
An infinite slab, of thickness 2d, carries a volume charge density $\rho$.Find the electric field, as a function of $y$, where $y=0$ at the center. Plot $E$ versus $y$ calling $E$ positive when it points in the $+y$ direction and negative when it points in the -y direction.
Why is... |
how can we explain the effect of pressure on the melting/freezing point from microscopic side of view? I mean how can we explain it with the manner of molecules and atoms not how we see it Macroscopic?
|
what do we mean by the selection rule $\Delta S=0$?
Can you give me some example for hydrogen atom?
For example if I want to go from $1s$ to $2p$ how can I calculate $S$ for $1s$ or for $2p$?
|
I read the first sound laser (or SASER) was made in 2010 here.
But if we're talking about the state of the phonons emitted then we could say that any sound created by a planar vibration has a unique wave vector $\vec{k}$ and its phonons are spatially coherent.
|
I just learnt how potentiometer circuits work, and I was taught that the resistance in the secondary circuit does not change the balance length as no current flows through the secondary circuit and thus the only potential drop is through the EMF of the unknown battery in the secondary circuit. However my proffessor men... |
Today, I was watching a video, and the man on the video said that we only "accept" $F=ma$. Then said that no one can prove $F=ma$. But I know we can derive $F=ma$ by momentum with calculus. I am confused, so do we only accept $F=ma$, or do we know the proof?
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For a reversible process, we define $ dS= \frac{dQ}{T}$ , so, the integral being negative would suggest that the entropy of universe decreases with each cycle of the engine because the clasius inequality states this quantity is less than 0
|
Assume we add a colorless and hyperchargeless $SU(2)_L$ fermion doublet to the Standard Model.
$$L=\left(\begin{matrix}L_u\\L_d\end{matrix}\right)$$
Then, considering gauge invariance, the lagrangian should contain a term
$$ML^TCi\sigma_2L$$
where $M$ is some mass scale and $\sigma_2$ is the second Pauli matrix. Under ... |
I have a silly question.
I have a state $\hat{\rho}$ and I make the transformation $\hat{\rho}'=\hat{a}\hat{\rho}\hat{a}^\dagger$ (I want to subtract a photon).
I expand in the position basis the density operator:
\begin{equation}
\hat{\rho}=\iint dx dx'|x\rangle \rho(x, x') \langle x'|
\end{equation}
and the action o... |
Often sequential Stern-Gerlach experiments are taken to motivate basic quantum mechanics. But I can't find a paper where these are actually carried out experimentally. I have two questions:
Who was the first to link multiple Stern-Gerlach experiments?
Where can I find the paper on this?
|
Isham (in his Lectures on Quantum Theory), in his initial chapters at least, gives examples of only such operators on such wavefunction state-spaces which have only nondegenerate eigenfunctions. I guess that this is due to the reason that it makes the (initial) formalism easier.
Hence for an operator $A$, with eigenval... |
Both Heisenberg ferromagnets and crystalline solids break the rotational symmetry in space. Now consider a crystalline ferromagnetic solid. By virtue of being in a crystalline phase, it already broke the rotational symmetry. Having broken that, how can it further break the rotational symmetry which is already broken (b... |
I'm having trouble determining when it's acceptable to use Gauss' Law and when I have to integrate Coulombs law. If I am given a line charge and asked to find the electric field at a point r from the line, is it correct to say that I can only enclose the line in a cylinder and find the field using Gauss' law if the lin... |
Quantum tunneling has been shown to be linked to uncertainty relations for some observables involved in the system. For instance, if we consider electrons tunneling through a potential barrier it can be shown (Razavy, Quantum theory of tunneling, chapter 2.1; arXiv:quant-ph/0507239 that the position and momentum uncert... |
Lets suppose we have spin 1/2 particle and some sort of Stern-Gerlach experiment setup (SG from now on).
So one SGz setup means one that is oriented for spin projection in z direction, similarly for other directions. So, if we prepare a beam of spin 1/2 particles and pass it through SGz and then just put some detector,... |
I am trying to reproduce the results of this paper1. In particular Eqs. (25) and (26). I would like to convert the proton decay width (given in units of $\rm GeV$) to a lifetime in years. The formula is below:
$$\Gamma (p\to \pi^0 \mu^+)_{\rm flipped}=
\frac{g_5^4m_p |V_{ud}|^2 |(U_l)_{21}|^2
}{32\pi M_X^4}(1-\frac{m_... |
For an infinite plane, I know that that using Gauss' Law, the field is simply $σ/2e_0$. However, this is true because the net field is directly upward everywhere. If the plane isn't infinite, this wouldn't be the case, but the net field at the very center would still be directly upward. Is there a way to use this symme... |
Take a ideal inductor (superconductor). Change in magnetic field produces electric field. But in a ideal inductor electric field inside is zero.
What makes the electric field zero in a ideal inductor when it
is connected to a circuit.
Another question is why is electric field inside a ideal conducting wire zero when it... |
I want to ask whether it is (theoretically) possible that there is a pulley with no mass but has friction in it....Why or Why not ? Also will the tension on both sides of it be the same or different (since it has friction)...??
|
I would want to know what is the physical interpretation of the heat equation with variable coefficients such that:
$$u_{t}-\frac{1}{1+t^2}u_{xx}=0$$
well, I think I got it, it means that the diffusivity decreases as time goes by
|
When we project an object vertically upwards its velocity at maximum height consider to be zero but still, it has acceleration due to gravity i.e $9.8\mathrm{m/s^2}$. But mathematically we know that acceleration is the first derivative of velocity with respect to time $(a=dv/dt)$. So mathematically if velocity is zero ... |
Euler angles is supposed to uniquely define the two differently oriented co-ordinate axes. Can someone help me in visualising how a set of three angle takes one co-ordinate axes system to the other co-ordinate system. It would be helpful if one can start with given two differently oriented co-ordinate system and one se... |
Newton's second law states:
$$F(\vec{x})=m\vec{\ddot{x}}$$
For $\vec{x}$ scaled by some arbitrary constant $s$, we obtain:
$$F(s\vec{x})=ms\vec{\ddot{x}} \Longleftrightarrow \frac{F(s\vec{x})}{s}=m\vec{\ddot{x}}$$
Which is clearly just $F(\vec{x})$! Therefore:
$$F(\vec{x})=\frac{F(s\vec{x})}{s} $$
for any $s$, which ca... |
Verify this theorem below:
Theorem: Suppose a conductor carrying a net charge Q, when placed in an external electric field E, experience a force F; if the external field is now reversed, the force also reverses.
what if we stipulate that the external field is uniform?
|
In physics, whenever we have 3 quantities $A$, $B$ and $C$ related as
$ A=BC $
where $B$ and $C$ are vector quantities and $ \theta $ is the angle between $B$ and $C$, if $A$ is proportional to $cos\theta$, $A$ turns out to be a scalar and if $A$ is proportional to $sin\theta$, A turns out to be a vector. Why is this... |
I’m a 3rd year physics undergrad and I’ve just finished my first particle physics course. I’m looking for an explanation (at my level) of what a sphaleron is? They were mentioned as an aside in one of my notes and I’m interested in learning more now. Thanks.
|
Can somebody explain why there is a large uncertainty in the mass estimation of neutron stars?
|
I'm going through the basic and popular optical quantum-eraser experiment with laser and polarizers and I have a question.
After applying the diagonally aligned polarizer at a 45 degree angle, the B1 section of the beam carries an interference that can be observed by the fringes at the screen.
But let say we could, so... |
The specific dilemma that I'm encountering is as follows: Let $n_\alpha$ denote the normal to a hypersurface $\Sigma$. Let $u_\mu$ denote the velocity of a particle randomly crossing $\Sigma$. They satisfy,
$$n^\mu n_\mu = \pm 1$$
and
$$u^\mu u_\mu = -1$$
Given these two, what can we say about the normalisability of t... |
A somewhat similar question is this one but it is not quite the same.
I am getting used to the abstract index notation used for tensor algebra. So far so good, but the is one issue that concerns me, In General Relativity by Wald, it is discussed how the difference between two connections $\tilde{\nabla}$ and $\nabla$ i... |
The second law of Sir Isaac Newton or also known as the fundamental relation of dynamics :
$$\vec{F}=m\vec{a}$$
Which can be derived using the definition of the force :
$$\vec{F}=\frac{d\vec{p}}{dt}$$
But only if $m$ is treated as a constant. What if $m$ is not a constant? absolutely we're not having the same result. ... |
Is it possible to have a non-integrable system in (1+1)D in Classical Physics? For some reason, I get the intuition that there shouldn't be any such systems. What if we consider (1+1)D systems in Quantum Physics?
Can anyone please clarify this for me and provide some examples?
Edit 1 :
Here (1+1)D refers to 1 spatial ... |
We did the Kallen-Lehman procedure in lectures for phi to the fourth theory. We also defined the wavefunction renormalisation. At the end our lecturer briefly mentioned that to carry it over to QED and for an electron, what we'd have is:
$<\Omega|\psi_a(0)|e^{-}(\vec{p},s)>=\sqrt{Z} u_a^s(\vec{p}) $
$<\Omega|\psi_a(0... |
Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave). Source: https://en.wikipedia.org/wiki/Double-slit_experiment
|
A body of mass 1kg is connected to an infinite number of masses by means of an infinite number of ropes, as shown in the sketch below. A measurement shows that the tension force in 1st rope: 1N. Second rope: 2N. Third rope 4N, etc.
Find m5, assuming there is no friction.
My approach is:$$
m_{1} g-F_{s_{1}}=m_{1} a
$$
... |
when the glass rod is rubbed with wool, it loses electrons and gets positively charged, while the wool gains those electrons and gets negatively charged.
we all now that but where electron store in wool ? do they store in surface or they can go deeper ?
dose electron goes to atom or just stay between molecule ?
why gl... |
I am reading the following Wikipedia page, but I am skeptical about what I am reading (it sounds too good to be true). Specifically, I am looking at the passage which states:
The number of variables $X_i$ need not be countable, in which case the sums are to be replaced by functional integrals. [...]
$$
Z=\int \mathcal... |
I know a battery creates a potential difference, making an electric field that exerts a force on the electrons, who start moving. But why is there a potential drop after a resistor for example? How does it go in hand with electric potential being a scalar assigned to a point in space? How can a resistor change the pote... |
For example, a human can sense if their head or toe is touched and the distance between his head and toe is more than the size of one atom;
is that human one thing not larger than one atom, yet strangely he can sense where his body (that is longer than one atom,) is touched, or that human is strangely not one thing, or... |
When discussing a single or double slit experiment, where light is shined through a very small slit, it is often compared to a water wave going through a similar, if larger, slit. It's my understanding that when a ripple hits a wall with a hole in it the reason the ripple "bends" and spreads out is because of internal ... |
I'm working on a thermodynamics problem which is as follows:
"Saturated humid air at 200 kPa and 15C is heated to 30C as it flows through a 4-cm diameter pipe with a velocity of 20 m/s. Disregarding the pressure losses, calculate the relative humidity at the pipe outlet and the rate of heat transfer, in kW, to the air.... |
An effective quantum field theory of a single scalar field $\phi$ is described by an action, $S(\phi,\{g_n\})$ where $\{g_n\}$ denote the coupling constants of the theory. The corresponding path-integral $$Z=\int\mathcal{D}\phi\exp[iS]$$ is usually defined with a finite UV cut-off $\Lambda$. When the cut-off is lowered... |
We talk a lot about this principle for electric potential at point by many charges but not for gravitational potential by other masses around it, why?
|
The following is from 'Discerning Fermions' by Muller & Saunders (2008: 532):
Let $|\phi_{1}\rangle, |\phi_{2}\rangle, ..., |\phi_{d}\rangle$ $\in$
$\scr{H}$ be an eigenbasis of $\scr{H}$ belonging to operator A acting
in $\scr{H}$. Let $P_{m}$ be the 1-dimensional projector on the ray to
which eigenstate $|\phi_{... |
Unlike the Cartesian coordinates, I find navigating through polar coordinates difficult. Is the system defined by the following Lagrangian $L$ defined in polar coordinates linear?
$$L = \frac{1}{2} m \left( \dot{r}^2 + r^2 \dot{\theta}^2 \right) - Dar^2 - \frac{K}{2} \theta ^2,$$
where $D$, $a$ and $K$ are constant pos... |
Normally the physical state of a system is represented by a vector. But it seems that some authors say that operators (density operators in particular) represent states. How should I understand this? In what sense do they represent states?
|
Please, Can anyone helps me to understand What does it mean a particle with no gauge interactions?
|
I have question about the Ising model, specifically the Ising Hamiltonian. From what I have read, the Ising Hamiltonian describes the energy of the system of spins with a certain configuration. What I do not understand is why the Hamiltonian can become negative if it is indeed the energy of the system? What is the phys... |
My textbook derives the rocket equation from conservation of momentum like so:
$$\begin{align}p_i&=p_f \tag{1}\\
mv&={(m-dm_g)}{(v+dv)}+dm_g(v-u)\\
mv&=mv+m\,dv-dm_g\,v-dm_g\,dv+dm_g\,v-dm_g\,u\\
m\,dv &=dm_g\,dv+dm_g\,u\end{align}$$
Here $dm_g$ is the instantaneous change in the amount of fuel expelled, and therefore ... |
The answer is C. What I don't understand is how the diameter would have any effect on the first harmonic frequency as the formula $$f=\frac{1}{2L}\sqrt{\frac{T}{\mu}}$$
|
They say that the vibrational kinetic energy is a measure of temperature. Temperature is also related to the entropy as the partial differential. It is a measure of the energy of the atoms within but which types of energy? Say hydrogen bonding increases with a decrease in temperature not the other way around. Which typ... |
Question:
A light-year is the distance light travels in one year and is equal to $9.46*10^{15}m$ Imagine you travelled at a constant velocity of $0.97c$ from earth to the next nearest group of stars, the Alpha Centauri group, which is at a distance of $4.26$ light-years. Calculate, in years:
a) the time it would appear... |
I attempt to understand the parity and dipole operator from Daniel Steck's notes: Quantum and Atom Optics (page no. 152, section 5.1.1). I have also attached a screenshot at the end of the question.
At the beginning of the section 5.1.1, the author defines the parity operator and derives some basic properties. Based o... |
I was reading about Unimodular gravity, this is a modified theory of gravity that postulates that the gravity is only invariant under volume preserving diffeomorphism. So it breaks the full diffeomorphism invariance.
And there is a theorem by Lovelock that says that modified theories of gravity can be classified in fo... |
I have a camera that outputs a JSON file for every image taken. In the JSON file, I can find camera-specific and also the photo-specific acquisition parameters used. The issue is I wish to estimate the focus plane distance of a photo exactly, so I wish to use the JSON file to do so. Assuming the thin lens equation hold... |
To my knowledge, at the point when a spring is being extended until the bottom of it is stationary, the electrostatic forces of attraction between the molecules in the spring balance out with the external force exerted on the spring. However, when extending a spring, wouldn't the molecules in the spring simultaneously ... |
If I attempt to find the displacement $x$, from equilibrium when a mass, $M$ is attached to an upside down vertical spring with spring constant $k$ I get two different answers when I use energy considerations and when I use forces. There is probably some simple conceptual mistake I am making but I can't identify it. He... |
Is it possible that entangled particles don't exchange information at all, e.g. maybe something happened at the moment they were split that made them opposite?
|
I have a question I could not figure out in Quantum Processes, Systems and Information book of Westmoreland and Schumacher. In section 6.4 question 6.23 it is asked that,
Show that there can be an entangled eigenstate of $Q\otimes1$ if and only if the operator $Q$ has one or more degenerate eigenvalues.
$Q$ here is a... |
Why can't we use $\frac{1}{2}(\gamma m)v^2$ to calculate kinetic energy of a particle moving at Relativistic speed?
|
It is sometimes heard that the complexity of chess is $10^{120}$, or that go is more complex than chess since it has a complexity of $10^{365}$.
I’ve been thinking: Is it possible to do something similar with the three-dimensional space we live on?
To do this, let's suppose a cube made of little Planck voxels (1 Planck... |
Suppose we have two wire loops of the same dimensions placed adjacent to each other. The first loop is connected to an AC source, the medium inside the first loop is air and the medium inside the second loop is a laminated thin iron core which has higher magnetic permeability.
The magnetic field due to the first loop ... |
is it possible to develop a model of a piece of ordinary matter and scan it to develop a model of what kind of elements are in the matter? Similar to an MRI scan?
If it's not possible, why? What challenges would need to be overcome?
Thanks.
|
Many of the aspects of QFT are traditionally done in ways incompatible with a rigorous mathematical treatment, calling for a variety of tricks to fix essentially what was caused by unjustified calculations or generalizations. One example for all is treating the Fock space as the state space of a collection of infinitel... |
In classical mechanics, one intuitive formulation of chaos/ergodicity (in the loose sense) is that most trajectories should fill up phase space densely over infinite time. A classic example of such a system is the Sinai billiard.
In classical field theory, the phase space becomes infinite dimensional, consisting of fi... |
To perform Quantum Teleportation, we need state of two entangle qubits in the Bell basis
$$\left(\frac{|00\rangle + \rangle11\rangle}{\sqrt{2}}, \frac{|00\rangle - |11\rangle}{\sqrt{2}}, \frac{|01\rangle + |10\rangle}{\sqrt{2}},\frac{|01\rangle - |10\rangle}{\sqrt{2}} \right).$$
To project in the product basis ($|00\ra... |
In Conway's Strong Free Will Theorem paper, the proof consists of two parts. In the first part, they proved the Specker-Kochen theorem. In the second part, they constructed two experimenters that are space-like separated, each possessing one spin-1 particle from an entangled pair, then they each made a measurement.
I d... |
A common model for electrical noise is to assume a flat frequency distribution, i.e. white noise. However, this results in theoretically infinite energy. So my question is: What has to be accounted for when going from ideal electrical white noise to more realistic noise? Is it the RLC-properties/transfer function of th... |
Recently many exoplanets have been found orbiting nearby stars. Assume there is a civilization with identical technology residing in a nearby (< 100 light years) solar system. Could they discover Earth or other planets orbiting the Sun?
|
Suppose there are $N$ radioactive atoms and the half life of decay is $t$. Then after one half life the number of remaining atoms will be $\frac{N}{2}$. And so after each half life the number will be halved.
Which means,
$1/2$ of the atoms will have a life of $t$
Half of the the remaining half or $1/4$ of the atoms wil... |
My first guess would be that the frying pan would be attracted to the induction coil just as any ferrous metal to a solenoid. But I recently found out that an induction coil can actually be designed to levitate (repel) the work piece in some designs (induction levitation).
Are the forces between an induction coil and ... |
I recently became interested in a notion of infraparticles as "true" scattering states in, for example, QED.
It is well known that S-matrix elements in QED suffer from infrared divergences due to soft virtual photons, which is usually cured by assuming a lower bound on detected photon energy by our detectors and summi... |
In this picture(all others on google are the same), the positive plate is at the top and the negative plate is on the bottom. This means for this experiment to make any sense, the oil drops must be negatively charged. If this is the case, then why are X-rays used to cause the oil droplet to be charged? Surely since X-... |
I was reading Jackson(p. 556-557 3rd edition), where I got confused about covariance of electrodynamics. The equation of electrodynamics are written in 'contravariant' tensor then why we call them covariance of elctrodynamics?
$\partial_\alpha F^{\alpha\beta} = \frac{4\pi}{c} J^{\beta}$
similarly we have another equat... |
When a DJ does a rewind (suddenly reverses the direction of the vinyl’s rotation under the needle), a sharp squeal is produced. This squeal is neither simply the music played backwards (as a film would be when viewed backwards) nor is it due to a higher pitch because of acceleration…it must be something else.
In mech... |
Is weight ≠ gravitational force, for an object on the Earth’s surface? Why is this? Is it because part of the gravitational force acts as a centripetal force? Does the normal contact force not nullify the centripetal force?
Also, If my tangential velocity (on the surface of the Earth) increases, does my effective weigh... |
The lens maker's formula takes into account the thickness of a lens. However, if one surface is planar, its focal length should be infinite. But that means that with the below formula, the thickness of a lens doesn't affect its focal length if one side is planar which isn't true.
What's wrong here? (assuming $n$ of air... |
I'm a beginner, and I'm trying to figure out how to prove that charge of Up quark is equal to 2 times the charge of down quark from the 10 representation of $SU(5)$. Please help.
|
A rod is subjected to tensile stress and it is plotted against the strain developed. This graphs can be found in any standard material science and mechanical engineering text books.
If the load is removed gradually at point C, then the rod will follow the path CC' and will have a permanent set OC'(if I'm not wrong).
... |
I know the statement "The third law of thermodynamics states that the entropy of a system at absolute zero is a well-defined constant. This is because a system at zero temperature exists in its ground state so that its entropy is determined only by the degeneracy of the ground state."
But I don't yet understand it's a ... |
Some year 12 circular motion questions for you. I have an experiment where an object of m mass is tied to a string of L length. Centripetal force (Fc) is known along with m and L. The object is spun around at constant angular velocity horizontal/parallel to the ground. I am comparing two models. Model 1: gravity is ign... |
I am very new to the subject, so please forgive my very naïf question. I learned that there are some non-hamiltonian systems which can become hamiltonian, just by a change of coordinates. I was given the Susceptible-Infected-Removed (SIR) model as an example:
\begin{cases}
\frac{dS}{dt} = - \alpha SI \\
\frac{dI}{dt}... |
I am trying to write the formulation for fluctuation in diffusion flux (Fick's law):
$$ \vec{j}= - \rho D\vec{\nabla} c $$
Then I describe fluctuation in concentration and density as the following:
\begin{align}
c ( \vec{x},t ) &= \langle c ( \vec{x},t ) \rangle + \delta c ( \vec{x},t )\\[.15cm]
\rho ( \vec{x},t ) ... |
Imagine a system of 3 point charges and some kind of circular "rail".
All charges have the same magnitude - 2 are positive and one negative.
One positive charge is placed at some distance from the center of the circular rail.
The two other, are "glued" together so they must move together, and they are placed on the rai... |
A bit of maybe unnecessary context
I'm reading "Lecture notes on Diagrammatic Monte Carlo for the Frohlich polaron". It says
It is usually unknown whether a series converges or not. The series is guaranteed to diverge at a phase transition, but it may happen sooner. In fact, most series in physics are asymptotic, whi... |
A quantum channel $\mathcal E$ is a completely positive trace preserving map.
Is $\mathcal E \otimes \mathcal F$ a quantum channel if $\mathcal E,\mathcal F$ are quantum channels?
What I have:
It is sufficient to answer this for $\mathcal E \otimes \mathit{id}$ since $\mathcal E \otimes \mathcal F = (\mathcal E \otime... |
In the following questions I will be only talking about spatial states so we can safely ignore the spin state.
1) First of all I want to ask why is it that 3 quantum numbers are all that is needed to specify a unique state in 3D? Because it is certainly not the case that you can only have 3 commuting observables. I sus... |
What is the smallest substance in the universe discovered, and it enters in the structure of neutrons and protons in the nucleus of an atom?
|
In the paper M. Holzmann, G. Baym, Phys. Rev. B 76, 092502 (2007) the following formula (Eq. (18)) is given for a Bose-condensed system:
$$
V\delta F=-\frac12\int d\mathbf{r}d\mathbf{r}'\:\delta\langle\Psi(\mathbf{r})\rangle^*G^{-1}(\mathbf{r},\mathbf{r}')\delta\langle\Psi(\mathbf{r}')\rangle,
$$
where $\langle\Psi(\ma... |
Consider a composite system (e.g. a system $S$ and a bath $B$) and fermionic operators $s_i$ and $b_j$, where $s_i$ annihilate fermions in $S$ and $b_j$ annihilate fermions in $B$. Obviously,
\begin{equation}
\{s_i , b_j \} = 0
\end{equation}
and hence the $s_i$ do not decompose as $\textrm{stuff}_S \otimes \textrm{id... |
I found this in my physics book :
The force between two conducting spheres having opposite charge is more
than the force between point charges of the same magnitudes and separated by
the same distance.
I was wondering why this is so. Can anyone help?
|
Following the notes here (Quantum Information Theory Tips 5 at ETH), we state the following result. For any quantum state $\rho_A$ and purifications $\vert\psi\rangle_{AB}$ and $\vert\phi\rangle_{AC}$, there exists an isometry $V_{B\rightarrow C}$ such that $(I_A\otimes V_{B\rightarrow C})\vert\psi\rangle_{AB} = \vert\... |
By a suitable combination of Dirac's $\gamma_\mu$ matrices one can define creation and destruction operators satisfying fermionic anticommutators. Is there a similar result for bosons in the context of Clifford algebra. My interest, at present, is confined to $(1,3)$ spacetime.
|
The Einstein field equations are, in geometrized units:
$$G_{\mu \nu} = 8 \pi T_{\mu \nu}$$
I know that black holes (take the simplest case of a Schwarzschild black hole) are vacuum solutions to the Einstein field equations. Does this imply that $T_{\mu \nu} = 0$? If so, how then does $G_{\mu \nu}$ have nonzero compone... |
Ultimate Goal: Calculate the mass moment of inertia that a finger experiences as it depresses a piano key.
Background on the question is at the end if you need, but I'll keep this high-level so that you don't need to be a Registered Piano Technician to answer this.
Imagine you have two interconnected levers (such tha... |
Consider a body with spherical symmetric mass distribution in asymptotically flat space with a total mass $M$. Assume it collapses to a black hole with mass $m<M$.
Does this body emit gravitational waves while collapsing if it maintains spherical symmetry during the collapse?
I know that from Birkhoff's theorem follows... |
As we know, the dispersion of spin excitation (magnon/spin wave) for ferromagnetic(FM) system is quadratic as $k\rightarrow 0$, but is linear for anti-ferromagnetic(AFM) system as $k\rightarrow 0$. I am confused about the reason for this difference. In other words, what is the physical meaning of "linear" dispersion an... |
Consider the translation in space operator in $1D$:
$$D(a)=e^{-ia\hat{p}/\hbar}$$
It is unitary - $D(-a)=D^{\dagger}(a)=D^{-1}(a)$ - which implies that $D(a)$ has eigenvalues on the unit circle like all unitaries do.
$D(a)$ acts on a function $f(x)$ by translating it -
$$D(a)f(x)=f(x-a)$$
Now consider the case of $f(x... |
I have read on my book (I do not put its title since it is not in English) the following sentence about a metal body which receives an external electromagnetic wave (with Js we mean its current surface density):
If the conductor surface S is open, the normal component of Js at the edges of S vanishes (Js is the vector... |
We know that friction can be calculated using
F=uN
Where u is just a constant for two surfaces in contact.
So , direction of friction should be the same as of normal but it doesn't happen.
Is coefficient of friction also a tensor quantity because direction of normal is not the same as direction of friction ??
If not ... |
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