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Recently I got a question where I needed to determine the time derivative of a position vector. However, the vector didn’t have the variable $t$ but instead had $x$, $y$, and $z$ as its terms, so I was confused:
Ex. $$\mathbf{r}=x\hat{i}+5y^2\hat{j}+10z^2\hat{k}$$
How can I derive this vector in terms of time when the... |
I am currently working with a differential equation, where I think I need to take the derivative of $ma$ (corrected as per comment). I am trying to write $F = ma$ as a MacLaurin series and eventually set it in terms of $m\ddot x(t)$. The problem is that I am not sure if I should write my MacLaurin series in terms of $x... |
I tried to calculate the time-like geodesics of the Morris-Thorne Wormhole $[1]$, $[2]$, $[3]$ for redshift function $\Phi(r) = 0$ and $b(r) = \sqrt{r_{0} r}$. But I don't know for sure if all the plots that I made are correct.
So, the metric is:
$$ds^2 = -e^{2\Phi(r)}dt^2+\Biggr\{ 1-\frac{b(r)}{r}\Biggr\}^{-1}dr^2+r^2... |
When a cylinder, (where both circles on either side are the same diameter), is pushed forward, it will move forward. However in a shape where one circle is a different size to the other, it moves in a circular path. I am sure that the bigger circle moves a greater distance than the smaller circle in a given time, but h... |
This recent video from Veritasium (https://youtu.be/pTn6Ewhb27k), explored the problem of measuring one-way speed of light and covered a few possible (and practical) solutions. However my understanding of the problem from that video and the other questions on stack overflow suggests that the crux of the problem lies wi... |
Hamiltonian represents energy. I can understand this when considering about harmonic oscillator, whose Hamiltonian is expressed as:
$$ \hat{H} = \frac{1}{2m}\hat{p}^2 + \frac{m\omega^2}{2}\hat{q}^2$$
This equation can be interpreted as energy very clearly, because $p$ is momentum and $q$ is position, so these terms rep... |
I was watching a YouTube video on the difference of winding a coil clockwise vs winding a coil counter clockwise. It said the poles would be opposite using the same battery configuration. I've been thinking about this and it seems to me the poles would be the same regardless of the direction of the wind. I've included ... |
So according to this formulary:
Also:
Therefore:
Now, if we substitute:
Then:
What happened to the 1/2 in the right side?
|
Given a spectrum of $N$ real eigenvalues, $\{E_m \}$ of some Hermitian operator, the connected spectral form factor is defined as follows:
\begin{align}
K_c(t) = \langle \sum_{m,n=1}^N e^{it (E_m-E_n)} \rangle - |\langle \sum_{m=1}^N e^{it (E_m)} \rangle|^2.
\end{align}
For random matrices, the average $\langle .. \ran... |
The water stream is heated in a boiler, at some constant pressure.
When entering the boiler, the water flow is in a saturated liquid state. After heating the outflow fluid has become saturated vapor.
My question is if I want to calculate how much heating energy is needed, do I use
$$Qb = Ug - Uf$$
or
$$Qb = hg - hf$$
U... |
Let's say I have a spatially constant but time-varying electric field in vacuum of the form
$$\textbf{E} = E_0 e^{i \, \omega t} \, \hat{x}$$ that describes some E-M wave. What is the magnetic vector potential $\textbf{A}$ associated with this field?
In my attempt, I used the relation $\nabla \times \textbf{A} = \textb... |
Can someone mathematize the statement of the quantum measurement problem? I am only interested in the statement of the problem (and not its solutions). Thanks.
Still confused. Stated in this way (as in the current answers), the measurement problem seems funny to me. The measurement of an operator $A$ on the state $|\p... |
In Goldstein's Classical Mechanics, he suggests the use of Lagrange Multipliers to introduce certain types of non-holonomic and holonomic contraints into our action. The method he suggests is to define a modified Lagrangian $$L^{'}(\dot{q},q;t) = L(\dot{q},q;t) + \sum^{m}_{i = 1}\lambda_{i} f_{i}(\dot{q},q;t),$$ where ... |
Okay, I came up with this great idea to intuitively understand retrocausality which is implicated in the delayed choice quantum eraser experiment.
Alice and Bob have decided to do an experiment.
If Alice wins at rock paper scissors, she will get the switch on, just like the first picture so idler photons will enter det... |
I just finished watching a video on gravity. It stated that an object weighs less the further it is from the center of the earth. Example being on a mountain top or at the equator being that the earth is not round but slightly oval shaped and so at the equator an object is also further from the center of the earth. So ... |
I was reading about the London dispersion forces and it is written that it arises due to an asymmetric distribution of charges in an atom at an instant which gives rise to a temporal dipole and this temporal dipole then induces a dipole in nearer atoms and thus they experience the intermolecular forces.
This site says ... |
I've tried googling for "Time dilation due to acceleration" but found nothing particular. Here when I entered title of the question the site have not shown same question asked already. Upon typing in the question the site found:
Gravitational Time Dilation vs Acceleration Time Dilation
Time dilation in a gravitational ... |
Although absolute translational motion is meaningless and unmeasurable (Michelson and Morley, etc), absolute rotational motion is meaningful (Newton's bucket) and measurable, using Foucault's pendulum. In 1851 Foucault showed this could be used to measure the earths rotation, $1 \over 4$ degree per minute.
What can we ... |
In principle, how would we demonstrate the existence of the hydrogen atom in quantum field theory and the standard model?
Has it been done in practice?
Some naive ideas:
Demonstrate that the familiar quantum mechanics model of the hydrogen atom is a limit of the SM in QFT
A non-perturbative calculation numerically on... |
In a crystal lattice, a non-zero Chern number shows non-trivial topology and a zero Chern number indicates trivial topology. But I am not able to differentiate the physical characteristics possessed by a crystal lattice with zero and non-zero Chern number.
Can anyone please explain, physically, what additional feature ... |
Also, for that matter, what does k_II mean?
|
Consider the following situation, with two identical point charges $q,m$ projected horizontally with velocity $v$. Originally the question asked to find the height of B when A strikes ground at a horizontal distance $l$ from point of projection. Although that can be solved for without knowing the trajectory of both the... |
Maxwell's four equations are enough to specify the fields (electric and magnetic) in a region, once you specified the charge density and current density. Maxwell's four equations basically give you the divergence and curl of the field. If I defined a matrix $A$ for some vector function $V(x,y,z)=(V_x,V_y,V_z)$ that loo... |
\begin{align}
v&=u+at\\
s&=ut+\frac{1}{2}at^2\\
v^2&=u^2+2as\\
s&=\frac{(v+u)t}{2}
\end{align}
I have just started with learning acceleration in school and I don't really understand why these equations are the way they are. I know how to apply them and use them but not why they exist.
|
I recently watched this video by Veritasium where he talks about the One Way Speed of Light and talks about the limiting case where in one direction the speed of light is $c/2$ while it's instantaneous in the other. He also says this is perfectly fine according to our Physics theories. He also points at Einstein's assu... |
I understand that the modulation depth of a sinusoidally modulated signal can be defined as the modulation amplitude divided by the mean value, as explained here.
But why would one wish for a high modulation depth in an experiment? What advantages does it bring?
Some articles state that they have achieved a high modul... |
The energy spectrum for the above, subject to the periodic boundary conditions such that the eigenfunctions are have a period of $L$, is given by
$$E_n = E_0n^2, \qquad n=0, \pm1, \pm2, \ldots$$
where $E_0 = (2\pi^2\hbar^2)/(mL^2)$. Each $E\neq0$ is doubly degenerate.
Then to find the density of states, I observe that ... |
Two light sources are at rest and at a distance D apart on the x-axis of some inertial frame, O. They emit photons simultaneously in that frame in the positive x-direction. Show that in an inertial frame, O', in which the sources have a velocity v along the x-axis, the photons are separated by a constant distance $$D\s... |
I am studying the electric field $E$, polarization density $P$, and displacement field $D$, but I'm a little confused about the relation between the electric field, polarization and displacement field.
If we consider a parallel plate capacitor with a dielectric in between and apply a voltage across it, opposite charges... |
Merzbacher in his Quantum Mechanics says that for the "particle in a box" potential ($V(x) = 0$ for $|x|\le L$ and $+\infty$ otherwise),
Since the expectation value of the potential energy must be finite, the wavefunction must vanish within and on the walls of the box.
However, I don't quite get this reasoning. Why m... |
I had struggle to find the answer to this question:
Imagine two charged identical particles, one stationary relative to earth, and the other one is free falling (to earth).
We know that an accelerated charged particle radiates. But the real problem is, according to Newton, the free falling particle will radiate but wit... |
I want to get a better understanding on particle being an irreducible representation. Does that mean one particular type of particles (say particle $A$) is a subspace of the "total" Hilbert space $H$ (which contains all the types?), and the restriction (to the vector space $V_A$ corresponds to particle $A$) of the repr... |
I'm trying to calculate the Segal-Bargmann wave function and the Husimi function for a particle in a 1-dimensional infinite potential well of width L (i.e. $V(x) = 0$ if $x \in (-L/2,L/2)$). In the Segal-Bargmann space, the Hamiltonian is:
$$
H(z)= \frac{p^{2}}{2m} = -\frac{1}{4m}\left[z^{2}+\hbar^{2}\frac{\partial^{2}... |
I need to know that how does one measure (approximate) the energy loss of a planet or satellite during the whole tidal locking process?
Where do I find this topic to study?
|
Let's say I have an electric field $\vec{E} = (0, 0, E_z)$, where $E_z$ in constant. Then the electric potential is $\phi = - \vec{E} \cdot \vec{r}$, where $\vec{r} = (x, y, z)$.
Calculating $\vec{E} = - \nabla {\phi}$ in cartesian coordinates is ok, we get the $\vec{E}$ we started with.
But I have a problem with trans... |
For a Gravitation Field Action Integral looks like:
\begin{equation}\label{1}
S_{gravity} = \frac{c^3}{16\pi G}\int R\sqrt{-g} d^4x.
\end{equation}
А Least Action Principle says the $\delta S_{gravity} + \delta S_{matter} = 0$.
But we know the $\delta S_{gravity}$ itself is zero:
\begin{equation}
\delta S_{gravit... |
My question is:
Is there a technique to distinguish the mean magnetic field from the fluctuations in the solar wind?
Thanks
|
If I want to calculate the underwater pressure I use this formula:
$ P = \rho g h$
But is this valid for any altitude? Is it the same if I want to calculate the pressure under a lake that it's at 2000m above ocean level than at the ocean? If not, how can I calculate the underwater pressure at a given altitude?
|
I'm trying to understand the connection of algebra of transformations under a commutator and algebra of Noether's charges under Poisson bracket.
I have a problem that results I infer from theoretical consideration do not match with results I get for simple example - free scalar theory in two dimensions. I am making a m... |
Landau and Lifshitz (Mechanics, Vol. 1) derive the form of the Lagrangian for a free particle by requiring invariance of action under Galilean transformation and assuming homogeneity and isotropy of the space-time. The same can be done for a relativistic free particle (see, here). Now, assuming the form of the Lagrangi... |
When writing Conservation of Energy equations, if you want to add a gravity component, you write, $mgh$. Where $m$ is mass, $g$ is gravitational constant, and $h$ is the height. If a mass has nothing to do with gravity on falling objects, why is it here?
|
I was playing around with the PhET simulation "Models of the Hydrogen Atom", https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom . In it you can simulate a hydrogen atom's electron absorbing and emitting photons, based on different atomic models. You can also plot the photons emitted/nm on a simulated spectrom... |
Note: there is no friction at all.
General problem:
A ball moves (in speed v1) toward a quarter of a circle (which was stand still before the ball touched it and can move on x) and walks on it until it leaves it.
How may I find the balls speed on x and y?
I have attached the following image to make the problem easier:
... |
There are a lot of questions and answers on this site about the unification of forces, and all of them univocally say that at high energy levels, all the forces get unified. But none of them answer my question specifically, that is, what is the mechanism that causes forces to unify at high energy levels.
The idea is ... |
If the magnetic field of Earth is generated in the core of the Earth can we deduce core's precession cycle by measuring the precession of Earth's magnetic field (not Earth as a material object) or the two features are not directly connected?
|
We can derive that, the potential energy of a dipole in an external electric field is
$$U=-\mathbf{p}\cdot \mathbf{E}$$
And Work done by the field on the dipole is
$$W=\mathbf{p}\cdot\mathbf{E}$$
Here, we use $U=-W$. All of my physics books tell the reason for $U=-W$ is that comes analogously from gravitational potenti... |
I am trying to find an alternative way of calculating the electric field inside and outside of a sphere with charge density σ, all of it in its surface. The sphere has a radius R.
I am trying to fin this field (inside and outside) by superposing the electric field of several circular loops.
Do you have any idea how to ... |
In many cases, a force is applied to only a small part of a rigid body, yet all the particles of the body accelerate immediately. How do particles on which the force does not act directly "know" that they are supposed to accelerate?
I know the answer probably involves the transmission of the applied force in some way b... |
I know that the earth being in the system has some effect on the energy, but I honestly don't know what the effect is. Does earth being excluded from the system mean there is no PE? In that case, is energy still conserved?
|
I would like to pose a quick question. I attempted (which seems successful) to derive the Joule-Lenz formula. My question: Where did I make mistake? Before going into my solution, it would be appreciative to say that I searched the results on the forum and am going to read other questions, thereby gaining more acknowle... |
If a constant force is being applied to a body, without any other external forces, F = ma says that that body will accelerate at a constant rate. This acceleration will continuously increase the body's velocity.
According to P = Fv, since the force is constant and the velocity is continuously increasing, the power requ... |
A current flowing through a wire creates a magnetic field.
A current flowing through a wire represents electrons moving very slowly in the wire.
A wire contains electrons.
If I have an isolated section of copper wire, does it produce a magnetic field when I move it?
If not, why not?
|
I came across this in the lecture notes of quantum field theory by David Tong. Inside time ordering interactions aren’t taken to be normal ordered. Interaction hamiltonian should be normal ordered otherwise it is not well defined (due to ordering ambiguity and related singularities). Most standard QFT textbooks don’t ... |
After calculating Floquet Hamiltonian and then it's eigenvalues I stumbled upon a problem with ordering of eigenvalues. I am using eigen library for c++ and for every Floquet Hamiltonian for given frequency my eigenvalues are picked at random so I can't calculate probability of transition from specific state.Is there a... |
Studying quantum angular momentum from my lectures and also from this useful collections of lectures (from Leonard Susskind) I have of course stumbled upon rising and lowering operators (a.k.a ladder operators).
I am completely fine with the definition of those operators and with the fact that applying them allows us t... |
"Paradox of radiation of charged particles in a gravitational field" - Wikipedia ( Paper by a guy I forget the same of)
On wikipedia (reliable ikr), there is a paradox occuring between whether or not a charged particle will radiate on the surface of the earth as via the equivalence principle is it indistinguishable fro... |
What is the general method to compute the $2 \to 2$ scattering cross section given an arbitrary Lagrangian ? I would like a step by step recipe that can be easily implemented in Mathematica.
For example, I want to input one of these Lagrangians
$\mathcal{L} = \frac{1}{2}\partial_\mu \phi \partial^\mu \phi - \frac{1}{2}... |
While studying many-body theory (in particular, field theory at positive temperatures) I came across the following exercise: given the grand-canonical Hamiltonian for a bosonic system
\begin{equation}
\hat{K}=\sum_a[(\epsilon_a-\mu)\hat{c}^\dagger_a\hat{c}_a+\gamma^*_a\hat{c}_a+\gamma_a\hat{c}^\dagger_a]
\end{equation}... |
I'm currently following this article to cosntruct a gauge invariant energy stress tensor for pure Yang-Mills gauge:
$$
\mathcal{L} = -\frac{1}{4}F_{\mu\nu}^aF_{\mu\nu}^a, \qquad F_{\mu\nu}^a = \partial_\mu A^a_\nu - \partial_\nu A^a_\mu + g\,C^{abc}A^b_\mu A^c_\nu,
$$
where $C^{abc}$ are antisymemtric structure constan... |
In some explanations about the OZI rule ( for example at page 38 here), I found that gluons have definite eigenvalue of the charge conjugation operator $C$. The eigenvalue is $-1$. How can this result be demonstrated?
|
I'm a little stumped by how to show that
$$
V_{\hat{\rho}}(\hat{A})V_{\hat{\rho}}(\hat{B})\ge{\lvert Re(Cov_{\hat{\rho}}(\hat{A},\hat{B})\rvert}^2 + \frac{1}{4}{\lvert Tr\hat{\rho}[\hat{A}\hat{B}]\rvert}^2
$$
for a mixed state, where
$$
Cov_{\hat{\rho}}(\hat{A},\hat{B}) \equiv Tr\hat{\rho}(\hat{A}-{\langle\hat{A}\rangl... |
I have seen both equations, $A^{\alpha}=(\phi,\vec{A})$ is from Wikipedia and $A_{\alpha}=(\phi,\vec{A})$ is from my lecture. Which one is right?
My thoughts: As far as I know, $A$ is a 1-form, so $A(p)\in T_p^*M$ for all $p\in M\subset\mathbb R^4$. In addition, $(\text{d}x^1{}_p,...,\text{d}x^4{}_p)$ with $(x^1,...,x^... |
There seems to be general disbelief over this formula, so I'm challenging someone to show me the fallacy in the proof below. The assumptions are that the two objects are rigid and spherically symmetric and that the fluid is of uniform density and incompressible. Note that the gravitational fields induce pressure gradi... |
I am self-studying General Relativity, and the course of study I am following has started to introduce me to index notation. The texts I am using (Carroll, Schutz) begin with a geometric slant on Special Relativity, and I am finding the index notation a bit of a challenge. From my textbooks, $\eta_{\mu\nu}$ = diag (-1,... |
I consider the tensor product $H_1 \otimes H_2$ for pairs of qubits.
they are described by a 4*4 density matrix $\rho$.
Bob and Alice share them and measure them randomly in many directions.
At the end they meet and try to calculate the elements of the density matrix (using a vertical direction for the basis).
One way ... |
What information does the snapshot need to be of? That is to say, what information holds the detail of the two waves?
Edit: I purposely left this question general because I want to know about superposition itself, without reference to the medium the waves are in, or even if it makes sense to isolate superposition from ... |
John Wheeler said “Matter tells spacetime how to curve and spacetime tells matter how to move.”
So, when objects fall to Earth they travel along the spacetime curves that they and all the surrounding matter create.
For the Schwarzschild black hole model the matter is all contained at the singularity. This means that sp... |
I am slowly going to develop intuition for dealing with Feynman diagrams but
have a couple of problems understanding the following
Feynman diagrams representing the Higgs production via gluon-gluon
fusion (source paper: On the interpretation of Feynman diagrams, or, did
the LHC experiments observe $H \to \gamma \gamma$... |
Given I diffeomorphism $x^\mu \rightarrow y^\mu = y^\mu(x) $, I want to show that the volume density is invariant, i.e. $ \sqrt{-g(x)}\,\mathrm d^4x \rightarrow \sqrt{-g(y)}\,\mathrm d^4y $. The first step I took was finding how $\mathrm d^4x$ transforms. We were given a hint to use the definition of the determinant, ... |
I am reading Peskin and Schroeder's chapter on functional methods and they compute the following correlation function:
\begin{equation*}
\begin{split}
\langle 0| T\phi_1\phi_2\phi_1\phi_3 |0\rangle
&=
\frac{\delta}{\delta J_1 }
\frac{\delta}{\delta J_2 }
\frac{\delta}{\delta J_3 }[-J_xD_{x4}]e^{-\frac{1}{2}J_xD_... |
Question: Two bulbs (50W and 80W) are connected in parallel in a simple circuit with a constant voltage supply of 50 volts. Determine which bulb is brighter.
My attempt: Since we know that the two bulbs are parallel with each other, the amount of current that passes each bulb is determined by the resistance of each bul... |
Kubo formula $\sigma_{ab}(\textbf{q},\omega)=\frac{1}{\omega} (\pi_{ab}(\textbf{q},\omega) - \pi_{ab}(\textbf{q},0))$ is usually given in terms of the current-current correlation function
$$\pi_{ab}(\textbf{q},\omega)=\int_0^\infty dt e^{i\omega t}\langle[\hat{J}_a^\dagger(\textbf{q},t),\hat{J}_b(\textbf{q},0)]\rangle.... |
I am struggling with this magnetic circuit.
Magnetic circuit of a coil with moving part
What is the equivalent cross section area I need to use to find the magnetic flux?
Should I use $A_c$ for the moving part or $A_g$? Or should I use $A_g$ for the stationary core? $A_g=A_c(1-\frac{x}{X_0})$
Which solution is correct?... |
There are 24 fermions in the standard model (if we consider left/right and particle/anti-particle as the same type).
Thus there are 24 masses to find. (Yes, it is generally considered quarks of different colors (red, green, blue) have the same mass but we'll count it as 3 different masses.)
Now we assume that the theor... |
I'm doing practice questions for an upcoming exam and I became stuck on this one (found on OpenStax here):
For the reaction, $n+^3He→^4He+\gamma$, find the amount of energy transfers to $^4He$ and $\gamma $(on the right side of the equation). Assume the reactants are initially at rest. (Hint: Use conservation of momen... |
In a pressure cooker, when T increases -P increases which means that the K.E of molecules increases. But According to equation PV/Tinc so T inc P inc and V dec. If they less volume I.e gas molecules does it means they occupy less space in the cooker.Does that mean that molecules don’t reach or go to some areas of cooke... |
So, my teacher was trying to explain me about Diamagnetic substances and he said that :
Suppose the atom of an element has 4 electrons revolving around the nucleus in 4 different orbits. The electrons will be revolving around the nucleus and also spinning about their own axis. So the net magnetic moment will be due to... |
Consider the following model in classical statistical mechanics. Take a finite box $\Lambda\subseteq\mathbb{Z}^d$ and consider the field $\phi:\Lambda\to[-1,1]$ whose Gibbs measure is given by $$ \mathrm{d}\mathbb{P}(\phi):=\frac{\exp\left(\frac{1}{2}\beta\sum_{x\in\Lambda}\sum_{y\sim x}\phi_x\phi_y\right)}{\left(\prod... |
Consider a free scalar field theory. My struggle is that vacuum correlation functions of fields are only Lorentz invariant under a subgroup of Lorentz transformations, despite the invariance of the vacuum under the complete group of Lorentz transformations! I expect that I am making suspect assumptions somewhere.
I ex... |
In the classical formulation of electrodynamics given an initial electric field $\mathbf{E}$ and magnetic field $\mathbf{B}$ a particle moving through this field experiences a force $\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B})$.
If I understand correctly when the particle accelerates its movement itself... |
I am a physics fan, but I am not a physicist. I don't even know that the question I have asked make sense or not.
There can be waves in the gravitational field. So I would like to know if there can be waves in other types of fields, such as electromagnetic field, Higgs field etc.?
|
I tried to calculate the time-like geodesics of the Morris-Thorne Wormhole $[1]$, $[2]$, $[3]$ for redshift function $\Phi(r) = 0$ and $b(r) = \sqrt{r_{0} r}$. But I don't know for sure if all the plots that I made are correct.
So, the metric is:
$$ds^2 = -e^{2\Phi(r)}dt^2+\Biggr\{ 1-\frac{b(r)}{r}\Biggr\}^{-1}dr^2+r^2... |
After watching a video by Veritasium about measuring (or, more accurately, not measuring) the one-way speed of light, I believe I have come up with a way to measure it. I'm guessing somebody else has thought about this setup before, so there is probably something I am missing that explains why it (most likely) isn't t... |
BACKGROUND
As far as the Heisenberg uncertainty principle is concerned, my understanding of commuting observables $\hat{A}$ and $\hat{B}$ is that the measurement outcome $a_i$ does not perturb (or correlate with) the measurement outcome $b_j$ because they $a_i$ and $b_j$ arise from projections onto orthogonal eigenvect... |
In which way do the Earth's rotational axis tilted 23.5°.
see in the image we have been told that the axis of rotation of Earth is tilted 23.5° from the perpendicular to path.
But can anyone say in which direction the earth is tilted .AO or BO. Is
the axis of rotation tilted towards sun or away from sun.
And still it ... |
I was wondering if there was a difference between velocity of the center of mass of an object vs finding the velocity of an object in general. The case I was looking at was in a ball rolling without slipping. I know that in the case of a ball rolling without slipping, the velocity of the center of mass would simply = r... |
I just came across this problem that I didn't even know existed, how to measure the speed of light in the universe in a specific, given direction with respect to the universe or "in one way/direction only". Found it from here: https://www.youtube.com/watch?v=pTn6Ewhb27k
Anyway, to briefly state the problem, hypothetica... |
I was watching a lecture and at some point they say that for a covalent bond of 1.1 eV and for particles with 0.026 eV mean energy, the number of particles requiered to break the bond is 42, that is 1.1/0.026=42. I’m wondering why we need to do this operation
|
Coulomb's law says that as the distance between two electrons approaches zero, the force becomes infinite. However this is just an approximation, and electrons are better described as fuzzy clouds of charge distributed through space. But bringing two electrons close together would increase the replusive force between t... |
I'm reading Quantum Field Theory in Strongly Correlated Electronic Systems, Nagaosa.
Consider 1D Ising model,
$$H=J_z\sum_i S^z_iS^z_{i+1}.$$
on page 3, it says
The groud stae is 2-fold degenerate because the Hamiltonian is invariant
under the transformation $S^i_z \rightarrow -S^i_z$, performed at all sites $i$.
Call... |
If we have a circuit made of a battery and a resistor the number of electrons with spin up will be equal to the electrons with spin down. If we put the resistor in series with a piece of ferromagnetic material which is magnetize either up or down, let's say it is magnetized up will it produce a spin polarized current? ... |
Wikipedia says:
Moment is an expression involving the product of a distance and physical quantity.
I don't quite get it. Moment is a vector, the cross product of the distance vector and the vector of the physical quantity, and it is linear. Why is it defined to correspond to an angular quantity like:
The moment of fo... |
I am not sure whether this is the correct place to ask, otherwise, please point me to the appropriate platform. I have been reading about fibre optic interferometric sensors and notice that most people use an optical spectrum analyzer (OSA) as the detector.
Therefore, I am wondering if it is possible to use a spectrome... |
I am a high school student and I am a little confused about standing waves on string, My confusion is that: we know ,A standing wave is formed by the interference of reflected wave and incident wave but I am not able to imagine at what places will the constructive and destructive interference occurs at frequencies othe... |
I am trying to find the quadratic Casimir of a 45 dimensional representation of ${\rm SU}(5)$. However, in many references, the dimension of the representation of ${\rm SU}(N)$ are $N, N^2-1, N(N-1)/2, N(N+1)/2$.
Therefore, the possible dimensions of ${\rm SU}(5)$ are 5, 24, 10 and 15. I have the formulae to find the a... |
Let's consider a (cubic) beam splitter with two electric input fields $E_1,E_2$ and two electric output fields $E_3,E_4$ as illustrated in the figure below.
For a lossless beam splitter, we almost always find the literature claim
$$
\vert\boldsymbol{E}_1\vert^2+\vert\boldsymbol{E}_2\vert^2
=
\vert\boldsymbol{E}_3\vert... |
I read this from Optics (Global Edition) by Eugene Hecht Page 347, Chapter 8: Polarisation. The author says that this is obvious but I seem to be missing something here. Is the incident wave out of phase with the wave propagating in the forward direction?
Thanks for your help!
|
Im having some confusion regarding the gravitational field equations we can get from a certain action. If Im given an action and they ask me to obtain the gravitational field equations from it I would only vary w.r.t. the metric. If they tell me also that the theory is coupled with, say, two scalar fields $\phi$ and $\... |
I have a velocity vector defined as, $$V^i=\frac{dX^i}{dt}$$
Then, is the following manipulation correct?
$$\frac{\mathbf{V}\boldsymbol{\cdot}\mathbf{V}}{V^i}=\frac{V_k\delta^k_{\,\,\,\,a}V^a}{V^i}=V_k\delta^k_{\,\,\,\,a}\frac{dX^a/dt}{dX^i/dt}=V_k\delta^k_{\,\,\,\,a}\frac{dX^a}{dX^i}=V_k\delta^k_{\,\,\,\,a}\delta^a_{\... |
We have the operator
\begin{equation}
A = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}
\end{equation}
I found its eigenvalue which is $\lambda$ = 0.
Now the question is whether the operator can be written as $ \hat{A} $ = $\sum_{n=1}^{2} a_n|a_n\rangle\langle a_n|$ ?
I think it can not be written in that form because ... |
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