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Given a chemical reaction of ideal gasses:
A <-> B
From my understanding, there are two partition functions that you can write depending on whether A and B can react to form each other.
Non-reacting:
$Q_{nr} = \frac{q_A^{N_A}}{N_A!} \frac{q_B^{N_B}}{N_B!}$
Reacting:
$Q_r = \frac{(q_A+q_B)^{N_A+N_B}}{(N_A+N_B)!}$
Where ... |
I was under the impression that light waves have 2 polarizations because even if the photon is spin 1, the photon is massless which imposes additional constraints. In the case of gravity, it is associated with a tensor (or a hypothetical spin 2), so I would have expected to have 3 polarizations (4-1 for travelling at $... |
I was being interviewed by XYZ, and was asked to prove that expectation value of momentum for a potential V=V(x) is zero when the potential is symmetric.
According to my knowledge expectation value of momentum is always 0 irrespective of potential being symmetric or not.
|
The BFSS matrix model (Wikipedia) "describes the behavior of nine large matrices" using
$$ H = Tr(\frac{1}{2}\{\dot X^i \dot X^i - \frac{1}{2}[X^i,X^j] + \theta^T \gamma_i[X^i,\theta]\}) $$
Could anyone show an explicit construction for these 9 matrices as used in the BFSS matrix model, and show how these 9 matrices i... |
I am trying to prove that with all things the same, a rapidly spinning disk requires more force to stop it than a slowly spinning one.
For example, when you first hit the brakes in a fast moving car, you must hit them really hard to get lock up. But if the car is moving more slowly, it doesn't take nearly as much for... |
I am trying to recreate all steps from 5.97 to 5.103. Can someone explain how to go from 5.97 to 5.99 ? I understand the denominator part, my issue is with the transformation from gamma to sigma matrices
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Okay so basically imagine you have a can filled with water. This can not burst open no matter how much pressure is put on the can, but it can be crushed, and the liquid cannot burst out.
What would happen if you put many tons of pressure onto this can?
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In the following example:
At the very last step, how does the author get that $\tan(\theta) = dy/dx$? To which $dy$ and $dx$ is this referring to? It can't be the same $dx$ that is labelled in the diagram, can it? Where do these $dy$ and $dx$ come from?
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Massive stars may undergo multiple fusion processes as they near the end of their lifespans. Our sun will eventually start fusing helium in its inner core so that carbon is formed. As this occurs, the radiation energy will be large, and the sun will expand into a red giant phase. After a while, as the star begins to ru... |
Generally the Christoffel symbol of the first kind is defined as
$$\Gamma_{\lambda\mu\nu}=\frac12\,(\partial_\nu g_{\lambda\mu}+\partial_\mu g_{\lambda\nu}-\partial_\lambda g_{\mu\nu}) \tag{1}$$
and the Christoffel symbol of the second kind is defined as
$$\Gamma^\rho{}_{\mu\nu}=g^{\rho\lambda}\Gamma_{\lambda\mu\nu}=\f... |
Suppose we are given a Hamiltonian $$H=\frac{1}{2}\left(\frac{1}{q^2}+p^2q^4\right)$$ where $q,p$ constitute a canonical pair of degrees of freedom.
Now we are asked to go to a Hamiltonian of the form of a harmonic oscillator, by some canonical transformation $(q,p)\rightarrow(Q,P)$.
I think we can write the new Hamilt... |
I'm trying to replicate some results from this paper (http://ieeexplore.ieee.org/document/44924/) on the changes in refractive index due to the band filling effect, however I'm stuck at some dimensionalities I don't unuderstand. The formula for the optical absorption near the bandgap in a direct-gap semidconductor with... |
I am following the book "An introduction to quantum field theory" by Peskin and Schroeder. In the section 'Discrete symmetries of the Dirac theory', it is written,
$P a^s _p P^{-1} = \eta_a a^s _{-p}$
where $P$ is the parity operator and $a^s _p$ is the annihilation operator of a particle of momentum $p$. And $s=1,2$ ... |
How do we use the background field method for renormalize a gauge theory?
|
Here, when referring to potential energy, I will take gravitational potential energy as an example. Consider the following diagram where two point masses $m_1$ and $m_2$ at a distance $r$ from each other exert a gravitational force on each other. Here I used the vector form of the law of gravitation which can be referr... |
I am interested in a way to determine electric field and current in a region where some kind of conducting wire is placed in dielectric with some voltage applied to both of them. I am interested in general case but as a simple example consider two infinite conducting half-spaces under some voltage difference with diele... |
I am doing a topology in condensed matter course and they begin with a sentence ( link here )
Actually, we can even solve the problem of an electron in an N site ring (triangle being =3). The trick to doing this is a neat theorem called Bloch’s theorem. Bloch’s theorem is the key to understanding electrons in a crysta... |
I was reading a high-school physics textbook, and it stated that the age of the universe is equal to 1 / Hubble's constant. They even give a derivation: $v = H_{0} D$ and $D = vt$, so subbing in gives $t = 1/H_{0}$. But this can't be correct as this states that a variable equals a constant, aside from that, it would ma... |
I have learned in my Statistical Mechanics class that one of the fundamental assumptions of thermodynamics is that all microstates are equally probable. However, in the case of the Hydrogen atom, we know that we will most likely see the case where the electron is in the ground state. If all microstates are equally prob... |
The square modulus of an amplitude must be real. Given that, I am having some trouble understanding the square modulus of a path integral being absolutely real. Given
\begin{equation}
\int\!Dq(t)\equiv \lim\limits_{N\to\infty}\left( \frac{m}{2\pi i\hbar \delta t} \right)^{\!\frac{N}{2}}\left( \prod^{N-1}_{k=1} \int... |
The moon will be totally invisible during Conjunction of moon, sun and earth.
After how many hours of conjunction, moon will be visible from earth.
|
I'm having a hard time grasping the concept of 'potential barrier'. I'm currently concerned about a rectangular potential barrier (I have attached a picture).
The classical analogy given is of a ball rolling up a hill (I have attached a picture). In that case the ball starts losing energy as soon as it starts climbing ... |
imagine I just know number system nothing else I want to intuitively understand development of units and dimension with very very clear definition of both of them what exactly is a unit how is it different from dimension don't use difficult words
|
In chapter 9 of their book [1], Altland and Simons consider the Landau Hamiltonian in the symmetric gauge,
\begin{equation}
H=\frac{1}{2m^*}\left[\left(-\mathrm{i}\partial_1-\frac{x_2}{2l_0^2}\right)^2+\left(-\mathrm{i}\partial_2+\frac{x_1}{2l_0^2}\right)^2\right],
\end{equation}
where $l_0=\sqrt{\Phi_0/2\pi|B|}$ is th... |
I am just looking for the correct Ansatz to a one-dimensional diffusion equation with a harmonic potential.
Let $n(x,t)$ be the density of particles and $\Phi(x)=\frac{1}{2}\alpha x²$ a potential.
Then the current density is
$$j(x,t)=-D\frac{\partial n(x,t)}{\partial x}-\sigma \left(-\vec\nabla_x \Phi(x) \right)$$
wit... |
I would like to know some applications of the Kronig-Penney Model and what parameters (effective mass, width...) are interesting to change in order to study those applications.
|
From Morin's Classical Mechanics, on the chapter of Small Oscillations in Lagrangian Mechanics, he does this approximation on the last equality, I don't understand what happened there.
I get the first approximation, where we neglect the terms of order higher δ^2.
|
Is there a way to experimentally test if the cosmological red shift observed is due to the expansion or intrinsic to the galaxy? If anyone knows how to do this or how to extract from the data please share this information here.
|
In many text books such as Gravitational waves volume 1 by Maggoire and General relativity by Hobson the solution to linearised Einstien field equations can be computed in the far-field using the standard greens functions method.
$$
\bar{h}^{\mu \nu} = -\frac{4G}{c^4} \int_\mathcal{V} \frac{T^{\mu \nu}(t-\frac{|x-x'|}... |
Standing waves have no net transfer of energy. But, when watching simulations of the first harmonic for a closed tube, I see what looks like a transfer of energy - the particles clearly appear to move one way and then the other. How do we reconcile this motion with no net transfer of energy?
|
It seems that Einstein's 1905 paper "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light" notes the discrete quanta of light energy, an idea that leads to thinking of light as consisting of "particles".
What experiments and/or understanding exclude the possibility that photons are simp... |
In a proof of the equivalence of the canonical and grand canonical ensembles (in the thermodynamic limit) in Jochen Rau's Statistical Physics and Thermodynamics (highly recommended!), the author evaluates the grand canonical partition function as
$$Z_G = \textrm{Tr}(\exp(-\beta \hat{H} + \alpha \hat{N})).$$
In evaluati... |
Let $\alpha,\beta$ non-zero real numbers, $f$ a function of time. I define $L_1=\alpha f + \beta$ and $L_2=p(t) L_1$.
I want to minimize $\int_0^T L_2$ under the constraint $\int_0^T L_1=v$, with $T$ being a free boundary.
By setting $T=T_0 + \epsilon \tau $ ; $f=f_0 + \epsilon \phi $ ; $\lambda = \lambda_0 + \epsilon ... |
If a charged particle (Say $+Q$) is placed between two charged particles of charges $+q$ and $-q$ (are of equal magnitude and those two charges are static),the electric potential in the midpoint is zero as
Net Potential at midpoint=Potential by +q + Potential by -q
=k(+q)/r +k(-q)/r
... |
Though the opposite is readily found, battery charging a capacitor, I am looking to scavenge small generation capacities to charge a battery. Things like piezoelectric effects or collecting electrostatic effects like https://youtu.be/fhj2BN-cbvg. Such small charges need to be collected to be useful and my thought was... |
In my understanding of QM I expect the quantum state of the proton $| p^+ \rangle$, say in the rest frame, to be an eigenstate of the QCD Hamiltonian $H_{\text{QCD}}$, which describes the dynamics of quarks and gluons, with eigenvalue the proton mass $m_{p^+}$.
$$
H_{\text{QCD}} | p^+ \rangle = m_{p^+} |p^+\rangle.
$$
... |
I've derived the Laue conditions from the requirements for constructive interference in a crystal lattice ( J. Drenth (2007), Principles of X-Ray Crystallography 3rd Edition ) and also then equivalated the Laue conditions to the Bragg conditions for diffraction.
From what I understand, the reciprocal lattice gives ever... |
Consider the Dirac field theory. In this theory the transformation of charge conjugation on a Dirac field is given by,
$U(C) \psi(x) U(C)^{-1} = \eta_c C \psi^*(x)$,
please note the $C$ give on RHS is Gamma matrix related to charge conjugation. Suppose we don't know what $C$ is. So in order to determine it we can deman... |
If you are in a spaceship and you spin a balanced centrifuge with a rock in it, does the spaceship rotate in the opposite direction as the centrifuge with the same angular, kinetic energy as the centrifuge?
Guess 1: the energy of the rotating centrifuge 50% is equal to the energy of the rotating spaceship 50%: equal to... |
I noticed something recently where while I was drinking milk, when the glass was upright in my hand and I tapped the side, it produced one pitch, but while I was drinking it, and so the glass was angled, the pitch was lower. The pitch didn't seem to change with the amount of milk, but rather with the tilt of the glass.... |
One possible explanation of the quantum to classical transition, or in other words of why we don't see macroscopic quantum effects naturally, is environment induced decoherence.
Basically, the system inevitably couples to some environment, and the inability to fully characterize the environment's state result in a loss... |
I am not able to understand rays coming from a source object are produced back in the mirror world.
It sounds completely realistic and relatable that rays are originated from and object and then reflected through mirror. Then how are the reflected rays produced back the mirror, it's just a plane surface how is this spa... |
Would rings still be formed if a plano concave lens is used in place of a plano convex lens in the Newton's ring experiment.
The locus of points with the same path difference in case of a plano convex lens is a circle, while I suspect that that shouldn't be the case for a plano concave lens though I don't have a rigoro... |
I've read that the refraction of light at the boundary of a medium can be described as follows:
-a line of connected people marching. one side of the line enters mud, and slows down. This causes the non-mud side to pivot towards the slower side, which then causes the line to change direction.
I'm helping my 9 year ol... |
Planck says
$$B_\nu(T)=\frac{2\nu^2}{c^2}\,\frac{h\nu}{\mathrm{e}^{h\nu/k_BT}-1}.$$
It is power emitted per unit area per unit angle per unit frequency. This is what I'm curious now.
Let's say we got a black body at T = 300K. I want to calculate power emitted when wavelength is 500nm. So I plugin in 300K and instead ... |
I am a retired theoretical physicist in the Netherlands. I am currently trying to promote the exact sciences by helping highschool students with their mathematics, physics and chemistry studies.
I am impressed with the general level and sophistication of the modern physics books used by these highschool students. The c... |
It is fairly simple to show that the Schrodinger equation is of the form,
$$\frac{d|\psi(t)\rangle}{dt}=-\frac{i}{\hbar}\hat{A}|\psi(t)\rangle$$
for some Hermitian $\hat{A}$,
from the assumption that time evolution is the result of an operator on the Hilbert space acting on the initial state,
$$|\psi(t')\rangle=\hat{U}... |
I am looking at a certain measure for macroscopic quantum states, namely the one in http://dx.doi.org/10.1103/PhysRevA.89.012116. I use the notation from https://arxiv.org/abs/1706.06173 (p. 15-16, chapter "11"). there, macroscopicity of states in cat form $|\mathcal{A}\rangle+|\mathcal{D}\rangle$ is defined by how wel... |
Suppose I have column of gas that starts from height $z=0$, the Gravitational potential energy at any point is given by $mgz$. Now I want to calculate the number density of such a column of gas given that it is in Thermal and Chemical equilibrium with a bath.
Quite naturally, I model it as a Grand Canonical Ensemble Id... |
I took this picture from wikipedia. As you can see the higher pressure the higher temperature.
However, As I read the article from this site they said that,
At higher temperatures, the molecules move quickly and spread out.
This means that there are fewer molecules in an area. Fewer molecules
result in lower air pres... |
Newton's third law states that for every force applied by object $A$ on object $B$, there is an equal an opposite force by object $B$ on object $A$. The strong form of Newton's third law states that for every force applied by object $A$ on object $B$, there is an equal an opposite force by object $B$ on object $A$, and... |
Gravitational time dilation would seem to prevent anything from reaching the Schwarzchild radius. It seems to me that the calculation of properties of General Relativity would be similar to the Gausian calculation that asymptotes but never reaches unity (x axis). In other words, time dilation would approach 0 but never... |
So I've been reading about the PN Junction and depletion region quite a lot, but I haven't really found a concrete explanation for the existence of a Voltage Drop, or Barrier Potential associated with the depletion region after the formation of the electric field due to diffusion of majority charge carriers from both s... |
I am trying to intuitively derive length contraction in special relativity using a thought experiment, without relying on Lorentz transformations. My aim is to obtain a derivation similar to how time dilation is derived using the classic light clock thought experiment. However, I have not been able to find or create a ... |
I have a question about the conformal diagram of an ‘astrophysical’ black hole which forms in finite time (but with no evaporation).
Usually I see the conformal diagram presented as something similar to
I understand that the $r=2GM$ surface is null so it must occur at a 45 degree angle on the diagram. Yet drawing this... |
Planck says
$$B_\nu(T)=\frac{2hc^2}{λ^5}\,\frac{1}{\mathrm{e}^{hc/λk_BT}-1}.$$
It's defined as energy emitted per unit volume per wavelength. I'm not sure if this includes per solid angle, but I really don't care for this question.
I understand that what per wavelength means only partially. For example, If I put λ =... |
I am currently working on a physics problem that asks me to form a dimensionless combination of the fundamental constants $e=\left|q_e\right|$, $\hbar$, $c$, and $\epsilon_0$ that is proportional to $e^2$. This dimensionless number is called the fine structure constant.
I have been struggling with this problem and woul... |
I was sawing a Youtube Video about Quasiparticles (for this topic it doesn't matter which one), but the video host present examples that were very far for being familiar to a wide audience.
In my experience as electrician, the classic quasiparticle example is the "electron hole" depicted as a positive charge that diffu... |
I am extremely confused on the concept of a $pV$ diagram.
I understand that Pressure times (change in) Volume equals the Work done by a piston; however, I am confused on how volume and pressure can increase at the same time. According to Boyle's Law, PV=k under a constant temperature. If this is so, how would volume an... |
Time seems to be simply a measure of change, or rather how we perceive time is by observing the rate of change. If no change can be detected, no motion, no chemical change, no change of state, not even nuclear decay, does time itself even exist for that closed system? Yes, an observer outside of that system could comp... |
I understand the equation mathematically-- $p$ times (change in) $V$ = Work done. However, I am confused about it conceptually. Work is (in a non-calculus context) constant force applied over a set distance. But, while the volume of, say, an ideal gas increases, pressure decreases--in other words, while the volume incr... |
On a $pV$ graph (where the Pressure is on the Y axis, and the Volume is on the X axis), I am conceptually confused on how the area under the graph is equivalent to the work done by the system (assuming positive change in volume = the system increasing in volume). I understand it mathematically (P times V = Work done).... |
In the Wigner's friend paradox scenario, there is an observer inside a lab, with a spin 1/2 particle inside waiting to be measured, which is generally in a superposition of spin up and spin down around the z axis. The lab is isolated, so after measurement the state of the system will be an entangled state of the partic... |
Can a system be in an eigenstate of the total angular momentum operator $L^2$ without being in an eigenstate of any of $L_x$, $L_y$, and $L_z$? What would such a state look like?
|
We know that water at 1atm can be superheated well beyond 100C. Can someone link to a paper with the current demonstrated record?
|
In lecture today, the professor was describing the superposition of 2 otherwise identical waves, one modelled by $$y_1(x,t) = Asin(kx-wt+\phi_1)$$ and the other by $$y_2(x,t) = Asin(kx-wt+\phi_2)$$Our prof then said that $$y_1(x,t) + y_2(x,t) = 2Asin(kx)cos(wt)$$ (He said to choose an $x$ initial and $t$ initial such ... |
For simplicity, let me assume that space is 1-dimensional and the position observable has countably many orthogonal eigenstates. Then the operator $\sum_{i}|x_i\rangle\langle x_i|$ would be an observable that can tell us whether the state of a system can be expressed in terms of some linear combination of position eige... |
On Peskin & Schroeder's QFT, chapter 11.4, the book discusses the computation of the effective action of linear sigma model.
I am troubled for the relation between renormalization condition and Higgs VEV (vacuum expectation value) appearing in page 376-377.
First, on the bottom of page 376, the book says we can apply t... |
I have a question which I got stumbled upon between two different options (MCQ), as it required to have only one correct option. So the question goes like this:
In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor :
options are: (`Wherever potential is mentioned it is... |
I'm an engineer and I've never studied particle physics, but I like it, and I like to see Feynman diagrams and try to understand as much as I can. Looking for a Feyman diagram involving the Higgs boson, I found the following picture which can be found in this pdf file https://cds.cern.ch/record/2759490/files/Feynman%20... |
Bullet spin causes a bullet to become a gyroscope. Specifically, bullets have their center of pressure in front of their center of mass. Therefore, when pressed, gyroscopic forces cause a bullet to spin 90 degrees instead of tumble. See this diagram:
The precession does not cause the bullet to point into the direct... |
I’ve been reading on Haag’s theorem and found this proof that uses standard QFT instead of the axiomatic kind: https://arxiv.org/abs/2011.08875
It essentially boils down to saying that the vacuum should be invariant under spatial translations $T|\Omega> = 0$ where $T$ is defined such that $T\phi(t,x) = \phi(t,x + a)$. ... |
What does shake-off mean in nuclear physics?
The word appears, for example, in the title of this article: "Shake-off in the ¹⁶⁴Er neutrinoless double-electron capture and the dark matter puzzle"
|
From what I know, the renormalization group tells us how the coupling constants of a theory change as the energy scale is varied. Thus as you vary the energy scale you trace out a path or flow in the space of all possible coupling constants.
With this picture in mind, how does one interpret the plots often associated w... |
I am trying to compute the (anomalous) transformation law of the free fermion stress-tensor, not with the usual CFT arguments, but by explicit computation.
We can define the classical stress tensor $$T=i\psi^{\dagger}\partial\psi.\tag{1}$$ The quantum counterpart will be divergent, we regularize by point-splitting. The... |
I know equations of Fanno flow but can anyone explain physically how friction increases subsonic velocity and decreases supersonic velocity through pipe ? is that for sake of boundary layer displacement thickness ?
|
Following the Picture below,
If I Conduct current through Permanent magnet Bar and hold the battery still. Will the magnet move in any direction ? Thank you.
|
Wondering if a rigid body can keep rotating about its axis with constant angular velocity without the application of any force or torque, to the object. Assuming that the object is not in influence of any external force (i.e. gravity etc.)
|
I have bought a resistor that works as a heater when a voltage is applied to it, and the seller provided me these $ \left(V (\mathrm{V}), T (\mathrm{°C})\right)$ points: $(6.20$, $200)$, $(7.75$, $250)$, $(9.20$, $300)$, $(10.70$, $350)$, $(13.20$, $400)$, $(14.70$, $450)$, $(16.20$, $500)$, $(17.30$, $550)$. Assuming ... |
I would like to know where I can read more details about how to prepare two entangled particles for which the axiom "TWIN" in the paper Free Will Theorem holds.
The particles must have spin 1 and any measurement of their squared spin components along three orthogonal directions has to give 1,1,0 in some order. The auth... |
I would like to know what are "scientitifics" therms to explain better what I mean.
I mean we do a cross section, normal to the trajectory of photons and we make it changing position all the way long while the emission occurs. What would look like the observation of interferences along the trajectory ?
A screen right a... |
I have already calculated the divergence of the electric field, i.e.
$$\vec{\nabla} \cdot \vec{E}(\vec{r})=\left( \begin{array}{rrr}
\frac{\partial}{\partial x} \\
\frac{\partial}{\partial y} \\
\frac{\partial}{\partial z} \\
\end{array}\right)\cdot \frac{Q}{4 \pi \epsilon_0}\left( \begin{array}{rrr}
\frac{x}{(x^2... |
In some of the physics problem I've been going over, the phrase "gradually pulled/moved/pushed" is coming up again. I can not understand what the implication of this is. Here is an example problem where it comes,
In the setup shown, a block is placed on a frictionless floor, the cord and pulleys are ideal and each spr... |
I am reading Theoretical minimum: Special Relativity and Classical Field Theory where you construct a Lagrangian for the field by the argument that it would be invariant under the Lorentz transformation, so basically any scalar function involving $\phi(x^\mu)$ since $\phi$ transforms as:
$$\phi(x) = \phi'(x')$$
But the... |
I was wondering if we put a concave mirror in water, what will be the difference in the image formed by it in air vs water?
Exception: Here I mean except when rays come from infinity (e.g., sun) because the rays won't be refracted at all.
I am considering all cases when the object is near the mirror.
My theory: I think... |
Suppose a square with constant area density $\sigma$ with a side $d$ and an object which is located on a distance $h$ from the plane of square.
What is the gravitational potential of the object when it's located just abovve center of the square, center of its side and on the angle.
My attempt
I decompose square into el... |
I am not looking for explicit solutions to the eigenvalue equations, but rather for general function spaces.
For free Dirac equation without potentials, the solutions of the Dirac equation, or equivalently the eigenfunctions of Dirac Hamiltonian, are elements of Sobolov space of order 2 on $L^2$, with tensor product of... |
I have a doubt regarding the SM hypercharge current associated with the $U(1)_Y$ global symmetry (note: I want to work in the unbroken phase, we have the doublet H and the Yukawas)
$\psi \to e^{i\alpha Y_{\psi}}\psi, \psi=Q,u,d.$
The hypercharge values $Y_{\psi}$ are fixed by demanding the SM to be anomaly free. Typica... |
I was reading the theory of superfluidity in the language of field integrals from the book 'Condensed matter field theory' by A Altland and B Simons. The quantum partition function is given by $$Z=\int D(\rho,\phi)\exp(-S[\rho,\phi])$$ where $$S=\int d\tau \int dr[i\delta \rho \partial_\tau \phi + \frac{\rho_0}{2m}(\na... |
I am studying how wave packets are defined in quantum mechanics, but I am finding it hard to intuitively understand why superposing an infinite number of waves of different wavenumbers $k$ may sometimes result in a wave packet that is localised.
I understand that constructive and destructive interference take place out... |
I read this in a paper : "... we cannot distinguish them by making measurements because they have the same density matrix". The authors are referring to two different decompositions of the same density matrix. Example:
$$
\begin{aligned}
&\rho=\frac{1}{2}|0\rangle\langle 0|+\frac{1}{2}| 1\rangle\langle 1|\\
&\rho=\frac... |
For a general rotation $R(t_1, t_2, t_3)$ where the $t_i$'s are the components of the rotation vector in the axis-angle representation. Is there closed formula for the derivative of $dR/dt_i$?
I only find derivative with respect to the magnitude of the angle, but not to the components of $t_i$
$$
\frac {dR(\theta)}{d\t... |
The capacitance per unit area of a parallel-plate capacitor is $\frac{\epsilon_0}{d}$.
But what if one of the plates is a mesh, but the distance $d$ is much much greater than the size of the holes in the mesh?.
My intuitive thinking would be that from the perspective of the solid plate the charge density on the mesh is... |
In my lecture notes, when talking about AFM Cantilever, there is graph shown below with following caption:
Resonance of a vibrating beam.
Amplitude (a) and phase (b) of a beam driven at a frequency $ω$.
(c,d) show amplitude and phase at $ω=ω_0$ as a function of the distance between probe (tip) and surface.
Can an... |
I hope this is the right platform to ask stupid questions like this, but this is driving me nuts right now. Probably embarrassing to say, but I actually have somewhat of a physics background, but also definitely don't consider myself well educated in Physics. But I always thought my high school mechanical physics is so... |
I've tried finding the potential energy by using PE = mgh then using PE = 1/2kx^2 to find k and setting PE = KE to find PE using velocity but neither is correct when finding the spring constant. I don't know if I have to take in account circular motion but none of the equations that I know are helping.
|
My question is whether two electrons can be entangled only with respect to their spins but not with respect to some other observable, such as position.
I initially believed that spin-entanglement doesn't entail position or momentum entanglement. But if particles $a$ and $b$ have a composite state given by $|\Psi\rangle... |
I can follow the proofs for these identities, but I struggle to intuitively understand why they must be true:
$$$$
1. The curl of a gradient of a twice-differentiable scalar field is zero:
$$\nabla\times\nabla U=\boldsymbol0$$
Conservative forces can be written as gradients of a scalar potential, so this means these f... |
In his chapter on the electroweak unification, Griffiths introduces the weak hypercharge explaining that his attempt at introducing full weak isospin symmetry with the Pauli spin matrices failed because the neutral current corresponding to the third isospin matrix does not contain right-handed fields (the actual weak n... |
When an electron orbiting an atomic nucleus is excited, does it shortly after get closer to the nucleus and lose potential energy or does it lose kinetic energy too?
|
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