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We know gapless Goldstone mode appears when the system exhibits spontaneously symmetry broken. Does this means whenever we observe gapless acoustic modes it is Goldstone mode i.e. spontaneous symmetry broken?
|
I'm trying to understand the equation of motion for rigid body dynamics in the presence of a quaternion joint for the root of a humanoid robot. But the dimensionality inconsistency issue is confusing me now.
Let $\mathbf{q}\in \mathbb{R}^{m}$ be a configuration vector of the humanoid body such that the first three ent... |
I understand that mass number and atomic mass are different by definition.Mass number is the total number of nucleons and isotopic atomic mass is the average atomic weight of all the known isotopes of the element which should be approximately equal to the weight of the nucleons(ignoring binding energy and negligible ma... |
Why do the red points in the following figure have the same pressure?
|
I'm currently fiddling around with gauge-phase-transformations in Fock space.
Especially, I'm trying to write a local gauge-phase-transformation as
an operator in a basis-independent way.
Here is what I have so far.
Consider a system of indistinguishable particles (each with a charge $q$).
Total charge
Let's take the t... |
This is probably a nonsensical question, but I'm having trouble wrapping my head around it. I'm thinking of the classic scenario where a stationary observer is watching a spaceship move horizontally. It makes perfect sense to me that a beam of light bouncing up and down will appear to move more slowly vertically, since... |
Consider the following protocol:
Alice and Bob share the state
\begin{equation} |\Phi^+\rangle=\frac{1}{\sqrt{2}}(|0\rangle|0\rangle \pm |1\rangle|1\rangle) \end{equation}
Alice has to teleport to Bob the state (which can be unknown even to her)
\begin{equation} |\psi\rangle = c_0|0\rangle + c_1|1\rangle \end{equation... |
Suppose I have three circuit components - two capacitors of capacitance $C$ each and a resistor of resistance $R$, all of which are connected in parallel. The resistance across any individual capacitor will be $R$, so will it's time constant be $RC$ or something else? I am doubtful that it will remain $RC$ as the secon... |
Is there a way to algebraically see why when I take the second derivative of a potential energy in a point where it is minimal (force is zero), I generally get the frequency (squared) of the oscillations around this point?
|
I am trying to solve the following advection-diffusion equation for transient flow conditions for radial flow.
The governing equation is as follows.
$$\frac{\partial T}{\partial t} = \frac{\partial^2 T}{\partial x^2} + \frac{1-2v(t)}{x} \frac{\partial T}{\partial x}$$
$$\frac{\partial T}{\partial t} = \frac{\partial^2 ... |
Consider (for example) non-relativistic electron-impact ionisation, in which an effectively stationary atom in state $I$ is struck by an electron of momentum ${p_1}$, producing an atom in state $J$ with two additional electrons, momenta ${p_2}, {p'_2}$. The electron-impact ionisation transition rate is then expressed a... |
From what I know:
The magnetic field strength, $\vec{H}$, is the field generated by a free current flowing on an electric conductor.
The magnetic flux density, $\vec{B}$, is a response of the medium to the applied excitation $\vec{H}$.
The link between them is given by the equation:
$$\vec{B}=\mu_0\left(\vec{H}+\vec{... |
In the 10th grade, meaning few months back, I've studied the potential and Kinetic energy (I was ignorant about the importance of calculus), but When I learned calculus, and the Constant of integration which is the initial conditions in physics. I remembered that also in the expression of potential energy we have :
$$E... |
During the review of some EM exercises I stumbled over a very interesting problem I just can't find the solution for.
Suppose we are looking at a waveguide with side length $\pi$.
The boundary condition are given as
$$\phi(x,y=\pm\frac{\pi}{2}) = 0$$
$$\phi(x=\pm\frac{\pi}{2},y) = U\cos(y).$$
The potential is constant... |
I am trying to understand physically why the air molecules at the nodes of a standing sound wave move around the least.
Is it because they act like springs? So the molecules at the nodes get compressed, by the molecules next to them. And the second they get the chance to start decompressing (and bounce off each other) ... |
I plan on making a large closed terrarium with a dry area and a wet area. How do I make sure that the evaporating water from the wet area does not condense into the dry area? I have found little to no info regarding this subject.
|
In solid state physics we might describe systems using second quantization and use the Bloch basis for the states of the quantum mechanical system. For example, to create an electron in band $n$ at $k$:
$$ a^\dagger_{nk}\left|0\right\rangle= \left|nk\right\rangle $$
My question is, how would a general annihilation oper... |
The expression for the first-order Born approximation to the scattering amplitude goes like
$$
f(\theta) \propto \int d^3 r e^{-i ( k - k_i)r} V(r)
$$
and so in particular the value of $ V(r) $ everywhere is relevant. However, if we want to consider for example scatters at $ \theta \sim 0 $ it would seem that the only ... |
As seen in Section 4 of Chapter 5 of Costello, K. "Renormalization and Effective Field Theory", or in section 5.2 $L_\infty$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism, the BV form of the Chern-Simons action is
$$S=\frac{1}{2}\langle A,dA\rangle+\frac{1}{6}\langle A,[A\wedge A]\rangle+\la... |
In the article I have been reading, we introduce the term "corrected diffusivity".
Diffusion alone and the rest of the article is pretty much clear, but I can't quite grasp the physical meaning behind corrected diffusivity.
The term is found in the Draken's equations which connects transport diffusion with corrected di... |
How the relation $\nabla_{a} u^{a}=D_{a} u^{a}-\epsilon v^{i} \nabla_{i} v_{j} u^{j}$ where $D_{a}$ is covariant derivate on the hypersurface
between 4-divergence and 3-divergence of the vector on the hypersurface is obtained?
Which book should I look into for hypersurfaces?
|
An infinitely large conducting sheet of thickness $d$ and of conductivity $\eta$ is uncharged. At an instant $t=0$, an external uniform and electric field $E$ is switched on. Due to this, the conducting sheet starts developing surface charge density $\sigma$. Now how do we find $\sigma(t)$?
For $\sigma(t)$, I think fi... |
I understand that the origin of atmospheric pressure is the weight of air.
Imagine if there is a cylinder consisting of two compartments separated by a frictionless piston filled with gas, the lower compartment should experience two types of pressure. One is from the weight of the piston; the other is the pressure of t... |
When discussing the cluster decomposition principle in Vol 1 of his QFT textbooks, Weinberg defines $S_{q'q}^C$ (connected part of the $S$-matrix) for single-particle transitions to just be $S_{q'q}$, which then says is equal to $\delta(q'-q)$. Here $q$ labels quantum numbers, so for example $\delta(q'-q)=\delta^3(\mat... |
In the lecture https://www.youtube.com/watch?v=-9G54aCkNH0 (or see https://www.theorie.physik.uni-muenchen.de/activities/schools/archiv/asc_school_14/komargodski_notes.pdf for notes), Zohar Komargodski begins by examining the Hamiltonian
$$H=\frac{1}{2}p_x^2+\frac{1}{2}p_y^2+\frac{1}{2}\lambda^2x^2y^2.$$
He argues that... |
A conical pendulum consists of a light string, with a length $$,
and a small ball with the mass $$. The ball moves with its
constant speed in a circular path with radius $$ in one
horizontal plane.
(a) What work does the string tension on the ball do then
the ball moves half a revolution from the position shown in
the ... |
When a paramagnetic material is placed in a strong external magnetic field, then you'll find that the magnetic momenta of the electrons in the material will align to the field, causing a net magnetic moment and magnetic field in the material. But why, instead of just aligning with the field, won't the electrons precess... |
I tried to make a plan for a turbojet engine with my physics knowledge and I'm stumped in the first step. For any sustained real engine, I need to somehow take a fraction of the energy output and use that to drive the engine into the next cycle. Take carnot cycle for example. For an engine based on that cycle, I need t... |
Because of uncertainty, you cannot measure both velocity and exact position. Is this because when you measure the position of a particle, it is freezing it in its frame of reference? When measuring velocity, you are measuring the particle as it moves through its frame of reference?
Would this mean that each moment in ... |
Consider a box sliding along a friction-less floor at a constant velocity.
Now typically atmospheric pressure is 14.7 psi on all surfaces of the object. But if it is moving at a constant velocity, wouldn't there be a void in the air on the backside as it displaces the air? So wouldn't the box feel that 14.7psi on the s... |
I know a neutron decays outside the nucleus into a proton and an electron and also that a neutrino has no charge but is there a particle that simply has no charge?
|
According to the uncertainty principle, certain pairs of physical quantities are complementary variables.
Wikipedia has a list:
Energy <> Time
Linear Momentum <> Position
Angular Momentum <> Angular Position
Mass-Momentum <> Rapidity
Electric Potential <> Electric Charge
Magnetic Potential <> Electric Current
Electric... |
Why is it that in M-theory, the 11-dimensional vectors are labelled with indices $0 \dots 9,11$. For example, the spatial momentum components are $p_{1}, \dots, p_{9}, p_{11}$. Why is the $10^{th}$ index skipped?
|
Consider the decay of a particle $X$ to two particles $c$ and $d$ in the rest frame of $X$.
Using energy and momentum (4-vector) conservation, show that the energy of particle
$c$ is given by:
$$E_c=\frac{\left(m_X^2+m_c^2-m_d^2\right)c^2}{2m_X}\tag{A}$$
and similary for $E_d$.
I have specific questions regarding th... |
Supposing a spaceship is moving in space in a straight line at very high speed, with a laser source on top of it flashing straight up (i.e. orthogonal to the spaceship's movement direction). Would the photons of the flash "inherit" the source's "lateral" movement and so travel continuously above the source (as if someo... |
Even though double well is a $\mathrm{1D}$ potential and it must not have degenerate spectrum, then why does double well have degenerate energy eigenvalue?
|
The other day I saw a green light emitted from some source far away, and I realised that if I looked at it out of the corner of my eye I perceived it completely white. What is the explanation for this? Should this be more of a biology of the human eye question perhaps?
|
Changes in the electric field makes changes in magnetic field and vice versa. What does this logically mean? It looks like an infinite loop. I don't understand how this helps the EM wave propagate. I don't quite understand Maxwell's equations because of my lack of vector calculus experience. But as far as I can tell, ... |
I am looking for an answer to the observation that a body always rotates about its centre of mass when freely tossed. It can be explained if the entropy is highest in the case when the axis passes through the com, however, I am unable to prove it.
I am doing this to be able to visualise the motion of a body in space, w... |
Let's suppose we have a point charge with no dimensions (zero volume and surface area) absorbing photons from Sun. Does it change the amount of photons and energy absorbed when we move the point charge close to, or far from the Sun? Since photons do not decrease in energy with distance and come one after another in a l... |
In electromagnetism, we have the continuity equation
$$\frac{\partial}{\partial t} \rho(\vec{r},t) = - \vec{\nabla} \cdot \vec{j}$$
which, upon integration over a finite volume $V$ bound by surface $S$ yields
$$\frac{d}{dt} \int_V \rho(\vec{r},t) = -\int_S \vec{j} \cdot d\vec{S}$$
The interpretation usually given of th... |
In Griffith's introduction to electromagnetism on page 479, there is this following equation:
\begin{align*}
\nabla V &\cong \nabla \left[\frac{1}{4\pi \epsilon_0} \frac{\boldsymbol{\hat r} \cdot \dot{\mathbf{p}}(t_0)}{rc} \right] \\
&\cong \left[\frac{1}{4\pi \epsilon_0} \frac{\boldsymbol{\hat r} \cdot \ddot{\mathbf{... |
I searched and viewed similar questions on here but still am very confused. Is it because of the observer's inertia? If so, shouldn't we feel a 'push' towards the point where we are actually accelerating?
Also, why would a small rock on a rotating disk be pushed towards the outside? The only force acting is inwards so ... |
I got confused while reading about the cosmological redshift.
Take an expanding Universe. If you look a galaxy moving with the Hubble flow, you will see the light of the galaxy redshifted. Suppose that you meassure the redshift and you get $z=z_{measured}$
In the image a telescope is placed in the middle of the circ... |
The standard (mathematicians') basis for the $\mathfrak{su}(2)$ Lie algebra is:
$$X_j = -i\frac{\sigma_j}2$$
where $\sigma_j$ are the Pauli matrices. In physics, observables correspond to real numbers, so following the standard procedure we convert these to self-adjoint operators, which have real eigenvalues:
$$X_j \ri... |
2D ising model explains phase transition (Para-ferro). How come a 2-D model explain a system where spins are distributed in all three directions?
|
When I want to calculate the entropy change of a system with two bodies with finite difference in temperature in an isolated system in thermal contact, do I calculate the whole difference in entropy as change in entropy generation or as change of entropy transfer or both?
|
In Rydberg Atoms book by Thomas F. Gallagher, Page 14, the author provides the general equation of spherical harmonics which is well-known. He states that there exist $l-m$ nodes in the $\theta$ coordinate, and none in the $\phi$ coordinate. The coordinate system taken by the author is given below in the figure.
I und... |
There was a fill-in-the-blank question in my university test. It was something like:
Quantum mechanics deals with ____
I wrote "everything" and my lecturer gave me no marks. He was expecting something like "small", "nano" or something. I tried to convince him that quantum mechanics deals with everything in the unive... |
Does tensor product of two Hilbert spaces explains interactions between the systems also? Or is it just the way to represent two spaces in a combined fancy way?
Let me make it more clear by an example. Consider two electrons in an atom. Can I explain whole system where electron are interacting by just tensor product of... |
The Maxwell-Boltzmann distribution provides information about the speed of particles of a gas:
Speed is actually kinetic energy which is connected to temperature via $ E_{kin} = 0.5 * m * v^2 = 3/2 * kT$. Hence, I wonder wether a spectral distribution can be expressed in terms of a Maxwell-Boltzmann-distribution? Is i... |
I'm reading "Relativity: The Special and the General Theory" by Albert Einstein. In the following extract:
Let us consider a space-time domain in which no gravitational field exists relative to a reference-body K. K is then a Galileian reference-body, and the results of the special theory of relativity hold relative t... |
What property of waves makes it unable to explain to the photoelectric effect, and how does that property make the wave theory fail in explaining the photoelectric effect?
|
Consider a simple resistance circuit with a cell and a resistor. It is stated that energy stored in cell appears as heat in resistance as current flows in ideal circuit (neglecting EM radiation) as whole.
POWER/RATE OF HEAT GENERATION = POWER/RATE OF ENERGY CONSUMPTION in CELL = VI
However we also know that flowing cur... |
I have a Hamiltonian of the form
$H = 2k(\alpha \alpha^* -\beta \beta^*) -2\lambda (\alpha\beta^* + \beta \alpha^* )$
and I'd like to decouple the $\alpha$'s and $\beta$'s if possible. I know I need to diagonalise the Hamiltonian, like this:
$H = (\alpha, \alpha^*, \beta, \beta^* ) \begin{pmatrix} 0& k & 0 &-\lambda \\... |
I am working through Leonard Susskind's The Theoretical Minimum: Quantum Mechanics. In this book a statement called the "spin-polarization principle" is introduced, which essentially states that:
For any state $|A \rangle$, there exists a direction vector $\hat{n}$ such that $\vec{\sigma} \cdot \hat{n} \, |A \rangle = ... |
Why equation of wave is written like $Asin(\omega t-kz+ \phi)$ , why $\omega t - kz+ \phi$ as domain of sine, how somebody came up with this kind of equation to represent a wave?
|
I am running an experiment where I have a vacuum chamber attached to a vacuum pump and a pressure sensor: I use the pump to vary the pressure in the chamber between atmospheric and 1/16-th of atmospheric pressure.
I have been considering using a different gas for the pump apart from air (probably helium or argon), so I... |
I have been trying to calculate the wavenumber for the 2p -> 5d transition in hydrogren. Using the formula: $ R_H (\frac{1}{n^2_f}-\frac{1}{n^2_i}) $ would give me a negative answer. I have never seen a negative answer to this type of question before, but though it feels intuitively wrong I can't think of why this woul... |
I am reading Mukhanov and Winitzki's book Introduction to Quantum Effects in Gravity and in second paragraph of Sec. 1.4.2 they say that : The spontaneous emission by a hydrogen atom is the transition between the electron states $ 2p \rightarrow 1s$ with the production of a photon. This effect can be explained only by... |
In David Tong's lectures on Electromagnetism, the current density is defined as $\vec J=q\rho \vec v$, where $\rho$ is the density of particles with charge $q$, and $\vec v$ is the average velocity. This should be the area density, and not the volume density right? It seems that Tong is assuming that this is the volume... |
I've been dealing with a couple of questions regarding Bohr's model except where the mass of the nucleus is not negligible compared to the mass of the (revolving) electron. According to my book (Physics for JEE Advanced by B.M. Sharma), you're supposed to derive the regular formulae for radius of the nth orbit and ener... |
I searched Physics Stack Exchange and google and could only find wordy articles on this, but what I am after is the actual mathematical calculation. I took General Relativity in Physics, and I tried calculating the radius of the visible universe myself, but my calculation is not quite right. What am I missing? My calcu... |
I'm solving this particular question (refer to image) in which a rod is released from equilibrium after one of the two springs to which it is initially connected is disconnected. In order to calculate the angular acceleration, I have used the torque and moment of inertia about (a) the centre of mass and (b) the pivot p... |
I learnt about the basics of RC circuits, taking a simple case of only a resistor and a capacitor connect in series to a battery.
But following this I faced several questions which involved a more complicated arrangements of resistors around a single capacitor.
My teacher and all the online articles I read told me to f... |
I try to calculate the radius of the rolling coin. The task was found in physics book https://www.amazon.co.uk/General-Course-Physics-1-Mechanics/dp/5922102257 (only in Russian). But unfortunately my solution leads to the answer that differ from the answer provided in the book (by coefficient 3). I am trying to figure ... |
I have a question about the number operator as applied to a quantum gas containing a mixture of different spins. Let us say the total number operator $\hat{N}$ counts the total number of particles in a state, which we define in second quantization by the usual expression, $$\hat{N} = \sum_{rs}\sum_{\alpha \beta} \langl... |
In the framework of QFT, quantum fields are the fundamental objects instead of point-like notion of particles. Particles, at least fundamental ones like electron, are understood to arise as excitations of the quantum fields.
We know from experiments that a stationary free electron has some electric field associated wit... |
Peskin and Schroeder's QFT book in equation (2.33) gives the momentum operator $\bf P$ as
$${\bf P} = - \int d^3 x \pi(x) \nabla \phi (x) = \int \frac{d^3 {\bf p}}{(2\pi)^3} {\bf p}a_{\bf p}^\dagger a_{\bf p}$$
where $\pi(x)$ is the momentum density conjugate of $\phi(x)$, the Klein-gordon field.
$$\phi(x) = \int \frac... |
Basically, an electric charger consists of a transformer, which transfers electrical energy from one inductance to another..
َAs i imagine the process physically the first circuit (inductance) should produce the same amount of magnetic flux, either the second inductance exist or not.. so, theoretically the electric co... |
So, I was told in my class that Safety devices like fuses should be connected on the live wire. But isn't the conventional current opposite to the direction of the flow of electrons? And what actually happening is that electrons are flowing into the load from the neutral wire? So how does that add up?
|
The near-range magnetic field $\vec{B}$ of a point charge $q$ at distance $\vec{r}$, moving at a non-relativistic velocity $\vec{v}$, is given by
$$\vec{B}=\frac{q}{4\pi\epsilon_0c^2}\frac{\vec{v}\times\hat{r}}{r^2}.$$
Faraday's law of induction for the induced EMF $V_c$ in a coil, with area $A$ and turns $N$, due to ... |
My question is rather straight forward, but the setup in order to pose the question is a little lengthy; please bear with me!
I am trying to calculate the average over initial states and sum over final states for Compton Scattering, using spinor helicity techniques. I'm having some trouble getting the amplitudes indepe... |
While working on a completely unrelated quantum computing problem, I ran into a quantity that can be mapped to a partition function of spins on a triangular lattice. It is not quite an Ising model, though, since interaction happens between triplets of spins, some configurations are not allowed, and I don't explicitly h... |
When a constant current is applied to a battery, its voltage jumps by a huge amount in a moment. It jumps up if we apply constant charge current and down if we apply constant discharge current.
I know about this effect from some papers and studying materials. For example, this picture illustrates Hybrid Pulse Power Cha... |
For a quantum harmonic oscillator in a coherent superposition, what happens if the energy is measured? Would it collapse to an energy eigenstate (a single excitation) corresponding to the result of the measurement, thus destroying the coherence? Similarly, for a quantum field in a coherent state (classical EM field wav... |
I need a very small amount of 2 cSt liquid for an experiment I am doing, but I only have 5 cSt oil and water which has viscosity of 1 cSt.
Is it possible to mix the two up in the right proportion and so end up with some 2 cSt liquid (say 50 ml or something like that), it just needs to be enough to fill a teacup.
|
Part 1: First of all, I wish to discuss my idea of electromagnetic fields. I have it this way that fields are simply Mathematical tools developed for analyzing the (forces and energy) associated with a system. I consider it would have been perfectly fine (but extremely difficult) if we had described the system directly... |
Particle Interactions: How come a photon cannot "give" partial energy while interacting with an electron fundamentally (with high probability) (as apposed to electron-electron interaction)?
for example:
An electron in an atom has 5 energy levels : $E_0$, $3E_0$, $5E_0$, $7E_0$, $9E_0$
light in certain wave length $\fra... |
first post here.
I've just started on George Sutton & Oscar Biblarz's Rocket Propulsion Elements and have stumbled upon contradictory solutions between the Eighth (PDF linked) and Ninth Edition (my hard-copy version) and would like someone to tell me which is wrong. I think the latest version is erroneous.
In Chapter 2... |
I am not well-versed with the theory of renormalization of QFT as of now (I just know that when you redefine your observables you get rid of the UV divergences and then get finite predictions from your theory) so this question might not make any sense.
When we do QFT in curved spacetime as described in sec $2.1$ of Par... |
I recently watched Sean Carroll's YouTube series on "The Biggest Ideas in the Universe". In his Geometry and Topology video, he says that the connection in Riemannian geometry describes how a vector gets parallel transported through the geometry.
I looked more into it and found that the Christoffel symbols are an array... |
At the Schwarzschild radius, the escape velocity is the speed of light for all objects. However, I'm looking for an equation that will calculate the escape velocity as the radius of the object increases from its Schwarzschild radius, while keeping its mass constant.
|
When one deals with a dispersion relation of the form
$$\epsilon(\vec{k})=\epsilon(|\vec{k}|)$$
then a simple transformation in polar/spherical coordinates is enough to find the density of states.
I read that for electrons in an arbitrary dispersion relation the DOS is given by
$$D(\epsilon)\propto\int_{\epsilon(\vec{... |
Einstein's General Relativity says gravity warps spacetime. Consider a hypothetical scenario:
A person travels into space from Earth.
He landed on a different planet in some far off galaxy where time runs slower than Earth. 1 hour on that planet is about 7 years on Earth. The person does not know anything about time d... |
Given a manifold, we can generalize the idea of derivatives in multiple ways: two of them being the Lie derivative and the covariant derivative. Whereas Lie derivatives do not require any additional structure to be defined on a manifold, covariant derivatives need connections to be well-defined. Also, Lie derivatives a... |
I know that black holes maintain the linear momentum of the object that created it. But if I throw a baseball into a black hole, will it absorb that momentum as well?
I think the answer has to be "yes" because momentum needs to be conserved, but I am having trouble getting my head around how a black hole can react to m... |
Mass = Force / acceleration (in this one the speed is changing through acceleration)
and
Mass = Energy / $c^2$ (in this one the speed is constant)
In both of these, there is a time component that I can't grasp. Beyond just reworking the formulas, how or why does mass change with time in both of these?
|
I understand the Laue condition (and the equivalent Bragg condition). I also understand the rotating-crystal method for analyzing crystals.
But I have a hard time to understand why in the Laue method a point like interference patterns emerges. It has something to do with reflection cones, but I can't get my head around... |
I have read on my physics book that the electric field due to an electric dipole varies as $1/r^3$ and I have also seen the for it . But how can I physically understand the $1/r^3$ nature of the field?
|
Presume there is a satellite orbiting the Earth in an orbit that follows a closed path around the planet (that is, escape orbits are not permitted here). As I understand it, there are two possibilities, ignoring the massive timescales that this might require:
The orbit can decay due to the action of the atmosphere
Th... |
I couldn't find any papers/articles addressing this particular issue. To elucidate, my question is the following,
Question: Given the maximally symmetric nature of AdS space-time, we also have that it is homogeneous and isotropic. Does the former imply translation symmetry (globally or locally)?
Either way, since far a... |
p.s. I am trying to get a handle on what actual computing operations a quantum computer program does. Any information on that would be appreciated [noting the issue that that might count as a separate question].
I have been watching the video “Quantum Computing for Computer Scientists” (https://www.youtube.com/watch... |
These notes on Electromagnetism (chapter 3.1.2, section "A Solenoid") say the following:
We solve Ampère's law in differential form. Anywhere other than
the surface of the solenoid, we have $\mathbf{J}=0$ and
$$\nabla\times\mathbf{B}=0\quad\Rightarrow\quad\frac{dB}{dr}=0\quad\Rightarrow \quad B(r)=\text{constant}$$
W... |
A spring with $N$ turns radius $R$ and spring constant $k$ with initial length $L$. Current $I$ is flown through it. Find the amount of compression in the spring.
I first tried this question using conserving energy and taking spring as an inductor. Initial magnetic energy $=$ final magnetic energy + spring potential en... |
I am a little bit confused how the electric field produced by dipole $P_1$ at $\vec{r_2}=(\ell,0,0)$ is equal to $\boldsymbol{E}_{1}\left(\boldsymbol{r}_{2}\right)=-\frac{k p_{1}}{l^{3}} \hat{z}$
and the electric field produced by dipole $P_2$ at $\vec{r_1}=(0,0,0)$ is equal to :$\boldsymbol{E}_{2}\left(\boldsymbol{r}... |
$\newcommand{\d}{\mathrm{d}}$In $d=2p+1$ dimensions one can have topologically massive $p$-form abelian gauge fields $A\in\Omega^p(X_{2p+1})$ by considering a Maxwell–Chern–Simons action:
$$S[A] = \int_{X_{2p+1}} \frac{1}{2g^2}\d A\wedge\star\d A + i\frac{k}{2}A\wedge\d A. $$
In this case, it is easy to show that the g... |
I have a problem in mind. There are 2 particles in a box. If they are distinguishable, there are 4 microstates represented by the picture below. If the particles are indistinguishable, there are only 3 microstates available (since the two states that are the lowest on the figure are the same state).
What I find strange... |
I was trying to intuitively understand the covariant and contravariant bases for a coordinate system and I came across this image on Wikipedia:
Edit: After reading the first two answers I think I may have not posed my question correctly so I have changed it a bit. I understand that vectors and dual vectors are vastly ... |
I'm reading Schwartz QFT, Chapter 18 (mass renormalization) and I'm confused about the equations about on-shell subtraction/pole mass. He writes:
The renormalized propagator should have a single pole at $\not p = m_P$ with residue $i$. The location of the pole is a definition of mass.
But $\not p$ has two spinor indi... |
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