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I was reading about the method of image charges, where they've (Irodov) mentioned an "infinite conducting plane". Is this just like an infinite sheet, or does it cover one half of the space?
The reason I'm confused is because its also given that the electric field of the fictitious charge is absent in the half-space it... |
Say we got conducting circular loop connected to a battery . The electric field inside the loop obeys equation $\vec{J}=\sigma \vec{E}$.
Since the current flows in a circumferential way around the loop the electric field will be circumferential as well which implies that the curl of the electric field will be non zero... |
What is the proof that we can use the location of virtual image in the lens formula to get the location of the image (convex/concave lens)?
The following problem might make my question more clear. The proof for the case of plane mirror is quite easy using ray diagrams but I'm getting contradictory results when I try to... |
I was just exposed to this concept in class, that the electric potential across a capacitor is zero after a long period of time, but it was never explained why. This is for an RC circuit.
|
In modern electrodynamics by Andrew Zangwill chapter 14, section 14.13.2 an analysis of RLC circuit is shown where Fourier transform of current, EMF, and impedance is used. And equation is $\hat{E}(\omega)=\hat{Z}(\omega)\hat{I}(\omega)$. Then it says in equation 14.148 that the physical current driven by a real electr... |
Heisenberg's uncertainty principle relates energy and life time $\tau$ of a particle as follow:
$\tau=\frac{\bar{h}}{1+x^2}$
Here energy is approximated as $1+x^2$ where $x$, the velocity of particle, varies from $0$ to $c$.
It means that particles with lower energy will have longer life time.
If I choose a particle at... |
I am currently reading S. Sachdevs Book on Quantum Phase Transitions focusing on the Bose-Hubbard Model (Chapter 9) and especially the Dilute-Boson Field Theory (Chapter 16).
When describing the fluid phase of the one dimensional model Sachdev says that this phase has quasi-long range order in the superfluid order para... |
Let $A$ and $B$ be two systems that does not interact initially ($t=0$), i.e., the density matrix of the initial total system is given by $\rho(0) = \rho_A (0) \otimes \rho_B (0)$. Suppose that interaction between the two systems is turned on after $t=0$. Then the density matrices of each system can be obtained by part... |
The General Setting
I have some confusion concerning the interpretation of the field-theory describing the Bose-Hubbard Modell especialy in the one dimensional case.
The general framework of the action describing the critical behaviour is the following:
$$\mathcal{Z}_B = \int \mathcal{D}\Psi_B(x,\tau)\exp(-\int_0^{1/T}... |
Two blocks of masses $2$ kg and $4$kg are connected through a massless inextensible string. The coefficient of friction between $2$kg block and the ground is $0.4$ and the coefficient of friction between $4$kg block and the ground is $0.6$. The forces $F_1=10N$ and $F_2=20N$ are applied on the blocks as shown in the f... |
My question has been asked two other times:
Spinor vacuum energy (misleading title) and
Vacuum Energy Calculation using Path Integral. I am not completely satisfied with the answers and it looks like they both have errors in their algebraic steps. Since it has been asked twice, I hope you will look at my VERY DETAILE... |
The reference that I checked shows that Neon has an excitation energy of 18.2 eV, while mercury has 4.9 eV. However, the reference also shows that the wavelength emitted by the mercury is at the ultraviolet range of the electromagnetic spectrum (254 nm precisely). How could this be, despite Neon having greater excitati... |
It is often said, that qubit should be maintained under very low temperature and kept highly isolated not to decohere.
But we can represent $|0\rangle$ with vertical polarization of light and $|1\rangle$ with horizontal polarization of light. The the superposition $\frac{1}{\sqrt{2}}|0\rangle +\frac{1}{\sqrt{2}}|1\rang... |
I have been issued a task to create a roller coaster comprised of a piecewise function. In my research I have come across the an equation to calculate the final velocity of the cart found at https://www.teachengineering.org/activities/view/ind-1996-frictional-roller-coaster-design-project-calculus.
\begin{equation}
v_f... |
I know how to write the matrix for the operator $S_y$ in the $\{|{↑}_z\rangle , |{↓}_z\rangle\}$ basis, but I don't understand how to write it in the $\{|{↑}_x\rangle , |{↓}_x\rangle\}$ basis.
Wouldn't the calculation become very complex? Any help will be appreciated.
|
I am currently studying special relativity mainly using this paper which uses spacetime diagrams to derive the formulas for the properties of special relativity (Time dilation, length contraction etc.).
In chapter II, the "Doppler k-Factor" is derived as $$k=\sqrt{\frac{1+\beta}{1-\beta}} \tag{9}$$ where $\beta=\frac{V... |
I have been trying to find the energy distribution of virtual particles i.e. to know what percentage of virtual particles would lie in a given velocity range.
Couldn't find anything on net and tried using Heisenberg energy-time relation to model it but it turned out to be wrong. See here.
Any help in this matter will b... |
I am trying to numerically solve the orbit of a space probe around the moon in a non-spherical gravitational field .
$
\Large
\begin{align}
\frac{d^{2} x}{dt^2} = - \frac{G M x}{(x^2 + y^2)^{3/2}}
- \frac{q\ G M x^\prime}{(x^{^\prime2} + y^{^\prime2})^{3/2}}
\end{align}
$
$
\Large
\begin{align}
\frac{d^{2} y}{dt^2} = -... |
State functions seem to always be described as relating state variables in equilibrium, wikipedia about state functions:
In thermodynamics, a state function, [...] is a function defined for a system relating several state variables [...] that depends only on the current equilibrium thermodynamic state of the system (... |
This seems like a simple question, but I cannot wrap my head around it. If $\hbar = c = 1$ then length is time, and mass is inverse length or inverse time. Hence $G$ should have dimensions of length squared or time squared or inverse mass squared. But what would be its numerical value (since that is not set to 1) in th... |
If we have two angular momenta, $j_1$ and $j_2$, which couple to the total angular momentum $J$, we can choose between two sets of basis systems,
$$ (j_1,m_1,j_2,m_2)\;\text{ vs. }\;(j_1,j_2,J,M). $$
The second one is useful, because $J$ being the total angular momentum of the system corresponds to a conserved quantity... |
Question statement:
A rocket is moving in a gravity free space with a constant acceleration of 2ms−2, along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of 0.3ms−1 relative to the rocket. At the same time, ... |
Why does the LASER beam quality factor (M^2) use squared value? Why not using just M?
i.e., Why define beam quality factor as
$M^2 = \frac{BPP_{Real}}{BPP_{fundamental}}$
not
$M = \frac{BPP_{Real}}{BPP_{fundamental}}$ ?
Is there any particular reason to use squared M?
|
I was reading about the Biot-Savart law and there were two formulas stated in the textbook.
One was stated as the Biot-Savart law
and the other was stated as the field due to a long, straight wire
My question is what is and why is there difference between two formulas.
|
I have to show that two eigenfunctions of an electron in a 1 dimensional infinite square well with different parity and different quantum numbers are orthogonal. I am attempting this by integrating the product of the two eigenfunctions
$\psi_n=A_n \sin(\frac{nx\pi}{a})$,
with $n_1$ and $n_2$, which are not the same. Am... |
We are given an action of the form:
$$S=\int d^4x\sqrt{-g}\left(-\frac14F_{\mu\nu}F^{\mu\nu}+V(B_{\sigma}B^{\sigma}) +R\lambda B_{\mu}B^{\mu}\right)$$
where $R$ is the curvature scalar, $\lambda$ is a constant, $F^{\mu\nu}=\partial_\nu B_\mu -\partial_\mu B_\nu$ is the field strength tensor and $V(B_{\sigma}B^{\sigma})... |
I have been told that potential in an electric circuit is defined as the work done in bringing a unit test positive charge to that point inside the circuit. Thus it satisfies the premise that potential at the positive terminal is greater and keeps decreasing as we move away from it.
Near the negative terminal work done... |
The equations for the potentials in E. M. are
$$\nabla^2 \phi + \frac{\partial}{\partial t} \left(\nabla \cdot \textbf{A} \right) = -\frac{\rho}{\epsilon_0} \tag{1}$$
$$\nabla^2 \textbf{A} - \frac{1}{c^2} \frac{\partial^2 \textbf{A} }{\partial t^2}-\nabla \left( \nabla \cdot \textbf{A} + \frac{1}{c^2} \frac{\partial \p... |
I am trying to understand the calculations of the latest Charles Dalang's paper "Scalar and Tensor Gravitational Waves", arXiv:2009.11827.
Since I just learned basic general relativity, I found it hard to prove equation (13) in that paper.
Here is my calculation for the variation of scalar field $\phi$ for ${\Large\var... |
Background: It is well known that the Schrodinger equation is equivalent to the Euler equation (with a "quantum potential" term) plus the probability conservation equation (which is formally identical to the mass conservation equation of the usual hydrodynamic theories). Establishing this mapping is quite simple and it... |
How much energy (watts) from sunlight could arrive to the focal point if we use Jupiter as a gravitational lens? and if we use it as an atmospheric lens by using refraction?
How far the focal point would have to be placed for each case?
Ps.: if no energy reached the focal point, then how much energy would reach if we u... |
A rigid block is tied to a practically inextensible string with no slack to a wall. The max value of static friction is 10N. An external force of 12N is applied to the block pulling it away from the wall. We have to calculate the tension and the friction force on the block to keep it at equilibrium.
Attempt: I'll assum... |
Consider a transformation from Cartesian to polar coordinates $(x,y)\rightarrow (r,\theta)$,
\begin{equation}
\begin{gathered}
x=r\cos\theta,\\
y=r\sin\theta.
\end{gathered}
\end{equation}
Here, we denote $x^{\,\mu}=(x,y)$ and $\bar{x}^{\,\mu}=(r,\theta)$.
Now, The question is the following,
In ... |
The topic is matrix elements in linear operators. When I read through the text, I found that the indexing used for $\Omega $ did not match the results of matrix multiplication given at the bottom of the page. The author abruptly switched from $\Omega_{ji}$ (equation 1.6.1) to $ \Omega_{ij}$. I have tried correcting (w... |
I know the difference between first and second order phase transition in terms of the discontinuity of the derivatives of free energy.
I am curious to know what happens as the system is viewed. Suppose a liquid is heated in a container. For a first order phase transition, a liquid, which has a finite volume (but takes ... |
A loop is moving down with some part of it in a constant magnetic field pointing into the screen as shown.
We know the emf due to magnetic force is given by
$\mathcal{E}=-\frac{d \Phi}{d t}$.
If the loop has a total resistance of $R$ then why is it that the current in the loop will be
$I=\mathcal{E}/R$.
|
I am trying to evaluate an integral in light-cone coordinates
Where light-cone coordinates in 1+1D are defined by
$x^+=\frac{x^0+x^1}{\sqrt 2}$ and $x^-=\frac{x^0-x^1}{\sqrt 2}$.
The integral that I need to evaluate is
$$\int dk^+dk^-e^{-\imath k\cdot x}\frac{1}{-2k^+k^-},$$ can have any method to do it,
If not can we... |
When we experiment with General Relativity on Earth, a tissue bends according to the experiment due to the placement of a mass, but of course there is a gravitational pull that causes bending. If we did the experiment outside the Earth, the tissue would not bend and the masses would not attract.
|
I will post a image elucidating what is my doubt. I think it is more interesting to post it than to just write the equations used in the text because maybe I am losing something in the lecture.
See the equation 1.3.5, why it is written in this way? That is, following the previous equations, shouldn't be $\left \langle ... |
For any system performing any kind of motion with $n$ degrees of freedom, are $2n-1$ integrals of motion and also $2n$ constants of motion always present? If yes, then is there always a symmetry for each constant? Can the initial conditions be thought as those constants? There are related questions but all have heavy m... |
The question in particular pertains to Section D.1 of https://arxiv.org/abs/2005.04234. In this section, they have written the conformal generators of 3d in terms of the spinor-helicity variables. Unfortunately, these generators seem to be useful for conserved currents and scalars of conformal dimension 2. How does one... |
If we take the common Otto cycle we have two isochoric and two adiabatic processes, plus exhaust & intake stroke.
Would it be more efficient to do the following:
Instead of cutting off the adiabatic expansion at a certain volume, continue with the expansion until the internal pressure equals the external pressure?
Us... |
I am aware of the relationship $N = V/h^n$ where $N$ is the quantum multiplicity, $n$ is the number of position (or momenta) degrees of freedom, $V$ is the volume of classical phase space and $h$ is planck's constant. What I don't know, however, is why this formula seems to work. I've seen the derivation (several ways,... |
In Polchinski String Vol 1:
Chiral gauge couplings. The gauge interactions in nature are parity asymmetric (chiral). This has been a stumbling block for a number of previous unifying ideas: they required parity symmetric gauge couplings. String theory allows chiral gauge couplings.
What are the approaches from String... |
`Suppose there exists a refrigerator that lowers the temperature of one kilogram of the ocean water by one degree. If the temperature difference between the two sources is 1$^\circ$C. Is it possible to know how much work is required to get it?
|
In textbooks, Bernoulli Equation and Continuity Equation are typically used with Fluids. It's unclear how they can be applied to air flows.
Once thing I noticed is that since $\rho$ is very small for air, so we typically ignore the term ρgy in Bernoulli equation.
In the example of Pitot tubes below, I can understand th... |
It is possible to get the Schwartzschild metric assuming spherical symmetry, vacuum solution and Minkowski spacetime when $r \to \infty$.
Is it possible an analytic solution for a geocentric system? I mean, taking the apparent daily movement of the celestial bodies as real. So, the (apparent) trajectories of moon, sun ... |
I am quite confused by the Brillouin zones. I know there is a dispersion relation $E=E(k)$ for the first Brillouin zone. But is this dispersion relation periodic across different Brillouin zones? Thinking in one way that larger $k$ should give rise to larger energy tends me to think that in higher-order Brillouin zones... |
I'm not a native speaker, and this question is about "how to say it in English".
Consider a 2D electronic waveguide. Wavefunction $\psi(x,y)$ can be written in form of separated variables $\psi(x,y)=U(x)V(y)$.
Now we add boundary conditions related to $y$-axis. Spectrum of $V(y)$ becomes discrete with energies $E_n$.
... |
If the external force has a line of action through the center of mass then friction behaves as it does normally; backward to motion:
But, if the force's line of action does not pass through the center of mass.. then something strange happens:
The book I am referring to explains this by the idea that balances out torq... |
The problem statement is given verbatim
In Si, the dispersion relation at the [001] X points is: $$E=\frac{\hbar^2}{2}\left(\frac{k_x^2+k_y^2}{m_t}+\frac{(k_z-G)^2}{m_l}\right)$$ where G is the reciprocal lattice vector at X points. Find the total density of states for the X points in silicon.
So my question is: how do... |
A spherical rain drop, falling in a constant gravitational field, grows by the absorption of moisture from the surrounding at a rate proportional to its surface area. If it starts with zero radius, find its acceleration.
My attempt
My assumptions are $m$ is mass of the rain drop, $r$ is the radius of the rain drop, $... |
Lets say I have two frames, $S$ and $S'$; they are in standard configuration and $S'$ is moving with speed $v$ away from $S$. I have a pipe in $S'$, which is at angle $\theta'$ from its $x$ axis. I can calculate the angle which would be measured between the pipe and the $x$ axis in $S$: $\theta$. I note that $\theta \n... |
In the topic of small oscillations, the system below has a normal mode described by:
$$n_{1} = \frac{x1+x2}{2}.$$
This normal mode is represented as the symmetric mode:
In that case, the center of mass moves as a simple harmonic oscillator. However, the picture also shows that both of them start in the same initial c... |
I have always heard that you can't get a quark by itself because "the energy required to split them apart is enough to create another." But, in the case of The Big Rip, the idea is that phantom dark energy would tear molecules and atoms apart because it's a much stronger variant of dark energy. So in this case, would p... |
I am curious if there are any alternative formulations of QFT generally, in the same way that QM can be reformulated into different, but equivalent formulations beyond Schrodinger wave mechanics and projectors on abstract Hilbert spaces?
Even if "traditional" QFT is the most useful form to use, I still think it would b... |
I am solving Statics and stuck in middle of a trivial understanding.
Let us say we have two like parallel forces acting on a rigid body. Force $P$ has point of application as A and Force $Q$ has point of application B. Something like this:
How do i prove that the resultant $R$ lies such that
$$P \cdot AC = Q \cdot BC$... |
The following results summarize the relation between orientifold and D-brane, and SUSY charge
$$
\begin{array}{l||c|c|c|c|c|c}\text{orientifold} &\text{O4} & \text{O3} & \text{O2} &\text{O1} & \text{O0} \\
\text{D-brane involved} & \text{D2} &\text{D3} & \text{D4} &\text{D5} & \text{D6}\\
\text{SUSY on the D-brane} & ... |
A Lorentz transformation can be seen as a change in reference frame. So, after apply a Lorentz transformation to a system (or change the reference frame), how should the state and field operator change? I can't find a book which introduces those things very well. I am considering three kinds of possible explanation. He... |
For my electrical engineering senior design I created an experiment to test magnetic flux (more voltage) increase from a material in a coil of wire. There is a large sending coil with A.C. voltage and a small receiving coil with an oscilloscope measuring voltage_pp. Its wireless power or those experiments were they lig... |
Electrons have very small mass and they are charged particles so they can be accelerated using strong electric fields. Also the mass of the electrons' mass will change significantly if it is accelerated to a speed comparable to the speed of light. Now I am wondering what will be the effect of that increased mass and th... |
I mistakenly poured water on my the area of my TV remote which has the cell and apparently the circuit connections.A thing to ponder is that why doesnt a circuit work when it becomes wet , despite it being a good conductor. I see this in case of modems , telephones
I searched on net and it said that water provides an ... |
In the arrangement shown in the figure the ends P and Q of an inextensible string moves downward with uniform speed u. Pulleys a and b are fixed. The mass M moves upwards with what speed?
How can v be u/cos(theta) as v should be vertical component of velocity u hence v should be u cos(theta)
|
Figure shows a loop falling down through a constant magnetic field which points into the screen.
Due to the Lorentz Force a magnetic force is present on the top part of the wire which pushes the charge and hence a current flows. This current circulates in the loop which obeys
$\vec{J}=\sigma \vec{f}$
There is no compon... |
This answer to a question about why Newtonian kinetic energy is quadratic in velocity shows that if an inelastic collision's KE loss is invariant under Newtonian boosts it has to quadruple when velocity doubles. A simple calculation shows that the famous $\tfrac12mv^2$ formula implies invariance of this loss. If a mass... |
I am a high school student and I am curious about the word moment and what it means in different contexts, whether it has a definite meaning or not?
I know it has some relation to different kinds of motion, like linear momentum (measures the "amount of motion" in a rectilinear path) or angular momentum (circular or hyp... |
The anti-commutation relations for Gamma matrices $\big\{\gamma ^\mu , \gamma ^\nu \big\} = 2g ^{\mu \nu} $ can be used for interchanging positions of the respective matrices in a given expression, for example : $-i\gamma ^\mu \gamma ^2 \gamma ^0 = i\gamma ^2 \gamma ^0 \gamma ^{\mu} $. Question - Do we have any similar... |
Why is the direction of cross products of two vectors perpendicular to the plane? How is that possible?
|
In the diagram the fixed pulley is ideal and the moving pulley is not
Therefore the tensions holding the movable pulley are different
My question is if the acceleration of the block is $a$ what is the acceleration of the movable pulley?
I'm able to comprehend it is $a/2$ when the movable pulley is ideal (with mass)
Bu... |
I'm currently in my second year of master.
From what I understand, in QFT, Noether's first theorem implies that for any continuous symmetry (i.e. associated to a $n$-dimensional Lie group $G$, $n\geq 1$), there are $n$ corresponding conserved currents and thus $n$ conserved charges.
From this question, I understand tha... |
A covalent bond, also called a molecular bond, is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding.... |
According to the equivalence principle, a freely falling observer constitutes an inertial frame. Thus, locally, Maxwell's equations apply in their usual form. According to these equations, an accelerated charge should radiate electromagnetic energy. But in this frame, a stationary charge on the earth does indeed accele... |
When you connect, let's say, three photodiodes or solar cells, with a load, and you measure the voltage across the middle photodiode. Will the voltage change if
the adjacent cells are in the dark
if they wouldn't be there at all?
(and how would it change?)
Would there be no bias at all?
|
My teacher gave the following definition while teaching chapter "Center of mass":
"It is defined as the product of mass of the particle and distance of particle from point about which mass moment is taken"
I could not understand this, so I searched the internet and found a common definition:
" the moment of inertia is ... |
If a force is applied tangentially to a rolling body then the equation relating the friction which comes into existence to prevent sliding and the force is:
$$ f_s = \frac{MR^2 - I}{MR^2 + I } F$$
This means that for a hollow cylinder/ring, the total friction force is zero (their $I= MR^2$).. but how? What makes their... |
Mathematicians have done a complete classification of all possible Lie groups. Is there a set of conditions that allows us to identify which Lie groups from the classification can possibly act as a gauge group for a Yang-Mills theory?
My vague recollection from a book that I can't recall is that the direct/semi-direct ... |
In Statistical thermodynamics Maxwell-Boltzmann statistics is considered a pre-quantum statistics. However in the mathematical treatment in all textbooks, and also in Wikipedia article, there is the concept of 'energy level' ($E_i$) involved in it. As far as I understand, energy level implies a quantization, which obvi... |
Could anyone please help me with this derivation? I am struggling to see how the Propagator
Can be expanded out into the form
This is a non-degenerate two-level system.
Any help would be greatly appreciated!
|
I have a question.
I have seen Heisenberg's equation of motion for observables:
$$\frac{dA}{dt}=\frac{1}{i\hbar}[A,H]+\frac{\partial A}{\partial t}.$$
However if I want to calculate for example the mean time dependence of an operator in the Schrödinger picture then I arrive at the following:
$\langle A(t)\rangle=\langl... |
So in my QFT course, my professor said that you can set $c$ and $\hbar$ to 1. And he gave us an example:
$$E = mc^{2}$$
And then set $c = 1$:
$$E = m$$
This seems completely ludicrous to me to do. Doesn't it change the result? Why can this be done and why isn't it wrong?
I mean, $E = mc^{2}$ gives you one answer and $E... |
Stefan's law tells gives an expression for thermal radiation emitted per unit time by a body of surface area A and temperature $T$
$$ u = \sigma A e T^4$$
In my book, it is written that in thermal equilibrium the energy of a body radiated out by stefan's law is equal to the energy radiated out. So, if a body is init... |
I have been using this specific heat calculator to calculate the energy in joules needed to cause a change in temperature in a mass of water https://www.omnicalculator.com/physics/specific-heat
The calculator requires the following values to be entered -
The desired change in temperature
The mass of material being he... |
Light after getting reflected from objects gets focused on retina by our lens. The images formed on retina is small, which is then sensed by our brain and depending on distance we feel size of that object.
If an object is at particular distance from us, the image on retina is not going to be the exact size which we fee... |
We have the following Hamiltonian
$\hat{H}=a|u_{1}\rangle\langle u_{2}|+a|u_{2}\rangle\langle u_{1}|$
with a $\in \mathbb{R}$ and $|u_{1}\rangle,|u_{2}\rangle$ an orthonormal system
The matrix representation of $\hat{H}$ in that system is
\begin{pmatrix}
0 & a\\
a & 0
\end{pmatrix}
the eigenvalues are a and -a, and the... |
In a paper by Turaev, he studies systems with a slow variation of parameters.
The following is on page two, right column:
He first discusses the one dimensional particle in a box, with ends at $x=-1$ and $x=a(\tau)$, where $a$ is periodic with period T in the slow time variable $\tau$. One assumes the validity of the a... |
To obtain images using a single-pixel camera we need a Digital Micromirror Device (DMD) because single-pixel cameras only possess a single detector (article).
From my understanding, a single-pixel detector can only detect the intensity of a single spatial point, whilst an array of detectors would be able to recreate th... |
Consider an electron is in a one-dimensional potential well of thickness $$, with infinitely high barriers on either side, and with the potential energy zero at the bottom of the well. The equation of the normalised wave function is
$$
\psi (x) = \sqrt{\frac{105}{2L}} \left( \frac{x}{2L} - \frac{x^3}{2L^3} \right).
$$
... |
Let us take $\mathbb{R^{d+2}}$ with the cartesian coordinates $(X_0,\dots,X_{d+1})$ and the following metric :
\begin{equation}\label{equ1}
ds^2 = -dX^2_0-dX^2_{d+1}+\sum^d_{i=1}dX^2_i.
\end{equation}
The $d+1$-dimensional anti-de Sitter space $AdS_{d+1}$ can be seen as the submanifold defined by the relation
$$-X^2_0-... |
I'm thinking of doing an experiment based on the question. But I have no idea if it will work. I've tried finding things on the internet, but they all talk about the diameter of the wire, not the coil. I think it might work(as in there will be noticeable time differences) but like theoretically what would be the explan... |
Consider a charged capacitor with its positive plate holding charge Q. Now I join the capacitor to an circuit with resistance R . So the capacitor starts to discharge. Small charge $q$ flows out of positive plate in a small time $dt$ . My textbook says that the instantaneous current that flows is equal to $d$(Q-$q$)/$d... |
I'm running an experiment in a video-game simulator (ish) called 'G-MOD'. I setup a typical pendulum setup, and measured the change in the period as a function of the pendulum's mass. I obviously expected the pendulum's period to remain a constant regardless of the change in mass. However, to my surprise, I noticed tha... |
I was watching this:
https://m.youtube.com/watch?v=UM8CDDAmp98
At around 22:33 It showed one side of the engine with what looked like some sort of liquid running on it.
The liquid was at the top of the cone and was running circularly along it. The rocket is in space, so that’s not water. It is ludicrously unlikely to b... |
We have a wire going around in a helix (just like an inductor) and a constant magnetic field exists along its axis throughout the space.
How do we calculate the flux through it? I can't understand where are the area elements upon which to calculate $\int B \cdot da$.
|
I know that in general the following statement is true: $$\langle\phi|\chi\rangle = \langle\chi|\phi\rangle^* $$
And for the operator $A$ then the following identity also holds:
$$ \langle \psi| A|\phi\rangle = \langle\phi|A^\dagger |\psi \rangle$$
Does this mean that (1) implies (2)
$$| \psi\rangle = |\chi\rangle|\ph... |
If my current understanding of phase transitions and the renormalization group (RG) method is true, RG is a kind of 'zooming out' process, since this procedure makes a block of neighboring spins and makes a new Hamiltonian.
Hence a fixed point in an RG flow means it's scale invariant, and every textbook says therefore ... |
I am just a curious physics student. This question is about the nature of light.
In a single-photons double slits (or multiple slits) experiment, the interference pattern or the distribution of the landing positions of the photons shows the wave nature of light. However, each photon is only detected at a single locatio... |
I know that small amounts of matter can be converted to energy via chemical and nuclear reactions, and that complete conversion is possible if matter meets anti-matter. Other types of conversion might proceed more exotically, e.g., in a black hole collision. But I have a more theoretical question; is there any reason i... |
An electron can cross the magnetic field of a steady magnet and flip its spin. What changes in the body of the magnet? Does some electron inside flip its spin opposite to that of the passing electron and if so, does it diminish the magnetic field of this magnet?
|
We know that an operator is Hermitian when:
$\langle f|\hat{O}g\rangle$ = $\langle \hat{O} f|g\rangle$
Parity operator in 1D is simply defined as:
$\hat{\Pi} f(x) = f(-x)$
I don't know anything about the eigenvalues of parity operator (that is asked in the next problem).
How can I show it is Hermitian?
$\langle f(x)|\... |
Let $\varphi$ be a scalar field whose particle has mass $m$. I have obtained the expression that gives the difference in energy relative to a particle with mass $m'$. The expression is
$$ \frac{E}{V}=-\frac{i}{2}\int \frac{d^4k}{(2\pi)^4}\log\left( \frac{k^2-m^2+i\varepsilon}{k^2-m'^2+i\varepsilon} \right) . $$
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