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The Clausius statement of the second law of thermodynamics says that heat flows from a hotter body to a colder body. Heat can flow in many different mechanisms. In the mechanism of radiation for transferring heat, the body emits radiation though there may not be a temperature difference between it and outside. A simple... |
Let's suppose that we have no symmetry breaking and the electroweak bosons remain massless (the W, Z and the photon). Let's also suppose that the coupling constants of SU(2) and U(1) are of the order of SU(3) of QCD. We know, that the Lagrangian has the kinetic "Maxwell" tensors for each vector boson (here I add just t... |
OK, so basically I need to find the latent heat of fusion of my frozen sugar water for my experiment, but I don't think I can use the normal styrofoam cup with water. Because when some of the sugar water melts, it will mix with the water, so I can't really measure the energy absorbed by the water since it's not totally... |
I found in the literature that galaxies with an inclination angle relative to the line of sight greater than 60 degrees are considered highly inclined. Does anyone know why this particular angle is considered? Why not 50 deg or 70 deg?
|
I'm currently taking a quantum mechanics lecture and am having trouble with the mathematical formalism.
I have to calculate the following:
$$\langle n+2|b^\dagger b^\dagger |n\rangle$$
and
$$\langle n+1| \left(b^\dagger bb^\dagger + \frac {\hat{1}}{2}\right) |n \rangle$$
for the first one I can use the notation $ b^\d... |
In quantum field theory, it is crutial that two experiments can not effect each other at space-like seperation. Thus $[\mathcal{O}_1(x), \mathcal{O}_2(y)] = 0 $ if $(x-y)^2 < 0$.
For the Klein-Gordan field we now the equal times commutation relation $[\phi(x), \pi(y)] = i \delta^{(3)}(\mathbf{x} - \mathbf{y})$, i.e. th... |
The tangent space $T_pM$ which is a real vector space on a point $p$ of a differentiable manifold $M$, has a cotangent bundle $T_p^*M$ at $p \in M$, such that for any $v \in T_pM$ and for any $w \in T_p^*M$, we get
$$
w(v) = r , \quad(r \in \mathbb R)
$$,
Or in other notation $ \left< w,v \right> = r$,
I am trying to r... |
This is in reference to equation 4.27 in Peskin and Schroeder. To derive a formula for the interacting vacuum in terms of the free vacuum we evolve the free vacuum in time with the full Hamiltonian and then take the limit as $T\rightarrow \infty(1-i\epsilon)$. We are taking the limit in a "slightly imaginary direction"... |
I'm not sure how to account for the weight of air when measuring different objects.
When I weigh myself on a scale am I also weighing all of the air directly above me up to the edge of the atmosphere?
If I weighed a car am I also weighing the air inside the car? Because air pressure falls as altitude increases would ... |
I'm trying to clarify the definition of simultaneity and/or relative simultaneity - for now, only with respect to two different reference frames that are not moving relative to each other.
There should be no confusion, when we say two events are simultaneous such as lightening striking two trees simultaneously accordin... |
In the $1+3$ spacetime with $c=\frac{h}{2\pi}=1$, the Dirac delta function is of mass dimension $4$. Also, various functions may have various mass dimensions and we can change their dimensions simply by differentiation.
Then, how do we keep the dimension consistent for a functional integration on function spaces? For e... |
I am reading Peskin and Schroeder Section 11.4. They derive a formula for the effective action p.372 Equation 11.63 using a scalar field interaction,
$$
\Gamma \left ( \phi _{cl} \right )=\int d^{4}L_{1}\left [ \phi _{cl} \right ]+\frac{i}{2}\log\text{Det}\left [ \frac{\partial ^{2}L_{1}}{\partial \phi \partial \phi }... |
If we have two interacting gases of different temperatures, then it may be possible that a packet of particles(*) which move at high speed go from the hot gas into the cold one (by chance) and raise the temperature of the cold gas by transferring heat. However, it is said by the Clausius statement of the second law the... |
I am wondering if the positively-charged air ions that are descending down from Earth's Ionosphere can be collected using a glass cup. Since a glass cup will allow an electric field to pass through it, and since there is an electric field between the Earth's Ionosphere and the ground, the positively-charged air ions de... |
I couldn't find my answer in the questions so I ask it here.
If $\rho$ is a density matrix then I'd like to prove the following :
$\langle n|\rho|m\rangle \langle m|\rho|n\rangle \ \leq \ \langle n|\rho|n\rangle\langle m|\rho|m\rangle $
the $m$ and $n$ kets are some vector in Hilbert space.
Any idea?
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My answer would be yes, since instead of starting with $2s+1=2$ electrons in the first shell you would have $2s+1=4$ electrons. This is a question my quantum mechanics prof posed in the last lecture, so I'm not sure if the answer really is that simple.
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Let $\rho$ a density matrix such that:
$$\rho=\frac12(I + \vec{r}\cdot \vec{\sigma})$$
Where $\vec{r}$ is a vector with the property $|\vec{r}|$ is less than unit.
And $\vec{\sigma} = (\sigma_x,\sigma_y,\sigma_z)$ are Pauli matrices.
The problem is express $\rho^{\frac12}$ in terms of Pauli matrices. Using spectral dec... |
Does information itself have any detectable mass? If so, how is the mass of information measured if at all possible? Mathematically, is it possible for information itself to have mass? What would be the equation to ask this question or to demonstrate it? Is there a practical, physical way to measure if information itse... |
In 3D space, it is common to choose the time-reversal symmetry acting on spin-1/2 doublet fermions as
$$
T = i \sigma_y K = \begin{pmatrix} 0 & 1\\ -1& 0\end{pmatrix}
$$
where $K$ is complex conjugation and $\sigma_j$ is a rank-2 Pauli matrix.
Alternatively, we can write it as a $\theta=\pi$ rotation along the $y$ ax... |
A book that I used to learn basic Classical Mechanics, called "No-Nonsense Classical Mechanics" by Jakob Schwichtenberg, defines the probability density in Koopman-Von Neumann Mechanics as
$$\rho(x,p,t)=|\Psi(x,p,t)|^2=|c(x,p,t)|^2$$ where
$$\Psi(x,p,t)=\int c(x,p,t)e_{x,p} \, dx \, dp$$ where $e_{x,p}$ are the basis v... |
In their "Free will theorem", Conway's and Kochen's states the "SPIN axiom":
"A triple experiment for the frame (x, y, z) always yields
the outcomes 1, 0, 1 in some order."
I understand that they mean +/- 1. I also understand the idea that the eigenvalues of the squared spin matrices in the three directions are 0 and 1... |
If we are given a time evolution function $K_t(\phi,\phi')$ which give the amplitude for a field starting in confiruation $\phi$ to go to configuration $\phi'$ after time t. What is the condition that $K$ satisfies causality and Lorentz invariance. (i.e. no signal can travel faster than light?). $\phi$ values of fields... |
If you have a time evolution function $K_t(\phi,\phi')$ which gives you the amplitude to go from a field state $\phi$ to a field state $\phi'$ in time $t$ this gives you all the information you require about the system if it just contains a scalar field. $\phi$ are scalar fields that are obey a Lorentz invariant field ... |
What car window configuration will let air in by me and make / let it exit away from me. I have a large divider between front and back seats that covers much, but not all the plane between. People in back often don't want windows open much. Basically I want all air in car to exit away from me and not circulate past my... |
This is a basic question about energy conservation and classical mechanics:
Question: Under what situations can this motion be perpetual?
Without gravity and without frictions.
Without gravity and with frictions.
With gravity and without frictions.
With gravity and with frictions.
Others setup (please state the... |
The Classical equipartition theorem can be resumed by the following statement
In equilibrium, nature seeks the equipartition of energy, in which each degree of freedom contains an average amount of energy $K_b T/2$
At high temperatures, this result is more or less accurate. But to low tempertarues, the typical exampl... |
In looking at the Lagrangian of a (free for simplicity) complex scalar field $\phi$, we have a kinetic term that goes like:
$$L_{kin}=(\partial^{\mu}\phi^{*})(\partial_{\mu}\phi)$$
Given instead, a kinetic term of the form:
$$L_{kin}=\phi^{*}\partial^{\mu}\partial_{\mu}\phi$$
Is this not equivalent to the first term? J... |
This question is related to this other one and it's about Bra-Kets formalism. Hope I'm not bothering you but the truth is I'm very confused.
Reading 1939 Dirac's publication on Bra-kets notation "A new notation for Quantum Mechanics" (pdf) he says that we can understand the wave function $\Psi$ as an empty ket.
$$\Psi... |
I'm just starting to learn Quantum Mechanics, and this question is confusing me:
we say that the probability of finding a particle in a state given by the Eigenstate $o_i$ is the modulus squared of the eigenvalue of the eigenstate, call it $|c_n|^2$. What is the difference in $|c_n|^2$ and the probability density $\rho... |
As I know tempering of hardened metal must be at temperature close to 150 celsius degrees.
So why exist so widespread idea that you must not use (good) knifes to cut hot products or to wash it in hot water?
(they telling that knife will lost it's cut properties... WHY?)
UPD: Absolutely sure that better do not clean go... |
Quantum Field Theory from Sean Carroll's Biggest Ideas in the Universe. I’m just checking to see if I’m on the right track of what he's explaining. He talks about a free field (non-interacting field), we then get $\Psi[\phi(x)]$ is the complex amplitude of the field configuration throughout the space. Take the magnitud... |
I haven't found anything written about this explicitly but from the questions I have done this seems to be the case. Is the velocity in $m_1v_1=m_2v_2$ always relative to the ground (or at least always relative to the same object)? It can't be the relative velocity to each other?
|
Ten bulbs are connected in series. one of them is faulty. check which bulb is faulty with a battery and connectors to connect . What will be minimum number of times one will have to connect the series bulb connection to the battery to find the faulty bulb considering all possible cases.
|
I am learning realitivity in college and in our class our lecturer explained four-momentum. When I was reading a book in QFT.
it writes the momentum as $p^{\mu} = (E,p^i)$. Why is one of the components energy? Energy and momentum have different dimensions
or is it different in quantum field theory?
|
As a matter of fact, I was learning stellar astrophysics where I couldn't understand the chain of events at the time of death of stars,
Once the hydrogen fuel core is exhausted, the stars start shrinking until the helium nuclei starts fusing under immense gravitational pressure. Due to powerful radiation pressure the s... |
For a project, I am looking to calculate the drop in temperature across a length, $L$ of PVC pipe of diameter, $d$. Water, initially at temperature $T_1$ enters the pipe with a constant flow rate of $Q$. The ambient temperature outside of the pipe is $T_A$.
From what I understand,
$$\frac{dQ}{dt} = \frac{\lambda \times... |
I took a quiz where i got two answers wrong and i want to know what the correct answer is and why.
Q1) In a material where both phonons and electrons contribute to the thermal conductivity, the thermal conductivity is always equal to the sum of the individual conductivities when:
a) the phonons are excited by electrons... |
A ball is dropped from the building 150 m high at the same instant a second ball is thrown upward from the ground. If the two balls pass each other at a point 60 m above the ground, solve the initial velocity of the second ball.
(I'm quite confused, like is the information provided above enough to solve for the initial... |
In some places , it says slit width is directly proportional to intensity while in other places intensity is directly proportional to (slit width)² .
|
Let's say we have a region filled with a linear homogeneous dielectric, filled with some free charge density $\rho_{f}$ such that outside of this region the electric field is zero.
Then we can write both inside and outside of this region $$\boldsymbol{\nabla}\cdot\mathbf{D}=\rho_{\rm f} \:\:\:{\rm and}\:\:\: \boldsymbo... |
I need to solve the following problem: a sheet of flexible but inextensible material (can be modelled as cable or chain in 2D) is fixed in endpoints and buckles up. Then a variable force is applied in one or more points. Under this force shape of the buckle changes because the sheet/chain/cable needs to preserve its le... |
Radiation, as far as I understand, is the transfer of energy through electromagnetic waves. The energy emitted from a hot body is known as thermal radiation. However, the accepted answer in this stack makes a distinction between thermal and coherent radiation.
What precisely is the difference characterizing the classif... |
I have a differential equation: $$\ddot{\omega}+2k\dot{\omega}+2k^2{\omega}-2{\omega}^3=0$$
As I understand it's a Duffing equation, but I can't find the first integral. How can I do it? I didn't find any articles. $k$ constant.
|
I see a formula in the Wikipedia entry on time dilation: $$ \sqrt{1-v^2-v_e^2-\frac{v_r^2\cdot v_e^2}{1-v_e^2}} $$ where $v$, $v_e$, $v_r$ are the actual velocity, the escape velocity from gravity, and the radial component of the actual velocity (all normalized against c). Descending into a black hole with $v=v_e=v_r=-... |
In this paper, there is an interesting figure:
Every attempt I've made to search online to confirm whether or not waiters/waitresses actually do this, has been unsuccessful.
Is there really an advantage to tilt the water as in scenario C of the figure?
|
The effective mass is defined as
$$
\frac{1}{m_{ij}^*} = \frac{1}{\hbar^2} \frac{\partial^2\epsilon}{\partial k_i \partial k_j}
$$
where, $m_{ij}^*$ is the effective mass, $\hbar$ is the Planck's constant, $\epsilon$ is the energy and $k_i,\ k_j$ are reciprocal latttice vectors.
I want to find distance between two poin... |
Suppose I drop something from 200 cm and another thing from 20 cm. Which will cause a deeper depression?
|
TL;DR: I want to calculate the transmission coefficient of a particle travelling into a finite double potential barrier system and I think I've got stuck by the fact that I have 9 unknown variables (amplitudes) and only 8 equations. How do I manage to solve this?
Problem
I have a particle (an electron) with energy $E$ ... |
Mark Srednicki's QFT book presents a regularization of the $\delta$ function in calculating the chiral anomaly (see section 77 of the book). This regularization reads
\begin{equation}
\delta (x-y)=\lim_{M \rightarrow \infty}\int \frac{d^4k}{(2\pi)^4} e^{(i\gamma ^{\mu}D_{\mu})^2/M^2}\circ e^{-ik(x-y)},
\end{equation}
... |
I am currently reading papers on the field theoretical description of phase transitions of the quantum rotor model for systems with algebraically decaying long-range interactions $J_{ij}\propto\frac{1}{|r_{ij}|^\alpha}$.
Dutta et al. (2001): https://journals.aps.org/prb/abstract/10.1103/PhysRevB.64.184106
Defenu et al... |
In the following problem:
(i) I have found the tension in $S_1$ to be $ 2 N $. However, I am a little confused about the force diagram I'm making for particle B. I am guessing that the weight on B is going to be $m_Ag + m_Bg$. Is that correct?
Also, what is the tension in $S_2$ going to be? I am trying to imagine this... |
If we take a charged conductor in a time-varying magnetic field and apply a varying force on it so that the Lorentz force on it is cancelled by the varying force, will an emf still be induced on the material?
|
Is there any way to derive the quantum mechanical operators that form the integrals of motion in quantum mechanics from the Hamiltonian for general systems?
Let's for simplicity focus on stationary problems.
For example if I have a system with a(n obvious) continuous spatial symmetry, like the electron in the potential... |
Consider a quantum random number generator (QRNG) X, which generates integers at random.
(Apparently, due to quantum statistical properties, this type of generation is truly at random, see e.g. "The quantum number generator".)
My question is: what is the probability that X generates a given integer $N \in \mathbb{Z}$ ?... |
I was doing some problems of the book "Problem Book in Relativity and Gravitation by A. Lightman, R. H. Price" and on problem 10.14 I dont understand why they say:
$\xi^{}_{\gamma;\beta}\xi^{\gamma}\xi^{\beta}=\xi^{}_{(\gamma;\beta)}\xi^{\gamma}\xi^{\beta}=0$
Also on their final step they use the killing equation in or... |
I'd like to perform a short-time motion estimation based on measurements from an Inertial Measurement Unit.
If I use the Runge-Kutta method, I will need to compute the k values at half-time steps (Ref).
Except that I don't have measurements at half time-steps! I don't think interpolating sounds right. Does it? Should I... |
In the following question (the second part), why doesn't tension change? I've solved the question. In the first part, when particle A is about to move, tension is $2 N$. In the second part, $X = 2.8$, but tension is still $2 N$ (and is used to calculate X).
I don't understand why tension hasn't changed, since a new hor... |
I'm reading Tong's Lectures on String Theory chapter 4 on conformal field theory. The PDF can be found here. I'm trying to understand his proof of claim 2 in section 4.3.3, but I can't seem to grasp what happens from the first line to the second line in equation 4.26.
If I start doing the derivation myself, the initial... |
I have a few simple questions about Feynman Diagrams:
Why, when $W^+$ or $W^-$ bosons are involved, sometimes the sign + or - is shown and sometimes not (example1, example2)?
Why the arrow is usually not shown on bosonic lines?
Sometimes I have the impression that for a single process, different equivalent Feynman dia... |
In the problem above what does the question means by given normal lying inside the mirror surface?
Is it has something to do that they have i and j components same.
I also wanted to know what does the question is trying to bring out by this certain thing.
Any help would be appreciated.
|
As I understand when a rubber band is stretched adiabatically (which I am assuming means no change in entropy and so no heat flow from surroundings) its polymers naturally are straightened and thus their entropy would be reduced, so in order to keep entropy constant, the rubber band's temperature must increase. So how ... |
A normal Lorentz coordinate problem might say:
At $t=t'=0$, two coordinate systems $S$ and $S'$ have their origins coincide with the $S'$ system moving with speed $v$ in the $+x$ direction relative to $S$. If event 1 happens at $x=a$, $t=0$ in the $S$ system then when/where does this event happen in the $S'$ system. I ... |
I don't know if this is a simple question to answer however, I have trouble understanding how a spherical object (such as a planet) with positive curvature can exist in Euclidean 3-space with no curvature. From my understanding Euclidean geometry seems to be the most likely description of space as we know it. Is our sp... |
Why is do we see different colors, instead of white spots like in the middle?
Why is the single slit less intense the further away from the middle you look?
|
We have a linear homogeneous dielectric material half filling a parallel plate capacitor. It's said that the field inside is reduced by a factor ,so we have
$\mathbf
{E}=\frac{1}{\epsilon_{r}}
\mathbf{E}_{\mathrm{vac}}$.
What's its proof?
( If anyone tries to prove it using the similaritiy of $E$ and $D$ ,I thin... |
I'm working on the Ward-Takahashi identity in Peskin (page 311), but I canʻt obtain Eq.(9.105) from Eq.(9.103)
According to Eq.(9.103)
\begin{align}
&i \partial_{\mu}\left\langle 0\left|T j^{\mu}(x) \psi\left(x_{1}\right) \bar{\psi}\left(x_{2}\right)\right| 0\right\rangle=-i e \delta\left(x-x_{1}\right)\left\langle 0\... |
I would like to know the analytical expression of the ground state energy of the XXZ model, if such formula exists (probably from a Bethe Ansatz solution) and if it is valid in all parameter regimes.
|
I find the term "microgravity" to be misleading, how was it coined?
NASA provide this definition:
Microgravity is the condition in which people or objects appear to be
weightless. The effects of microgravity can be seen when astronauts
and objects float in space.
Presumably the word "micro" is not being used in its m... |
My question is about the invariance of the space-time interval $ds^2$ under orbifold symmetries, such as in the Randall-Sundrum model.
In this model, the space-time is 5-dimensional with metric
$$ds^2 = e^{-2A(y)}\eta_{\mu\nu}dx^\mu dx^\nu - dy^2$$ where $\eta_{\mu\nu}$ is the usual Minkowski 4D metric and $y$ is the 5... |
I'm trying verify the proof of the sum rule for the one-dimensional harmonic oscillator:
$$\sum_l^\infty (E_l-E_n)\ | \langle l \ |p| \ n \rangle |^2 = \frac {mh^2w^2}{2} $$
The exercise explicitly says to use laddle operators and to express $p$ with
$$b=\sqrt{\frac {mw}{2 \hbar}}-\frac {ip}{\sqrt{2 \hbar mw}} $$
$$b^\... |
On the solution of problem 10.6 of the book "Problem Book in Relativity and Gravitation by A. Lightman, R. H. Price" they mention using the Killing equation:
$\xi^{}_{\mu;\nu}=-\xi^{}_{\nu;\mu}$
and contracting both the $\mu$ and $\lambda$ indicies to arrive at the equation:
$\xi^{\nu;\lambda}_{\space\space\space\space... |
Suppose I have the state $|\psi\rangle = \frac{1}{\sqrt{2}}(|01\rangle - |10\rangle)$ that I want to measure in an arbitrary basis $$|A\rangle = \alpha|0\rangle + \beta|1\rangle \text{ and } |B\rangle = \beta^*|0\rangle - \alpha^*|1\rangle$$
From my understanding, if I measure $|\psi\rangle$, the probability of seeing... |
I was conversing with my professor about the forces acting on a ball that is thrown onto the air. He said that you would have the weight of the ball, air resistance and buoyant force. Although, I wonder if the buoyant force has a significant impact on the result, assuming that the ball's density is considerably greater... |
In Goldstein's
$$
Q_{j}=\sum_{i} \mathbf{F}_{i} \cdot \frac{\partial \mathbf{r}_{i}}{\partial q_{j}}=-\sum_{i} \nabla_{i} V \cdot \frac{\partial \mathbf{r}_{i}}{\partial q_{j}}
$$
which is exactly the same expression for the partial derivative of a function $-V\left(\mathbf{r}_{1}, \mathbf{r}_{2}, \ldots, \mathbf{r}_{... |
I mainly understand the concept of quantum measurement from an axiomatic viewpoint, and can't seem to find an answer to what I am wondering. If it is addressed somewhere else, pointers and/or keywords to search would be greatly appreciated.
Consider a finite dimensional Hilbert space $H$, a density operator $\rho$, an... |
Let's take a spacetime as a pair $(M,g)$ where $M$ is the manifold and $g$ the metric.
I've seen that there exist a generalization of manifolds. This generalization consist in accept singularities in the manifold ( http://www.map.mpim-bonn.mpg.de/Manifolds_with_singularities#:~:text=Manifolds%20with%20singularities%20a... |
Considering the following expansion of operators in SU(2) in commutators
$$[[V, \rho], V] = \left[\left[v_0 + \sum_{i=1}^3 v_i \sigma_i^3, \rho_0 + \sum_{j=1}^3 \rho_j \sigma_j\right], v_0 + \sum_{l=1}^3 v_l \sigma_l \right] = \sum_{i,j,l=1}^3 v_i \rho_j v_l [[\sigma_i,\sigma_j],\sigma_l]\tag{1}$$
So
$$[\sigma_i,\sigma... |
The automobile steered by an Ackerman mechanism has the schematics below. According to the author (Reza N Sazar, Vehicle Dynamics: Theory and Application), the steering angles must not violate the relation below.
\begin{equation}
\cot{\delta_o} - \cot{\delta_i} = \frac{w}{L}
\end{equation}
However, the book is not expl... |
This is a derivation of equation of internal energy of an ideal gas from Heat and Thermodynamics-Zemansky.
I am not sure if attaching images like i have would cause inconvenience. I had to type the whole thing if i had to ask my question.
Can anyone explain how the equation tells us that atomic velocities have no pr... |
When taking the inner product of a wavefunction $\Psi$ with itself, denoting the inner product as $(\Psi,\Psi)$, since $$\Psi(x)=\int \psi(x)\vec{x}dx$$ letting $$\overline\Psi(x')=\int \overline\psi(x')\vec{x'} dx'$$ would $$(\Psi,\Psi)= \int \overline\psi(x')\psi(x)\delta(x'-x)dx'dx$$ or would the $dx'$ not be includ... |
In looking at explanations of the twin paradox, two examples are given to show that acceleration is not a factor:
First, where one rocket flies out past the star and a second rocket flies back to earth.
Second, where the rocket flies out and instantly turns back, with no acceleration.
In the explanations I've seen, it ... |
I am trying to understand, how composite operators in gauge theory are renormalized.
In this paper the authors consider the renormalization of Yang-Mills stress-energy tensor:
$$
\mathcal{O}_{\mu \nu}^{(1)} [A] = -F_{\mu \sigma}^{a} F_{\nu \sigma}^{a}
-g_{\mu \nu} \mathcal{L}_0 [A]
$$
In the second section it is menti... |
I just need help finding out what makes them stick together. I tried looking here and I found why they stick but not how.
|
What would it look like if you were inside a perfectly spherical "room" that was completely mirrored (seamless) with a small, single source of light?
Previously I'd wondered/theorized about a cubic mirrored room, but got a basic impression after stumbling onto a related Flikr album:
(Photos by Ron Brinkmann, with ... |
Say I'd like to find the potential created with a conducting sphere and an external point charge. When using the method of images to find the potential, we know that that potential is unique for the region of interest (outside the sphere), as long as it is defined on all boundaries and as long as the charge density is ... |
(I think this question is really about any truncation of the perturbation series, but I want to avoid having to think hard, so I'll talk about tree-level only to ask the question.)
Let's start with scalar field theory in $d$ spacetime dimensions, with an action:
$$
S = \int d^d\! x\; \frac 1 2 \phi(m^2 - \partial^2)\ph... |
It is a problem from Kleppner mechanics:
A bead of mass $m$ slides without friction on a rod that is made to rotate at a constant angular speed $\omega$. Neglect gravity.
(a) Show that $r = r_0 e^{\omega t}$ is a possible motion of the bead, where $r_0$ is the initial distance of the bead from the pivot.
(b) For the m... |
In the given situation there wheel is rotating about its own axis as well as about the axis PQ. Now my Query is that which torque of which force is responsible for the rotation of the wheel about axis PQ. I could not find any external torque on the rod plus wheel system which is in the vertically upward direction .Pls... |
In Nielsen and Chuang we define the partial trace operator, defined as
$$\operatorname{tr}_2(|a_1\rangle\langle a_2| \otimes |b_1\rangle\langle b_2|) = |a_1\rangle\langle a_2| \operatorname{tr}(|b_1\rangle\langle b_2|)$$
They go on to say that $\operatorname{tr}_2(|11\rangle\langle00|) = |1\rangle\langle0|\langle0|1\r... |
I am designing a balanced-arm lamp structure for a robotics project and I obviously want the lamp to stay on its base without falling when the arm is extended. For that, I applied the conditions for static equilibrium and I come to an equality (relation between the masses and the distances of the base, head, arm, etc. ... |
I am trying to understand what the intrinsic impedance of a medium means. I understand the mathematical definition of it, but it doesn't speak much about the concept to me.
What does intrinsic impedance mean conceptually? All I understand is that the electric field intensity is going to be much higher than the magnetic... |
If $L(q,\dot{q},t)$ is a lagrangian of a system, then $L' = L + \frac{dF(q,t)}{dt}$ is also a valid lagrangian and both lagrangians will lead to the same equation of motion.
But, what if I choose $F(q,t)$ such that $L'=0$?
\begin{equation}
L + \frac{dF}{dt} = 0 \\
F = - \int{L dt} = -S
\end{equation}
where $S$ is the ... |
The heat equation is often written as $\frac{\partial T}{\partial t} = \frac{\kappa}{c} \nabla^2T$ where $\kappa$ is the thermal conductivity and $c$ is a heat capacity per volume.
I often see $c$ written as $c_P$ implying that it is the heat capacity (per unit volume) for a system held at constant pressure, but I was ... |
It can be shown that particle in a box and free particle have the same energy at certain wavenumbers (at an integer multiple of $\pi/L$ , where $L$ is the length of the box)
I am aware that the general wavefunctions of the two particles spoken of are different, but I can't get over the fact that both particles have a $... |
So for a model like this one, can there be two electrons in one energy level?
And I don't understand the Pauli principle that two electrons can't be on the same energy level when there are 2 electrons in the first shell of most atoms???
Does this then mean that shells and energy levels aren't the same thing?
|
I am trying to derive the explicit form of the effective interaction Lagrangian (Hamiltonian) for fermions interacting via a scalar particle (Yukawa's potential). For that, I am using the Lagrangian
$$ \mathcal{L} = \mathcal{L}_\psi + \mathcal{L}_{\phi} - g \bar{\psi}\psi \phi $$
where $\mathcal{L}_\psi$ is the Dirac L... |
What is the $C$ in $ PV^{\gamma} = C$? I always saw it as a result out of the mathematical calculations that we do but I recently saw this video which made me think that the constant may have more meaning that meets the eye.
See this video at 4:11
He writes $ S = PV^{\gamma}$ .. but where exactly is this equation from?... |
If your answer was that the sun's atmosphere absorbs some photons, I don't think so. Because the atom, after absorbing a photon, it seeks stability and emits an electron in a short time compared to the time the light reaches the Earth. If I am wrong, correct me.
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The change of Gibbs free energy (for a single phase or constitute system) is
$$dG = -SdT + VdP +{\mu}dn$$
By using the fact that $T$ and $P$ are intensive properties and $n$(mole) is an extensive property,
$G = n\mu$ is derived in my lecture note.
But I am not sure about that, because, with the definition of $dG$, $G$ ... |
What time dilation effect would occur when two objects would approach each other at e.g. 90% the speed of light? For each of the objects the other object appears to be moving at 180% the speed of light relative to itself. In this case the formula for calculating the time dilation 'factor' can't be applied. How do I cor... |
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