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As we know, we usually call fusion such a reaction in which two light nuclei make a heavier one and release energy.
For fission, a heavy nucleus breaks into light ones.
My question is, in proton-boron reaction, the product is He, which is not heavier than boron. It is more like fission rather than fusion. Why do we cal... |
A friend of mine does not believe that four-momentum is conserved independently in each vertex of a Feynman-diagram; and, as a consequence, that propagators/virtual particles do not obey a dispersion relation.
They won't trust my claims, and pointing out that this definition is the one producing correct cross-sections ... |
In old-fashioned Quantum Electrodynamics, one can find diagrams such as these (probably Stückelberg was the first to use this notation, a kind of predecessor of Feynman diagrams):
In modern QED this process (electron-electron scattering) is represented by this Feynman diagram:
I didn't bother to reduce this picture i... |
A question in my book goes as follows:
A planet P revolves around the Sun in a circular orbit, with the Sun at the center, which is co-planar with and concentric to the circular orbit of Earth E around the Sun. P and E revolve in the same direction. The times required for the revolution of P and E around the Sun are $... |
When an object is on an inclined plane the force of gravity acts downwards on the object and the normal force is perpendicular to the surface of the inclined plane. When we normally solve these problems we often break the force of gravity into 2 components. One of those components is parallel to the inclination of the ... |
I have a full bridge rectifier with Forward Voltage, per Element $1 \ \mathrm{V}$ at $8 \ \mathrm{A}$, does this mean that between $-1$ and $1 \ \mathrm{V}$ at input the bridge will not forward current?
|
Given the recent Gaia parallax data out to large distances, has anyone used that data to match objects with observed redshift data?
I have taken as much Gaia object data as I can and compared it with some Sloan survey redshift and other data but an find no matching objects that appear in both, so far. I am looking for ... |
All the signals traveling down a copper wire are traveling along the same wire, why don't they mix and interfere with each other?
|
I was wondering what the expectation value of a wave function might be if the corresponding integral diverges. For example, if I graph the probability density $\Psi (x) = \sqrt{\lambda/\pi} \exp(-\lambda(x-a)^2),$ I get . So I expect that the expectation value $$<x> = a.$$
To obtain via algebra, I evaluate the expressi... |
Let's suppose that an apple is falling down towards the Earth.
From Newton's law of universal gravitation: the force exerted on Earth by the apple is $$F = \frac{GM_1 M_2 }{r^2}$$
From Newton's second law: the force exerted on Earth by the apple is $$F =\underbrace{M_1}_{\rm Earth's\ mass} \times \underbrace{a}_{\rm ... |
In his famous 1908 "Space and Time" lecture, Minkowski introduced the concept of worldlines and thus of a block universe with a single remarkable sentence: "To never let a yawning emptiness, let us imagine that everywhere and at any time something perceivable exists."
In Minkowski's substance-filled block universe, the... |
When we place an uncharged grounded conducting sphere in a uniform electric field, then due to the external field, charges will be induced on its surface. But if the sphere is grounded, then why won't the charges get neutralised?
|
One can arrive at the equation for the magnetic field around an infinite wire in several ways(biot savart law, I used the integral form of Ampere's law). The solution is well known and of the form
$$
B_{\phi} = \frac{\mu I}{2\pi r},\quad B_{r}=B_{z}=0
$$
with permentivity $\mu$, current $I$ and distance $r$ from the wi... |
So I was reading through some lectures notes and I found this:
The equation of motion of a non-ideal string is $\frac{d^2y}{dt^2}=c^2\frac{d^2y}{dx^2} + ac^2\frac{d^4y}{dx^4}$ and we are asked to compute $\omega(k)$. But with no previous step, the writer says:
$\omega^2 = c^2k^2 + ac^2 k^4$.
I usually work problems as ... |
I want to try to render (computer graphics) auroras in a physical manner as realistic and realizable as possible. I'm aware that the phenomenon hasn't been completly explained yet (as far as my own research goes). But while searching for information, I've seen many different statements about how the plasma behaves when... |
The Hamiltonian of Quantum 2D Ising gauge theory is given by:
$$ H=-\sum_p \prod_{i\in \square}\sigma^z_i -g \sum_{i\in \text{links}} \sigma^x_i$$
This $H$ is invariant under the local symmetries:
$$ G_i=\prod_{l\in +}\sigma^x_l \,\,\,\,\, (i \in \text{vertices})$$
Now, we can look at $G_i$ in two different ways:
1- T... |
We say that motion isn't absolute.but why?if we measure motion relative to "space" it will be absolute for all observers. isn't it?
Is space also relative like motion?
If space has no "special point" so how we measure acceleration. If we rotate instead of straight motion , we feel acceleration . But the entire universe... |
Good Afternoon,
By definition, an observable $O$ for a system of N identical particles is symmetric just in case $\langle\psi|O|\psi\rangle = \langle\psi|P^{\dagger}OP|\psi\rangle$ for any permutation operator $P$ in the permutation group $S_{N}$. (Or, equivalently, $[P, O] = 0$ for any $P$ in $S_{N}$).
Now, it seems t... |
A general (pure) Gaussian state has the form $\newcommand{\on}[1]{\operatorname{#1}}\newcommand{\ket}[1]{\lvert #1\rangle}\ket{\alpha,\xi}\equiv D(\alpha)S(\xi)\ket{\on{vac}}$, with $\ket{\on{vac}}$ the vacuum state, $D(\alpha)\equiv\exp(\alpha a^\dagger-\alpha^* a)$ the displacement operator, and $S(\xi)\equiv\exp(\fr... |
My phyiscs textbook only discusses what will happen if a live wire touches a metal case and how it turns alive, however, I was wondering, will the same effect happen to the metal case if touched by the neutral wire instead?
|
In solid states, the lower temperature meant more stable structure and transition fro bcc(packing fraction 0.74) fcc(packing fraction 0.74) to hcp(packing fraction 0.68).
1.a. Does this mean atom, such as Fe, at bcc had larger lattice parameter and lower density than Fe at fcc (At same temperature and pressure)?
1.b. F... |
I'm going over the notes of D.S. Duffin at Tasi on Conformal Bootstrap (arXiv:1602.07982) and I can't seem to understand something rather fundamental.
In order to derive the restriction imposed on a two point function in a CFT he argues that
"In a scale-invariant theory with scale-invariant boundary conditions, the si... |
Part of the definition of a virtual image is that it cannot be formed on a screen. I understand this is the case when the screen is right next to the image, since there are no physical rays that can hit the screen. But what I don't understand is why an image can't form on the screen if the screen is located sufficientl... |
Suppose that Alice wants to teleport the state $|\psi \rangle = \alpha |0 \rangle + \beta |1 \rangle$ to Bob. My issue is why quantum teleportation is needed to transmit this state. Why is it not possible for Alice to do many measurements which could give information on the coefficients and then transmit this informati... |
I am talking about the possibility of reliably cooling an arbitrary quantum system of FINITE size (for example, localized on earth), to its ground state through any means, like exposure to a special kind of environment etc. By reliable, I mean that for the given system, can we calculate a finite time T after which it h... |
As in my previous two posts (1 & 2), a unitary two-dimensional TQFT is specified by a set of real numbers $\{\lambda_i\}$ such that the partition function is
$$
Z(\lambda)=\sum_{i=1}^n\lambda_i^{g-1}\tag1
$$
My main question is whether there is a natural, "first principles" construction of such a TQFT other than by spe... |
When we throw an object up into the air, ignoring air resistance, etc, we define acceleration to be -9.8 m/s^2. When it goes down after its journey up, like a parabola, do we define the acceleration as 9.8 m/S^2, OR still the same as -9.8m/s^2?
I know that acceleration due to gravity is always constant, but would it be... |
I'm curious how the observed quantum-mechanical properties of a hydrogen atom would change under very high gravitational fields. Do the energy levels change? Do the chemical bonding properties change? Does that atom become asymmetric (electrically polar)? etc.
In the context of a black hole, what happens to a hydrog... |
I'm a high schooler who just finished learning Maxwell's Equations. I'm trying to visualize the movement of a charged particle in a field.
I have an infinite sheet of positive charge oriented on the xz plane and located on the +y axis, moving at a velocity $v$ in the $+x$ direction. A test charge $Q$ of mass $m$ also m... |
I'm currently trying to work through Physics by HRK, Edition 5. I've come across this problem in the Fluid Statics section which I, being an amateur, decided to google. The exercise reads:
A barge filled with scrap iron is in a canal lock. If the iron is thrown overboard, what happens to the water level in the lock? W... |
I am reading a review article on Weyl semimetal by Burkov where he writes, top of page 5:
A 3D quantum anomalous Hall insulator may be obtained by making a stack of 2D quantum Hall insulators [Ref. 23].
Ref. 23 in his paper is the generalization of the 2D TKNN invariant to the 3D case.
I am a little confused about wh... |
Why must the covariant Lagrangian of a free particle be a first-order differential?
|
According to cosmological inflationary models, different universes governed by different effective/low-energy laws of physics could exist, but the most fundamental laws of nature would remain the same. In other words, while the effective laws of physics would change, fundamental laws would stay the same.
But is this al... |
For calculating the amplitude of the coherent elastic neutrino-nucleus scattering, I face the problem in finding the coupling constant for the vertex of nuclei and the Z boson.
$$ \gamma^\mu(g_V-g_A(\gamma^5))$$
In this case if we have a nucleus (A) with Z number of protons and N number of neutrons, how we can we find... |
If a uranium atomic bomb directly hit a stockpile of weapons grade uranium, would the chain reaction also detonate the stockpile?
what about a stockpile of nuclear reactor fuel rods?
what about a stockpile of various nuclear weapons?
what about a plutonium bomb or a hydrogen bomb?
what about all possible permutations o... |
I read in a newspaper that we can't predict the trajectory of a hypersonic missile and that this property renders the missile undetectable.
However, what I could not understand is why can't we predict it's trajectory? What factors do we have to look at for predicting the trajectory of such high speed missiles? Is this... |
The metric of 2D plane is
\begin{equation}
ds^2=dr^2+r^2d\phi^2,
\end{equation}
which is singular at $r=0$ (is it because vanishing Jacobian?). It is said this singularity is removable if
$0<\phi<2\pi$. So how can I see this point? It seems even if $\phi \in (0,2\pi)$, $r=0$ is still a singularity.
|
The weaker notion of symmetry, in the sense of Wigner's theorem, is a transformation on the states that leave all quantum mechanical amplitudes invariant. This tells that such transformations are represented by Unitary operators. See the answer here by @ACuriousMind.
Now, instead of demanding that all quantum mechanica... |
I am doing a problem set about dimensional analysis and water waves. Before the last question which I have trouble with, I found the following two relations:
$$\begin{equation*}
v\propto\sqrt{g\lambda}\\
v\propto\sqrt{\frac{\gamma}{\rho\lambda}}
\end{equation*}$$
Where $\gamma$ is the surface tension, $\lambda$ is the ... |
Let $\mathcal{N} : M_n \to M_n$ be a unital quantum channel (hence trace preserving and completely positive).
Do we have the inequality $Q^{(1)}(\mathcal{N}) \leq \chi(\mathcal{N})$ ?
Here $\chi(\mathcal{N})$ is the Holevo capacity (or Holevo information) of $T$ and $Q^{(1)}(\mathcal{N})$ is the coherent information of... |
As far as I remember, if we stretch a solid iron bar mechanically, some portion of the work done by, say, the hydraulic pistons, makes the bar's temperature increase before it pulls apart. I want to know if the same happens for a simple spring. Can we say that if we contract a spring, its temperature would slightly inc... |
Edward Witten has stated that QFT is not mathematically rigorous, and that string theory helps us in unifying the forces much better. Can you give me a suitable example in which QFT lacks mathematical rigour?
|
What is the difference between laser beams and ion beams, especially in inertial confinement fusion?
In inertial fusion, we use lasers as well as ion beams for driving the reaction. What is the difference?
|
So, I am trying to get my head 'round the workings of electromagnetism.
Pretend I am 5 years old.
Protons send out photons to electrons that cause the electrons to accelerate towards the proton, and vice versa. Is that correct?
When those same photons from protons are received by protons though, the recipient protons m... |
According to my education as a sailplane pilot our troposphere is in good approximation subject to adiabatic processes.
Using adiabatic equations of (nearly ideal) gases, the temperature gradient with pressure can be derived easily:
$dp/dT = \frac{p}{RT}\cdot c_p$
On the other hand, I read recently, that in meteorology... |
I learned that X-ray diffraction happens due to the periodic arrangement of atoms in a crystalline material, so can X-ray diffraction studies be done on liquids and non-crystalline materials?
|
Hello friends I was stumbled when I learnt the scattering theory from textbook titled "Quantum Field Theory for the Gifted Amateur", which has related the scattering probability to the matrix elements of S-matrix:
$$<p_{i1}p_{i2}|\hat{S}|p_{f1}p_{f2}>$$
where $p_i$ and $p_f$ are the initial moments and final moments af... |
I recently went through Field Theory of Non-Equilibrium Systems by Alex Kamenev (2011) and I wanted to understand certain points in detail. My current problem is to understand how one can calculate expectation values in the continuum notation presented in this book.
Specifically, I do not understand completely the foll... |
There are arguers that say the Universe is streching about every its point but also tell it is infinite. How it can possibly be?Maybe we should reinterprete what infinity means.
|
Gravitational waves have been detected emanating from the decaying orbits of massive bodies, such as binary neutron star or black hole systems.
To my understanding, two such bodies in what would otherwise be a stable orbit, will instead slowly radiate away their orbital momentum as gravitational waves and spiral inward... |
As we already know that the electron emits light photons when it travels from one orbit to another, and that causes this transition is the electron absorption of the incoming photon. But when the electron absorbs a photon, it moves to a farther orbit. Does the outgoing photon have a wavelength similar to the wavelength... |
So I wonder if the thermal velocity of a gas can be considered as a 'real' velocity of particles, or it is just totally quantum phenomenon.
To elaborate my question, the wikipedia(https://en.wikipedia.org/wiki/Thermal_velocity) says that the thermal velocity of Hydrogen at 20C is about 1754m/s. However, the sun and the... |
In David Tong's lecture notes on quantum field theory, at the bottom of page 23, we are applying the quantisation of the harmonic oscillator to the field to obtain expressions for the field operators in terms of ladder operators.
If we write the field $\phi(\vec x,t)$ as its Fourier transform: $$\phi(\vec x,t)=\int \fr... |
Nanoparticles such as gold and silver are becoming more and more used to print circuit or enhance electrical properties of another material. But I have not been able to find sources that clarify how current transport takes place between nanosized particles. In particular, what I am trying to learn is the following:
Sup... |
Show that in the case of the Schwarzschild metric: $R^{\mu\nu\rho\sigma}R_{\mu\nu\rho\sigma}=\cfrac{48G^2M^2}{r^6}$
I am currently studying Relativity on my own. But in my book I found that this problem "is left as an exercise for the reader" and I really have no idea how to demonstrate what they are asking of me and I... |
why to diffraction, the spacing between the scatterers and the wavelength should be similar in size, For example in xray diffraction to determine crystal structure?
If it not similar what does happen?
|
I have a negative infinite sheet of charge moving at a velocity $v$ in the $+x$ direction. A test charge $Q$ with mass $m$ moves at a constant velocity $v$.
My Question is simple: How will the test charge $Q$ move? Will it keep going in the $+x$ direction at a constant velocity $v$, as if no electromagnetic forces act... |
I have some doubts on the following derivation of the EOM of a stationary string.
Let $F_x, F_y$ be horizontal and vertical tension of the string
$\mu$ be the mass per unit length of the string [kg/m]
$$\frac{F_{2y}}{F_{2x}} = \tan\theta_+ = y'(x + dx)$$
$$\frac{F_{1y}}{F_{1y}} = \tan\theta_- = y'(x)$$
$$dm = \mu dx$$... |
https://en.wikipedia.org/wiki/Bubble_(physics)
https://en.wikipedia.org/wiki/Soap_bubble
https://www.instagram.com/p/CE4FSctpCdu/?utm_source=ig_web_button_share_sheet
Is it possible to create air bubbles other than soap water as origin?
Can we classify air bubble as solid, liquid or gas?
Can we measure air bubble's wei... |
I am given two concentric conductive spherical shells, one of radius $a$, and the other of radius $b$, with $b>a$. The space between these shells is filled with a dielectric of relative permittivity $\kappa$. The inner shell has a charge of $+q$ and the outer shell is grounded.
I would like to solve for the potential w... |
I need to calculate the components of the radiative flux tensor and the pressure tensor, but I am having a little trouble figuring out what the integral should be. The flux is defined as
$$F_v = 4{\pi}H_v$$ where $$H_v = 1/4{\pi} \int I_v {\hat k} d{\Omega}$$
and
$${\hat k_i} = (sin{\theta}cos{\phi}, sin{\theta}sin{\ph... |
So the professor of my physics 3 class assigned this problem regarding forced oscillations.
A mass of 0.30kg hangs of a massless rope. The center of oscillation can move as shown in the figure. When the driving frequency $\omega$ is zero, the pendulum oscillates 100 times before its amplitude is about 35% of the initi... |
By definition, a primitive cell contains only one lattice point but may contain more than one atom. What is an example of a real crystal that has a primitive cell with more than one atom per cell? I looked up the INTERNET but could not find one. I am not interested in conventional/nonprimitive unit cells which contain ... |
First of all, I apologize if some specific terms are not accurate but I'm using the translations that Google gives me.
The test where I found the problem asks to calculate the variation of internal energy (ΔU1) of a thermal reservoir (the cold one), in a generic reversabile heat engine cycle. He gives me the temperatur... |
In Linearized gravity one can perform coordinate transformations
$$x^\mu \rightarrow x'^\mu=x^\mu+\xi^\mu(x)~~~~~~\text{with the condition } \Biggl|\frac{\partial \xi^\mu(x)}{\partial x^\nu}\Biggr|\ll1$$
It seems to me that the condition prevents me from rotating my coordinate system. If I wanted to rotate around the ... |
I have an inertial measurement unit (IMU) with an accelerometer that reports the acceleration (a) along the $x$, $y$ and $z$-axis in milli-$g$. I can get the Euler angles for roll ($\phi$) and pitch ($\theta$) as follows:
$$
{\phi= \;{\arctan}\;{{{{\rm a}_y}} \over {\sqrt {{\rm a}_x^2 + {\rm a}_z^2} }}}
$$
$$
{\theta}... |
The wave nature of electrons was proved in the Davisson and Germer experiment since the Galvanometer they used showed a sudden peak in the value of current.
Now I have some doubts regarding this.
1 : Does the amperemeter or galvanometer which we use in our general circuits also measure the value of the current obtained... |
I asked this question on the biology site. Some suggested I ask this question here.
https://biology.stackexchange.com/questions/95588/why-does-this-oxygen-duration-chart-have-increased-times-above-30-000-ft-msl
This oxygen duration chart from an airplane shows the amount of time a pilot can be on oxygen at a specifie... |
Why do we not define work done as the difference between two quantities that depend entirely on the initial and final states.
Why is work a path function? What is the reason?
|
We all know that when light hits a plane surface, it reflects back.
And when the light hits plane surface, then if incident angle is greater then critical angle then it reflects back into the medium, this phenomenon is called total internal reflection.
Now the thing that always confuses me is: what is the difference ... |
We typically draw light-cones to study causal relation between two space-time points.
Source : Wikipedia
Space-Time is manifest as the metric in various calculations. If one considers that something like Quantum Gravity does indeed exist then shouldn't the quantum fluctuations in metric make the sharp-lines of light-c... |
Reading David Tong notes on QFT, he mentions about Gupta-Bleuler condition $$\partial^{\mu}A_{\mu}^{+}|\Psi\rangle=0\tag{6.54},$$ which makes sure that matrix elements vanish,$$\langle \Psi|\partial_{\mu}A^{\mu}|\Psi\rangle=0.\tag{6.55}$$ I also came across Ward identity $p_{\mu}\mathcal{M}^{\mu}=0$ in Schwartz QFT. At... |
Spontaneous symmetry breaking occurs when there is a degeneracy in the ground state. Typically it is easiest to determine the degeneracy by finding some operator with a nonzero vacuum expectation value (VEV) that has a nontrivial transformation under the broken symmetry.
As long as it can be shown that the ground state... |
I am a little confused about the way most textbooks and notes I've read find the beta function for QED. They find it by looking at how the photon propagator varies with momentum $q$, in particular in the context of a $2\rightarrow2$ scattering process which is proportional to $e^2$, and arguing that the moving in the a... |
I have read on many websites about the Bohr's model of atom but I couldn't find the reason or prove for why can there be more than one electrons in an orbit or counterproof for one electron in each orbit ( like the one with the planets in our solar system).
Can anyone give me the reason why there exists more than one ... |
First time poster here so I hope I'm not missing anything.
The question
"Consider a simple, lattice model for a polymer. In this model, the polymer sits on a square lattice,
and at every lattice point, the polymer can do one of three things: go straight or choose between
the two directions which makes right $90^{\circ}... |
I'm studying the kinetic theory of gases I managed to derive that pressure is inversely proportional to volume and directly proportional to the average kinetic energy of the gas particles. Similarly, volume is inversely proportional to pressure and also directly proportional to the average kinetic energy. But why does ... |
In the photoelectric effect, electrons are physically ejected from the material. In the photovoltaic effect, electrons are knocked out of their atomic orbitals but remain within the material.
What causes either the photoelectric or photovoltaic effect to take place upon photon absorption? Is it material dependent - i.e... |
Puzzled physics teacher alert!
A problem in our text asks to solve for the mass of a car and provides you with the area of contact of the tires with the road and the GAUGE pressure in the tires. The intent is for you to use the product of Pressure and the total Area to solve for a force (weight) from which you can det... |
I was reading about single slit diffraction in Fundamentals of Physics by Halliday and Resnick. So, to derive the equation for first minima, they divided the slit into two halves. If the width of the slit is $a$ and the observation screen is placed far away, for the fist minima we get, $$\frac{a}{2}\sin\theta=\frac{\la... |
Why is a consideration of a cavity filled with photons used to derive Planck's law? In other words, how is this cavity related to a blackbody of temperature T emitting radiation due to thermal/vibrational motion?
|
I've started reading about the wave-particle duality but, after a few steps, reached a dead end:
Schrodinger equation solutions for a free particle is a sum of terms of the form:
$$\psi(\mathbf{r}, t) = Ae^{i(\mathbf{k}\cdot\mathbf{r}-\omega t)}$$
however, a single element of this form can not normalize, thus, can no... |
Densely packed strings (perhaps in a fuzzball scenario) should impact one another frequently and transmit sound. If they're densely packed enough, the sounds produced might be affected by the fact that strings instead of particles are colliding. Has anyone done work on the role of sound in string theory or just more ge... |
I found this expression for the time-evolution operator:
$$\begin{split} U(t) & = T_{\leftarrow}\exp\left[-i\int_0^t ds H(s)\right] \\ &= \exp\left[-\frac{1}{2}\int_0^t ds\int_0^t ds' [H(s),H(s')]\theta(s-s')\right]\exp\left[-i\int_0^t ds H(s)\right]\end{split}$$
with $H$ Hamiltonian and $\theta(s-s')$ the Heaviside st... |
Why are both axes spinning the same way before colliding? Conversely, in order to collide both spins must be the same?
|
I was recently exposed to an interesting way to solve the 1-d Poisson equation in electrostatics
$$
\epsilon_0\frac{d^2\phi}{dx^2} = -\rho
$$
for potential $\phi$ and charge density $\rho$.
If the charge density has no explicit spatial dependence, we can introduce a function $V(\phi)$ that generates the charge density
... |
Can I think of Newton's Gravitational Constant as a fundamental parameter of nature (based on our current understanding of physics)?
I realize that it is very unlikely that $G$ is actually a fundamental parameter since, among other things, it has units. I am trying to come up with an easy-to-understand example of "a pa... |
To quote from WIKIPEDIA
The simplest form of a blast wave has been described and termed the Friedlander waveform.[11] It occurs when a high explosive detonates in a free field, that is, with no surfaces nearby with which it can interact. Blast waves have properties predicted by the physics of waves. For example, they c... |
What is the meaning of box shape in the ion beam pulses?
i mean in plasma we say the ion beam irradiating the capsule is box shaped. what does it mean?
|
I heard often times that the Higgs-Boson/Higgs-Field is responsible for assigning particles their mass. My question is, if there already exists a particle responsible for mass, why do you need another particle such as the Graviton?
|
I am trying to prove Schwarz Inequality by following QM book by R. Shankar. I got almost to the end where I am having trouble.
I have noticed that there are similar questions on this website, but no one provided the answer I am looking for.
I would greatly appreciate it if you can help me with the missing steps. Also, ... |
Note: I'm probably using the wrong letters/notation here. I apologize. I use $\omega$ to represent an object, and $\mathcal{U}$ is the universe. I'm not sure how else to do it. $m(\omega)$ and $x(\omega)$ are the mass and position of the object, respectively.
I've stumbled upon a roadblock in my understanding of fields... |
I have been learning some field theory and learning about Lagrangian and Hamiltonian density. In classical mechanics, the Hamiltonian is the energy of the system in terms of position and momentum. I understand that similarly, the Hamiltonian density is the energy density in terms of the field and the conjugate momentum... |
I am looking at a nuclear powerplant reactor that has 3.2GW "thermal capacity" and 1GW "nameplate capacity".
What does the thermal capacity entail? Is it how much heat the reactor produces?
|
how are the thermal expansion of a solid and the stress tensor related?
\begin{equation}
\int_{\mathbb{R}^{3N}}\frac{\Delta E_p}{\Delta V}\rho_{H_h}(u)du=\frac{2}{3V}\int_{\mathbb{R}^{3N}}E_p\rho_{H_h}(u)du+\frac{1}{6V}\int_{\mathbb{R}^{3N}}\sum_{ijk}\Psi_{ijk}r_i^{eq}u_ju_k\rho_{H_h}(u)du
\end{equation}
this is th... |
In Shankar's principles of quantum mechanics, the dirac delta function is introduced for generalizing inner products to infinite dimensional spaces. The dirac delta function is such that
$$δ(x-x’) = ⟨x│x'⟩.$$
In the examples, I'm asked to show that
$$δ(ax) = δ(x)/|a|.$$
According to the definition above and the general... |
The following expectation of a time ordered exponential is easy to work with:
$$ \left\langle n \right| T \left\lbrace e^{-i \int_{t_1}^{t_2} V_A(t’)dt’ }\right\rbrace T \left\lbrace e^{-i \int_{t_0}^{t_1} V_B(t’)dt’ }\right\rbrace \left| n \right\rangle $$
with $t_2>t_1>t_0$ and where $T$ is the time-ordering opera... |
Basic question:
Lets assume we have an object (cuboid) in the air, with area A, width w at height h. Is the pressure from above always equal to pressure from below at that object or is the pressure equal if the width w is infinitely small?
|
It is said that all digital devices these days emit blue light rather than UV; long term exposure can hurt our eyes. Why doesn't viewing the blue sky for a long time hurt us? Is there any big difference between these two blue lights?
|
Suppose $\Psi$ is a Dirac spinor, then let the transformation matrix $S$ be defined as usual: $\Psi'=S(\Lambda)\Psi$, where $\Lambda$ is the Lorentz transformation matrix.
Then the questions is: for two Lorentz transformations $\Lambda_1$ and $\Lambda_2$, do $S(\Lambda_1)$ and $S(\Lambda_2)$ obey $$S(\Lambda_1)S(\Lambd... |
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