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I am following Sidney Coleman's lecture of Quantum Field Theory.
In ch 24.3 (starting from page 516) he discussed how to use isospin concept to consider the scattering of one nucleon and one pion. I understand that nucleon has isospin $I=1/2$ and pion has isospin $I=1$, and therefore the total isospin when we combine n... |
I want to know, what's the difference between green and dark green physically?
I know the darkness of color depends the brightness of context, but if the brightness of context is fixed, and I change only brightness like on photoshop:
nothing changes around, so what is "brightness" in physic? its the same wavelength (g... |
In the Van der Waal's equation in volume correction term, a given molecule is able to exclude 4 times of its volume from the volume of the container. Why is it so?
From the Wikipedia page on the topic, it says:
To see this, we must realize that a particle is surrounded by a sphere of radius 2r (two times the original ... |
S is an inertial reference frame with origin at O.
A unit rigid* rod AB is at rest with respect to S. A and B are end-points of the rod.
$xA=0$ and $xB=1$
At $t=1$, point A start accelerating towards right with a constant acceleration of 'a' until time $t = 2$. After that point A stops the acceleration and continues ... |
I am running a 3D molecular dynamics solution of a Lennard-Jones fluid with $N$ particles in a box, and I want to plot the velocity autocorrelation function.
From this resource, I see that $$\psi(t) = \left\langle \sum_{i=1} ^N v_i(t) \cdot v_i(0) \right\rangle$$
is the non-normalized VACF.
My problem is that I don't u... |
I have a similar question as Two particles system
That is:
why for two-particle without interaction will have wave function $\psi(x_1,x_2)=\psi_a(x_1)\psi_b(x_2)$
And when we exchange it will have the form
$\psi(x_2,x_1)=\pm\psi(x_1,x_2)$.
and expression
$\psi(x_1,x_2)=A[\psi_a(x_1)\psi_b(x_2)\pm\psi_a(x_2)\psi_b(x_1... |
Are angular velocity, angular momentum and torque "real" vectors in the sense that acceleration and force are? Or are they only considered vectors to explain phenomena like gyroscope procession? Or are they considered vector quantities for other reasons?
It seems to be the case that we only assigned a vector to these r... |
Two commuting operators $\hat{A}$ and $\hat{B}$ always share a complete set of common eigenfunctions. However, in the presence of degeneracy, every eigenstate of $\hat{A}$ need not an eigenstate of $\hat{B}$ and vice-versa. For instance, in case of ${\rm 1D}$ free particle motion, the Hamiltonian $\hat{H}=\frac{p_x^2}{... |
Here is the full Question
The question gives you two Rate constants and asks for what time will the ratio of "sum of stable nuclei of Ca:Ar" be equal to 99.But what is this ?If i think of number of nuclei in terms of concentration then the ratio of them is coming to be simply $$ \frac{k_1}{k_2}$$ and its value is alre... |
In an article from the University of Chicago, July 17, 2020, it is stated that
"Judging cosmic distances from Earth is hard. So instead, scientists measure the angle in the sky between two distant objects, with Earth and the two objects forming a cosmic triangle. If scientists also know the physical separation betwe... |
I've been going through significant figures video on khan academy and it says the product of two numbers cannot have more significant digits than the significant digits in any of the inputs.
Example:
length = $301 m$
width = $2 m$
area = $301*2 = 602 m^2$
But since the width has only $1$ sigfig, we must round area to $... |
Wikipedia and plenty of other sources give values for the luminance of the sky, of e.g. $\mathrm{2\ kcd/m^2}$. What area is the denominator representing here? How can something like the sky, that doesn't have an area, have a luminance at all?
|
Take a spin $1/2$ particle with its spin pointing along $\hat{n}$ defined by
$$\hat{n}=(\sin{\phi}\cos{\theta},\sin{\phi}\sin{\theta},\cos{\phi})$$
We are measuring the spin along $\hat{n}$ and the operator corresponding to this observable is $\vec{S}\cdot\hat{n}$.
$$\vec{S}\cdot\hat{n}=\frac{\hbar}{2}\begin{pmatrix} \... |
I have a set of data with decibel values of -10.5, -9, -9.5, -9.5, -9, -9. How do I find the average of this data set? I am not measuring energy specifically or anything along those lines, only the amplitude of the sound waves. I have taken the simple arithmetic average of this data but I am not really sure if this is ... |
I am currently studying Physics of Photonic Devices, Second Edition by Shun Lien Chuang. Chapter 1.3 The Field of Optoelectronics says the following:
One can grow a few atomic layers of $\rm AlAs$ on top of a $\rm GaAs$ substrate, then grow alternate layers of $\rm GaAs$ and $\rm AlAs$. One can also grow a ternary com... |
I am studying the math of tensors, I have an understanding of the concepts of covariance, contravariance, dual spaces, Einstein notation and so on. I am a bit confused about the notation though.
My quick questions:
Is $v^ie_{i}$ a tensor? ($v$ are the components of a vector and $e$ are the basis vectors)
Is $v^iv_{i}... |
I know excited atom can emit photon at any direction as long it stays consistent so the total angular momentum and spin states are conserved, this is spontaneous emission. What about stimulated emission? Does it means more photons of same angular momentum and spin are absorbed by the one atom so the only exit is pointi... |
While calculating the matter density of the universe, we need to find luminosity. How do we experimentally estimate the luminosity of a star?
|
I was reading this article from Ethan Siegel and I got some doubts about a sentence about entropy, specifically when Ethan explains the irreversibility of the conditions of the hot-and-cold room, as in this figure:
In his words:
It's like taking a room with a divider down the middle, where one side is hot and the oth... |
I would like to get some comment about the following obtained result.
I consider the one-dimensional time-dependent Schrodinger equation for two non-interaction particles with masses $m_1$ and $m_2$:
$$
i \hbar \frac{\partial \Psi}{\partial t} = - \frac{\hbar^2}{2m_1} \frac{\partial^2 \Psi}{\partial x_1^2} - \frac{\hba... |
The main argument used to solve the twin paradox is based on the accelerations and decelerations of the observer considered to be in motion. In the twin paradox of the version described here, accelerations and decelerations are bypassed, thus the main argument is disarmed.
We consider three twin brothers, Mov (moving),... |
There is a quantum harmonic oscillator such as the vibration of diatomic molecules. [1, 2]
The molecular vibrations are quantized and the energy spectrum of the system is discrete, $\hbar\omega\left(n + 1/2 \right)$.
On the other hand, we have macroscopic classical harmonic oscillator such as the mass-spring system. I ... |
The following Wikipedia page uses $x_\varepsilon (t) = x(t) + \varepsilon (t)$ in the proof.
https://en.wikipedia.org/wiki/Hamilton%27s_principle#Mathematical_formulation
But in my mechanics book (by David Morin), the author uses something similar to $x_\varepsilon (t) = x(t) + \varepsilon \eta (t), \ \varepsilon \in \... |
I am currently studying Physics of Photonic Devices, second edition by Shun Lien Chuang. Chapter 1.3 The Field of Optoelectronics says the following:
The control of the mole fractions of different atoms also makes the band-gap engineering extremely exciting. For optical communication systems, it has been found that mi... |
For a $n$-atomic gas in any sort of geometry,
The formula for $f$ is
$$f = 3n- \text{number of constraints}.$$
The way I was taught this formula was like each $n$ particles< there is $3$ ways it can move so $3n$ now from these ways we need to exclude the number of constraints on it's motion. But now I'm confused, becau... |
Suppose two atoms collide (considering one atom to be at rest), in a way such that the energy loss during their collision is more than sufficient to excite the atom (which is at rest) but the remaining energy is not sufficient to excite the first one.
My doubt is, if the energy is completely transfered to the atom at ... |
Blue vector is the magnetic field vector. Red vector is the velocity vector of the point charge (light grey) q. Green vector is the force vector (force on moving charge q due to the magnetic field). I have heard that workdone by a magnetic field on a moving charge is zero. Let's say that a charge q which was already m... |
In the Lagrangian picture of special relativity we usually define the action $$S = -mc^2 \int d\tau.$$ This is clearly 0 for massless particles, so it says absolutely nothing about their motion. Despite that, from this Lagrangian we obtain momentum and energy (after passing to the Hamiltonian) and eventually conclude $... |
I'm (almost self-)studying group theory trying to understand what "quantum field theory" really means. I have some confusions regarding the group theory, because it is a really wide topic given in my course "as it is", without proofs and nothing, so I'm trying to understand at least the most basic things by myself.
Thi... |
I am trying to solve the 1-D diffusion equation in a tube of finite length that extends from $-L\leq x \leq L$. I have assumed that the radius is much smaller than the length of the tube so that we can neglect variations in the radial direction. Suppose I inject some amount of a substance at $t = 0$ such that the conce... |
In Physical Chemistry by Peter Atkins and Julio de Paula, the exponential factor $e^{-E_{a}/RT}$ indicates the fractions of particles/molecules that have at least the energy $E_{a}$. I'm slightly confused because from what I've learnt in statistical thermodynamics the exponential factor should be proportional to the fr... |
In deriving a general propagator to the time-dependent ($H = H(t)$) Hamiltonian problem, Shankar works to first order in $\Delta = T/N$ (a small time interval for large $N$) and argues that by integrating the Schrodinger Equation over the interval $\Delta$ we get:
$$|\psi(\Delta)\rangle \approx |\psi(0)\rangle + \Delta... |
My question is kind of old and asked but I still didn't get the answers, if I don't consider the ohm's law or hydraulic analogy and answer this question solely by logic. Why should voltage differ in series and not in parallel with same resistors? The energy for charges to move through the resistors in both the orientat... |
I have two questions on the general topic of energy potentials that diverge at infinity.
First of all, the inverted harmonic oscillator. I found this post on Physics SE, Inverted Harmonic oscillator.
The answer from fellow user Mazvolej states that
"<...> The QHO does not permit analytic continuation, because it's ene... |
I recently started reading about the topic "Waves" and started learning it from Transverse Waves. After building enough intuition I moved on to longitudinal waves especially sound waves. While reading the same from "The Concepts of Physics-by H. C Verma", I came across the following part:
The fact that displacement is... |
I have seen that the solution of the quantum pendulum is obtained by solving the Mathieu's equation form of the Schrodinger equation and it also depends on a parameter 'q' called the energy barrier.
But can we approximate the energy levels of the quantum pendulum to that of the quantum harmonic oscillator? Under what l... |
I have a question about normal force:
How do you find it's magnitude when there is just on contact point betwenn bodies and not directly below the center of the mass? For example, how would one calculate normal force and friction in situation like this one the picture?
|
I'm trying to understand the role of dark matter/energy in universal evolution. What I know is they occupy a large percentage of our unverse's energy density, and to observe them we use type Ia supernova as a "candle", but I still confused with two point
what's the exaclty method that we used (with type Ia supernova o... |
I read on Wikipedia:
Quantum mechanics predicts that certain physical phenomena, such as the nuclear decay of atoms, are fundamentally random and cannot, in principle, be predicted.
What does that mean exactly? I thought nothing can be predicted with arbitrary precision. Yet, we still often model physical phenomena t... |
In a mechanics problem involving finding final velocity of falling chain when half of chain has fallen from incline I am getting two results by applying two different methods , one involving taking centre of mass of whole chain and other by applying centre of mass of two parts of chain (fallen and incline) part.
The ... |
In SR the 4-divergence of the 4-position gives the dimension of spacetime.
What is the dimension of spacetime in GR, i. e, The covariant divergence of the covariant position?
|
Suppose i have a man standing on a plank.There exists friction between the plank and the man but there isn’t any friction between the plank and the ground. If the man starts running on the plank towards right then by conservation of momentum, the plank must have a velocity towards the left as seen from the ground.Since... |
There is a beautiful question I ran into:
A gas tank filled with gas at temperature $T$. The gas is at rest first. It is accelerated to a constant velocity of $V$. Assume the process is adiabatic.
Will the temperature of the gas change? (if yes - will it increase or decrease?)
I think there is a nice discussion we ca... |
I think I've understood the general idea of the WGC (proposed in https://arxiv.org/abs/hep-th/0601001). From a more recent review, I quote:
In a consistent effective field theory (EFT) coupled to gravity, gravity must always be the weakest force.
(The reference is https://arxiv.org/abs/1711.00864). This implies that ... |
The formula for calculating pressure would be:
$$P=\frac{F}{A}$$
i.e. force per unit area.
But, I'm confused, shouldn't the $A$ factor also consider the thickness of the surface? E.g. a sheet of paper $200\ \mathrm{m}$ in length and width may not be able to reduce the pressure exerted by the feet of the elephant as wou... |
The solution for the wave equation for the electric field is generally: $$\vec{E} = E_0 e^{i(\vec{k}\cdot\vec{r} - \omega t)} $$
My question is about the complex part, why do we use complex numbers? Why isn't it described by a cosine function without an imaginary part? Is it only out of comfort, making phase shifts mor... |
If I have a conducting spherical shell of outer radius $R$ and inner radius $r$, the electric field inside is $0$. The argument commonly given is:
Pick a point $P$ inside the shell (i.e. radius < $r$) and draw a sphere such that $P$ lies on its boundary. Then the charge contained by this sphere is $0$, so the electric ... |
In water the speed of light changes to $2.25 \cdot 10^8m/s$. Can a electron travel faster/travel at the same speed in water. I don't see any violation of SR. So shouldn't it be possible for an electron to travel at say $2.5 \cdot 10^8m/s $. Water is just an example.In other mediums like hydrogen electrons in exc... |
I have a question concerning the quantization of phase-space variables $(q_1, q_2, q_3, p_1, p_2, p_3)$ with the Hamiltonian
$$
H = \frac{3}{2}(p_1^2+p_2^2 +p_3^2)
$$
and the following non-commuting second class constraints:
$$
\Phi_1 = q_1+q_2+q_3=0\\
\Phi_2 = p_1+p_2+p_3=0.
$$
The general method proposed by Dirac in ... |
This equation is related to a similar question I have asked before here-Diffusion profile for localised release.
I am trying to solve this equation numerically in MATLAB. I have approximated the density of the substance 'A' by a normal distribution at $t=0$ so that I don't have to deal with the Delta function. Suppose ... |
As energy is proportional to the speed of light at what percentage of the speed of light would an object's energy reach the Planck energy level?
|
Partially motivated by this question, I get the impression that it is generally more difficult to make accurate statistical predictions in Physics about "the small" (microscopic phenomena) than "the big" (macroscopic phenomena).
Why? Do we know what explains this relationship between scale and uncertainty?
For example,... |
Given the definition here.
What are the symmetries of:
$$\mathcal{S}[\phi_2,t_2;\phi_1,t_1]=\langle\,\phi_2\,|e^{-iH(t_2-t_1)/\hbar}|\,\phi_1\,\rangle.$$
which is the amplitude to go from the field configuration $
\phi_1$ at time $t_1$ to $
\phi_2$ at $t_2$ for a scalar Klein Gordon field.
Some I know. It must be invar... |
In most audio editing software(like audacity) waveform can be viewed. Zoomed in these look like actual waveforms. Out of curiosity I downloaded some frequency sweep test files(which are intended to test the linearity of associated devices). In all of these files the amplitude was constant, only the frequency was increa... |
It is well known, how to construct Einstein gravity as gauge theory of Poincare algebra. See for example General relativity as a gauge theory of the Poincaré algebra.
There are
Construction of covariant derivative:
$$ \nabla_m = \partial_m -i e_m^{\;a}P_a -\frac{i}{2}\omega_m^{\;\;\;cd}M_{cd}.$$
Impose covariant con... |
When speaking about the grand-canonical ensemble of a statistical system, one usually works with a case, when there are several conserved quantities - total number of particles $N$, angular momentum $J$ or some other kind of charge. And the grand-canonical partition function has the form:
$$
\mathcal{Z} = \text{Tr } e^... |
In a magnetostatic exercise I am given an infinite cylidrical pattern with current density $\vec J$ flowing in the cylinder's axis direction.
My question is, in which cases is the electric field everywhere zero?
|
I'm studying differential geometry basics for general relativity. I know that spacetime is modeled as a 4-dimensional smooth manifold. Smooth manifold means that we consider a restriction of the maximal atlas such that all charts in it are compatible. A smooth manifold is specified once we choose an equivalence class o... |
In the book called Electricity and magnetism by Purcell, in page-240, he writes that Q in a surface is defined as
$$ Q = \epsilon_{o} \int_{\partial S(t)} \vec{E} \cdot \vec{dA}$$
Now, I'm quite confused with this definition because the Electric field of charge distribution is defined using charge distribution and now ... |
I was thinking if we had two parallel plates seperated by $d$ meters and with voltage difference of $V$, then one has an electric field between those plates with strenght,
$E=\frac{V}{d}$
Now, if one place a piece of wood between the plates for instance, would the electric field straight change? How would it change?
|
In the above diagram, assume that the level is solid and massless:
In the left setup, both mass are fixed on the level. As we know, it is not a stable mechanical balance. For any tilt, the level will tilt more.
In the right setup, both mass are hanged from a fixed location from the level. It is also the normal and o... |
I'm having a lot of trouble figuring something out. I am aware that permanent magnets can be demagnetized due to strong enough external magnetic fields. My question though, is whether this kind of demagnetization is linearly proportional to the strength of the external field or if there is a minimum external magnetic... |
Can someone explain the meaning of this fermionic segment that is orthogonal to the time axis?
I am relatively new to Feynman diagrams and have so far only observed lines orthogonal to the time axis that correspond to exchange particles. What sort of interaction does this fermionic middle line between the vertices desc... |
Given state $|\psi\rangle = \frac{|00\rangle + |01\rangle + |11\rangle}{\sqrt{3}}$ I was calculating the reduced density matrix $\rho^A$.
The given answer was $\rho^A = \frac{1}{3}\begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix}$
But I am getting a different answer first, I calculated $|\psi\rangle \langle\psi|$ which was ... |
I am studying the $S$ duality between 11D supergravity and type IIA superstring theory from Adel Bilal’s paper. The author says:
Of course, eleven dimensional supergravity is not expected to yield a consistent quantum theory. It should only be the low-energy limit of some consistent theory, baptised M-theory.
I don’t... |
Is there a way to convert a pair of altazimuth coordinates (one for each of two observers) into vectors so as to compute the difference between them (i.e. both altazimuth coordinates point at the same object in the sky, and by subtracting the vectors one could obtain a vector between the observers)?
|
I just recently discovered this theory. It claims to derive quantum mechanics from general relativity. I found this interesting and perhaps promising, but I'm afraid I don't have enough expertise to say with confidence that this theory is worth anything.
|
The temperature can be interpreted as a measure of kinetic energy per particle. In fact, denoting with $f(\vec{v}) d \vec{v}$ the number of particles with velocity in $d \vec{v}$ one obtains that the pressure exerted on the walls of the container of area $A$ along the direction $z$ is
$$
p=\frac{1}{A} \int d F_A=\frac... |
I am considering the calculation of the vertex correction due to electron-phonon interactions. Specifically, I am looking for solutions to the integral (Eqn. 1)
$$\int dq G(q)D(q-p)G(p+k)$$
where $dq=d^4q/(2\pi)^2$. The fermionic Green's function is given by
$$G_\sigma(p,\,\omega)=\frac{Z}{\omega-v_F(|p|-p_\sigma)+i\de... |
Right now, I'm studying thermodynamics, and I am a bit confused on the differentials.
For example, the equation for work is $W=p*{\Delta}V$, and usually people change it to $dW = p*dV$.
But, as long as it is not isobaric process, pressure is changing, so can't you also do $dW=dp*V$? I know we usually do $dV$ since the ... |
Two transparent plastic sheets say of red and blue color overlap as shown in figure . An observer looks at a clear sky through the sheets.
He will observe light coming through sections as,
SECTION 1: Red color, less bright than usual
SECTION 2: Blue color, less bright than usual
SECTION 3:Dark,almost no light
Now the ... |
I saw some where frequncy means how fast a signal is changing and i am confused.
Since frequncy means how much cycle a signal completes in unit of time and we may say how fast a signal is moving but the changing here i don't get. Can some body help? Thanks in advance.
|
I've read elsewhere about the energy of a wave or wave packet, and the amplitude of its probability amplitude, affecting its odds of quantum tunneling...
But what about the wavelength or frequency of a particle(s)?
|
I had a doubt about a question:
Raindrops falling with terminal velocity strikes on a surface normally. Force exerted by the drops per unit area is $F$. if the number of drops striking the surface per unit time becomes one fourth and size of drops become double then force on the roof per unit area will be:
Ans: $8F$
... |
The energy levels of a infinite square well is given by :
$$\epsilon=\frac{h^2}{8ml^2}(n_x^2+n_y^2+n_z^2)=\frac{h^2}{8ml^2}r^2$$
The number of energy levels below a certain energy level for large quantum numbers (for large r), $\epsilon$ is given,
$$\phi(\epsilon)=\frac{1}{8}(\frac{4\pi r^3}{3})=\frac{\pi}{6}\Big(\frac... |
I understand main sequence stars become subgiant when hydrogen is depleted in their cores and they start hydrogen shell burning. But I don't understand why this process is divided into two distinct phases, instead of being a continuous expansion as more and more helium builds up in the core. Why is there a sudden point... |
Suppose an inextensible massless rope is placed on a pulley surface. Obviously there will be a normal force between the pulley and rope, right?
Why is the normal force of rope on the pulley ($N_{pulley,rope}$) not considered while analyzing the free body diagram of pulley?
I have added a picture showing where I was c... |
Recently I came across this problem :
There are two identical parallel plates of length $L$ and breadth $B$ on the XZ plane . One plate passes through $Y = 0$ and the other passes through $Y = d$. Between them is a dielectric medium whose Dielectric constant changes as $\kappa = \kappa_0(3 + \frac{y}{L})$. Calculate ... |
Going by the Wikipedia explanation, a derivative measures the 'sensitivity' of a function to tiny nudges in its input.
How well does this fit with the velocity being the derivative of position? I can't see an intuitive relation between the two concepts. But I don't understand what the 'order' of smallness must be? How ... |
I am looking to understand the equation and physics of audio transmission through walls. I wish to model the indoors transmission of sound between rooms and I wish for any academic (not tutorials) material on the transition of the wave, as well as, physical approximations of physical parameters such as different materi... |
One can draw/imagine as many unique (curved/straight) lines as he/she wants in some specified finite area (assuming that each line is unique if it doesn't overlap with another line). Then how can the number of field lines in a particular area be a fixed quantity? This statement is contradicted by the fact that a partic... |
Groenewold in his book On the Principles of Elementary Quantum Mechanics (1946, Springer Netherlands) page 45, maps the canonical momentum $p^2$ in the classical phase space to a general canonical operator ${\mathbf{x}_1}$:
\begin{equation}p^{2} \rightarrow {\mathbf{x}_1}. \tag{4.06}
\end{equation}
Hence, the Poisso... |
While drawing ray diagrams for plane and spherical mirrors, what is generally taken as the point of observation?
Eg, If a concave mirror is presented with, say a wire turned into a triangle, placed from focus towards the mirror, the image can be obtained following rules of reflection but where would the eyes need to be... |
So I came across this equation in my EM book and I would like to determine the vector $L$.
$L$, $p$, $q$ are vectors, $P\times L$ means $P$ cross product $L$ and a is a constant.
$$aL + P \times L = q$$
I've tried to get rid of the product vector but still I couldn't find a way to determine $L$.
|
What changed around them or inside them? How does this mechanics work?
For just example energy is a foggy cloud when atoms are "more defined spheres". So from that point: "spheres" in static 3D "net" positions without movement at same moment energy with movement through this net... Why atoms move and they are "unstable... |
I was reading an article from abcnews about Why so many people survive being struck by lightning. Later in the article it says the following:
But direct strikes make up only a minuscule portion of all lightning
strikes, said Cooper.
"The vast majority of deaths are caused by ground current, where
lightning hits a di... |
One derivation of enthalpy by Kittel and Kroemer uses: $dW’ = dW + d(PV) = dU + d(PV) - dQ = dH - dQ$. My understanding is, however, that $dW$ already includes $d(PV)$, so I find it redundant to add $d(PV)$ to the work. If $d(PV)$ and $dW$ are separate, then what kind of work does $dW$ denote (most work done by gases i... |
As far as I know, immiscible liquids form emulsions when mixed, so will Pascal's law apply to this emulsion?
|
Why is the probability for each momentum in a loop (e.g. vacuum polarization) equal?
Why has a infinite momentum the same probability to occur than a virtual particle with low moment. I know - these particels are virtual and in some sense not physically.
But at the end, we want to describe our universe - so in some se... |
Could you please tell me how Hilbert spaces are geometrically linked with our spacetime?
Both host functions of $x$, $t$, $m$, ... and there must be a mathematical link between them?
A drawing would be welcome.
Second question, related:
Is there a space that englobes both?
|
In mechanics, the conjugate momentum is defined to be $\pi=\dfrac{\partial L}{\partial \left(\frac{dx}{dt}\right)}.$ This can be regarded as a partial derivative with respect to a derivative of a dependent variable ($x$ depends on $t$, the latter being the independent variable). In (scalar) field theory, the number of ... |
If a sound source is placed 1 meter away from a decibel meter reading X decibels at ambient pressure, what would that decibel meter read at the same distance at 500 hPa of pressure, or really any pressure P? Everything else is kept constant. Is there a formula to determine this? Since there is no sound reading at a com... |
For the Derivation of the Schwarzschild solution my Professor use:
$R_{\mu\nu} = 0$ since we are in vacuum.
I see that we are in vacuum, but we assume a mass at point $r = 0$.
Thus, the curvature is nonzero.
But from $R_{\mu\nu} = 0$ we get $R = 0$ (Ricci scalar), that means the curvature is zero.
Where am I wrong?
|
I don't know if this is a valid question to ask, but I am wondering about the following: We are given a set of $\mathcal{c}$-number Lie-Brackets
$$
[q_i,q_j] = 0= [p_i,p_j] \\
[q_i,p_j] = c_{ij},
$$
with $c_{ij} \in \mathbb{C}$. Is it possible to obtain a quantum theory from this algebra? If yes, is there some kind of... |
Why are there several different versions of the scalar field solution, with a different coefficient in front of the exponential in the solution? Why don't all the authors use the same convention? I mean why do different quantum field theory books have different conventions regarding the normalization?
|
Suppose potential is given by $V(x) = -\int^x F(x')dx'$,where $F$ is force. To show energy $E(x,v)= \frac{1}{2}mv^2 +V(x)$ is conserved when Newton's laws holds.
We need to use the fact that $V(x)$ is differentiable,and we know $V(x)$ given in closed interval is differentiable if and only $V(x)$ is absolutely continuou... |
Context: Consider the advection-diffusion equation with periodic boundary conditions (PBC) over a flat square domain $L \times L$.
The scalar density $\rho $ is transported by a prescribed field $\mathbf{v}=-\nabla U$, where $U(\mathbf{x})$ is a scalar potential that has the periodicity imposed by the PBC. The density ... |
The following table gives us the correspondence between objects in Type IIA Superstring theory and M-theory:
The D6 brane is magnetically dual to the D (10-6-4) = D0 brane and so magnetically couples to the RR gauge field $A_{\mu}$. My question is: what about the D8 brane from IIA superstring theory? What does it corr... |
I am looking to study QM but I found out that I don't understand all the complex number representation like plane waves and many more. So what are some good books to study this topic of complex analysis used in plane wave representation etc in the beginner level? The book should be of a beginner level and I like it to ... |
I realise that a magnetic dipole moment is essentially defined on the basis of torque, which also seems to imply that a magnetic field imposed on a current-carrying closed loop can only induce a torque, and never a net force.
Are there any exceptions to this?
|
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