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I have recently become interested in special relativity. I would like to stress that I am not a physicist, but just a curious person. I read that a piecewise twice continuously differentiable curve $\gamma$ in the Minkowski spacetime can be used to represent any massive particle, and every vector tangent to $\gamma$ is... |
When my window is open, the wind from outside blows the curtains into the room, but sometimes after that it's pulled towards the mesh. It doesn't happen every time, so I think this happens randomly. Does this happen when the speed of the wind decreases causing the pressure on the curtains from outside to increase, or d... |
I was reading Philip W Anderson's essay "More is Different" (https://www.tkm.kit.edu/downloads/TKM1_2011_more_is_different_PWA.pdf) and at some point he links the isotropy and homogeneity of space and matter with fundamental symmetries of nature:
„By symmetry we mean the existence of different viewpoints from which th... |
In order to be able to move together through the solid, the electron and hole making up an exciton must have the same group velocity. Given the dispersion $E(k)$ the group velocity is given by
$$v_g=\frac{1}{\hbar}\frac{dE}{dk}$$
I was told that it is possible for an exciton to be formed from a conduction electron and ... |
I am mostly concerned with the correct notation, so I can be able to derivate the correct expression regarding the prob. of measuring an arbitrary eigenvalue $a_n$ of an observable $A$ that has a discrete non-degenerate spectrum, while the system is in a mixed state.
I will start with a simple case, so that it is easie... |
I'm currently reading Griffiths' book about Quantum Mechanics but I cannot understand how he derives the formula for the time derivative of the expected value of position in 1 dimension.
He writes:
$$\frac{\mathrm d\langle x \rangle}{ \mathrm dt} = \int x\,\frac{\partial}{\partial t}\left(|\psi|^2\right) \mathrm dx =\f... |
I'm not quite understanding the concept of a magnetic dipole.
From what I've seen, we can treat a given conducting loop as a magnetic dipole ONLY in the approximation where we consider its potential (and consequently the resulting magnetic field) in the limit where the distance from the coil is much greater than the si... |
We know and have actually measured in the lab with self-interference neutron experiments the 4π-symmetry (720° rotation Dirac Belt characteristic) of all spin-1/2 particles (except the neutrinos) thus the charged fermions.
Also we know that all normal Bosons like photons are spin-1 particles and therefore have a normal... |
Consider a current-carrying loop. I am trying to work out the magnetic field at the a certain point on the wire due to the other points of the wire. I will call this point P. I am trying to calculate this to find out the effect of the current on the change in radius of the loop. It seems quite obvious that the radius w... |
I'm reading this paper about QED counterterms:
https://southampton.ac.uk/~doug/qft/aqft3.pdf
In this paper by calculating the electron self energy we have following expression:
$$\Sigma(p^2,m) = -\frac{\alpha}{2\pi}\left((\gamma \cdot p-4m)\left(\frac{1}{\epsilon}-\gamma_E+\operatorname{Ln}(4\pi)\right)+\gamma \cdot p-... |
Lets consider this scenario in deep void of space where other curvatures of large objects are negligible in this case and we bring 2 objects lets say $A$ and $B$.
We give it a force slightly lower Force ($F$) than the gravitational force of attraction ($F_{g}$) of both objects in sense of Newtonian gravity in the oppo... |
I am reading an article and the authors give this definition of the matter density parameter $\Omega_m$
$$\Omega_m=\frac{8\pi Ga^2}{3\mathcal{H^2}}\overline{\rho}=\frac{\mathcal{H}_0^2\Omega_{m0}}{a\mathcal{H}^2}$$
where $\Omega_{m0}=8\pi Ga_0^2\overline{\rho}_0/(3\mathcal{H}_0^2)$. Since the density scales as $\rho=\r... |
Bargmann's theorem is usually stated for a simply connected Lie group with vanishing second Lie algebra cohomology $H^2(\mathfrak{g},\mathbb{R})$. I found a generalization of this result in a thesis https://www.math.ru.nl/~landsman/Nesta.pdf, which accounts for $G$ being not simply connected. The theorem reads:
This i... |
This implies that our first-order correction always overestimates the true change in the energy. I was trying to think of the second-order correction in terms of a second derivative but can't think of a good reason.
|
I have been interested in the following question and I just wanted to present my solution to see if it makes sense. Consider a heavy object of mass $M_o$ which is being dropped from a height $H_o$ into a cup of mass $M_c$ attached to the end of a (thin) plank of mass $M_p$ and length $L$. The other end of the plank con... |
Here is the question. Now I want to understand the alternative method below to solve the angular momentum. Normally in a point we can decompose the angular momentum about the point into distance vector from the point to the center of mass cross product the momentum of the system, if it is a rigid body, plus the angula... |
Consider that you are receding at a velocity faster than the cosmic speed limit (say, $2c$ with respect to $A$) due to the expansion of our universe. According to me, $A$ is moving at $2c$ and thus for me, it is invisible. Similarly, according to $A$, I am moving at $2c$ and thus for $A$, I am invisible.
Now consider $... |
For a process $A + A \rightarrow B + B$ scattering, Griffith says that the rules yield this integral
$$-i(2\pi)^4 g^2\int \frac{1}{q^2 - m^2_c c^2} \delta^4(p_1 - p_3 - q)\delta^4(p_2 + q -p_4)d^4q$$
so far so good. However, he also says that replacing $q$ with $p_4 - p_2$ and doing this integral we have
$$-i(2\pi)^4 g... |
Consider an integral:
$$I^{ij}=\int\frac{d^d\textbf{p}}{(2\pi)^d}p^i p^j f(\textbf{p}^2).$$
How can we show that this is equal to:
$$I^{ij}=\frac{\delta^{ij}}{d}\int\frac{d^d\textbf{p}}{(2\pi)^d}\textbf{p}^2 f(\textbf{p}^2).$$
My attempt is to rewrite like
$$I^{12}=\int^{\infty}_{-\infty}dp_1 dp_2 p_1 p_2\int\frac{d^{d... |
To highly clarify my question, let me define what I mean by a random event: "the event e is random, if and only if by having all the data about an event e, we cannot predict the consequences of the event e"
e.g. according to this definition, computers don't generate numbers really random. They just get a seed that is t... |
I am studying evanescent field and diffraction limit and I have one question.
Given a field $ U(x,y,0)$ we can decompose into 2D plane waves.
$U(x,y,0)= \int \int dk_x dk_y \tilde{U}(k_x,k_y) e^{+i(k_x x + k_yy)}$
if we want to have $U(x,y,z_0)$ we can propagate each wave to the plane $z_0$ in this way.
$U(x,y,z_0)= \i... |
I am a little bit confused about whether the inner product between the Riemannian metric tensor and Minkowski metric tensor is equal to the Kronecker delta function:
$${\eta}^{{\mu}{\nu}}{g}_{{\mu}{\alpha}}={\delta}^{{\nu}}_{ {\alpha}}.$$
Is the above inner product correct and valid?
|
A cat moves along the x-axis with a uniform velocity u. A dog moves with a uniform speed $v$ such that at every moment it is aimed towards the cat. Initially, at $t = 0$, the dog is perpendicular to the cat at a distance $l$ away from it. Find the equation of the trajectory of the dog.
My Approach:
(I used a hand-dra... |
$p(\mathbf{x},t\vert\mathbf{y},t)=\delta\left(\mathbf{z}-\mathbf{y}\right)\tag{3.5.7}$
For a small $\delta t$, the solution of the Fokker-Planck equation will still be on the whole sharply peaked and hence derivatives of $A_j(\mathbf{z},t)$ and $B_{ij}(\mathbf{z},t)$ will be negligible compared to those of $p$. We are... |
I have now seen at several places claims of the form "each state looks like the vacuum at short distances" or similiarly that the "leading singularity of correlation functions is universal", i.e.
$$<A|\phi(x)\phi(y)|A> \sim <\Omega|\phi(x)\phi(y)|\Omega>,$$
for $x,y$ close, where $A$ is some state and $\Omega$ the vacu... |
Following this question: Why can the Klein-Gordon field be Fourier expanded in terms of ladder operators?
I can see that the when we Fourier transform the $\phi(\vec{x})$ operator and plug it into the KG equation it tells us that
$$\bigg( \frac{\partial^2}{\partial t^2}+|\vec{p}|^2+m^2 \bigg)\bar{\Phi(\vec{p})}=0;$$
th... |
Consider the relativistic Lorentz force equation given by
\begin{equation}\
\frac{d}{dt}\left(\frac{m\dot{x}}{\sqrt{1-|\dot{x}|^2/c^2}}\right)= E(t,x)+\dot{x}\times B(t,x).
\end{equation}
Here, $E$ and $B$ denote respectively the electric and magnetic fields and are given by
\begin{equation}
E=-\nabla_x V-\frac{\parti... |
This notes explains how thermodynamic potentials $\Phi$ can be used in Boltzmann factor:
$$p = \frac{e^{-\beta\Phi}}{Z}$$
For example, The author claimed that in order to study macrostates instead of microstates, the appropriate potential in this case would be Helmholtz energy $\Phi=E-TS$.
But what I don't understand i... |
I am now in my 6th semester of my physics bachelor and now I'm searching for a complex analysis book.
It shouldn't be too long and deep and not too "mathematical" (I don't need every proof). Applications (preferable in physics) would also be great.
Many illustrations for visual understanding would also be perfect
|
If so, that means gravity is only 9.8 m/s^2 at the surface of the earth?
|
As I think I somehow understand electromagnetic induction and after watching several experiments on YouTube with magnet pieces left to fall through coils which had connected ends to permit the electric current to flow through them, I imagined how this feature can be used to easily generate electricity at home by just m... |
This thread has the following 2 goals:
Knowing how to properly write the below considered cases.
To help individuals who might want to know the correct expression and calculation for a specific case.
It will be a lengthy one, but I believe it benefits, me personally, but also other members of the community as well.
I... |
Feynman diagrams arise mathematically essentially as neat graphical ways of organising the terms in Wick's theorem for time-ordering. But at the same time we're supposed to interpret them as some sort of "physical process". Like nucleons "exchanging" a meson and so on. But why should the neat mathematical tool have any... |
Physics sometimes uses a technique called the method of differentials, which seems magical and not very systematic. This makes me unsure which variable I should take the differential of, and sometimes when I choose different differentials, I get the wrong result in my calculations (which may be my own fault). So I'm wo... |
I am studying the definition of the stress element from the book Theory of Elasticity from S. Timoshenko and J.N Goodier. In page 3 it is shown that from taking the moment of forces acting on the element along the x-axis (which must be zero to be in equilibrium), body forces are neglected compared to the surface forces... |
The time rate of change of neutron abundance $X_n$ is given by
$$\frac{dX_n}{dt} = \lambda - (\lambda + \hat\lambda)X_n$$
where $\lambda$ is neutron production rate per proton and $\hat\lambda$ is neutron destruction rate per neutron.
Given the values of $\lambda$ and $\hat\lambda$ at various values of time, I need to ... |
Two days ago I posted a post that discusses a very generic gauge transformation. I repeat it here. Suppose we have an action $S=S(a,b,c)$ which is a functional of the fields $a,\, b,\,$ and $c$. We denote the variation of $S$ wrt to a given field, say $a$, i.e. $\frac{\delta S}{\delta a}$, by $E_a$.
Then $S$ is gauge i... |
In summary: If the SE doesn't work with SR, what specifically, in terms of the math, is the reason for this? I'm specifically interested in how this relates to the creation and annihilation operators of QFT, as I previously was under the impression that those operators didn't work with the Schrödinger equation, but m... |
Follow up from my previous question,
I am not sure if a partition function for a system should be constant or not. If not, what are examples of constrained systems with partition function that varies with the system's state?
Here is a particular example that came to mind:
Consider a closed rigid container of temperatur... |
The problem comes from a past exam, which is apparently causing a lot of
confusion between my classmates and teacher. I'll put a slightly paraphrased
version here:
Light of a single wavelength from a distant point source falls approximately
normally onto a diffraction grating positioned with its lines vertical. A
st... |
I'm working with $L_2(\mathbb{R}^n)$, and I have operators of the form
$$ H = - \frac{\hbar^2}{2 m} \Delta + V(x_1, \dots, x_n) $$
where $V(x)$ can be very involved dependence on $x$.
What's a good algorithm to use for computing the spectra of such operators?
Here's what I'm looking for in such an algorithm:
I only ca... |
If we apply pressure on static fluid surface vertically, how could same pressure be applied by fluid in horizontal direction ?
|
I note that there are several question related to absolute rotation so this may be a duplicate but I didn’t see an exact double. In any case, mine is this:
In a hypothetical universe made up by only our solar system, one would not have a rotational reference in absence of distant stars. Therefore any planet could be co... |
I have recently read about the quantization of the energy levels that the electron in a neutral hydrogen atom can be in, and I noticed that all available treatments seem to treat the nucleus as a point charge $+e$ which determines the shape of the electronic wavefunction. However, are there any treatments which conside... |
I would like to understand how exactly a rotating helicopter propeller creates equal but opposite torque on the helicopter body. I learned that if there is no contra propeller (tail rotor), helicopters spin due to unbalanced torque created by the rotating propeller.
So, there’s an electric motor and gas turbine engine ... |
Recently, I saw a question in my exam regarding surface tension. It was mentioned in the answer key that the surface tension of copper and cadmium in the molten state increases with an increase in temperature. In contrast, the surface tension of other liquids continuously decreases with an increase in temperature. Why ... |
In many books, I've seen equations that describe the conduction of charge across a material. It seems all of them define some drift velocity as proportional to the electric field inside the conductor, which makes sense to me given that charges move from atom to atom instead of movent in free space, so as long as the fi... |
The angular momentum is quantified in Quantum Mechanics, it can only take multiples of $\hbar$ https://en.wikipedia.org/wiki/Angular_momentum_operator#Quantization
The previous statement seems to apply to any inertial reference system in which the measured particle is measured; however, the angular momentum is a quanti... |
A question on the IB HL Physics paper of a couple of years back looks like this:
In the second image, taken from this video solution, you see that the given answer should be D.
Now, I have an issue with this and would like to see where I'm going wrong, in case.
First, there's always the ambiguity (typical of these te... |
How does this work? Why are there multiple reflections? And why are the "inner" ones smaller?
|
So, the dirac equation exists
$$\hat{H} = -i\hbar c(\partial_x \gamma_1 + \partial_y \gamma_2 + \partial_z \gamma_3) + m c^2 \gamma_0$$
and describes spin 1/2 particles, and can be generalized to arbitrary gauge fields by modifying the momentum term.
The spin portion of the gamma matrices are built from the elements of... |
Where in the Maxwell Equations it can be seen that the modes can jump between two waveguides in close proximity to each other? Below is coupling coefficient between mode $\nu$ and mode $\mu$:
$$
\tag{42}\tilde{\kappa}_{\nu\mu}=\omega\displaystyle\int\limits_{-\infty}^{\infty}\int\limits_{-\infty}^{\infty}\hat{\boldsymb... |
I am a beginner in quantum mechanics and some confusion came up in the notations while reading about the Hermitian property of operators.
I was told that an operator $\hat {A}$ is Hermitian if the following holds true: $$\int \psi_i ^* \hat {A} \psi_j d\tau = \int (\psi_j^* \hat {A} \psi_i )^*d\tau =\int(\hat {A} \ps... |
I am considering the following derivation for the Lorentz force from a wire.
I am having difficulty understanding why the Lorentz transformation for forces involves the term: $$\frac{1}{1-\frac{vu}{c^2}}$$. The 4-force is given by: $${\mathbf {F}}=m{\mathbf {A}}=\left(\gamma {{\mathbf {f}}\cdot {\mathbf {u}} \ove... |
A rotation matrix parametrized by Euler ZYZ angles, $\alpha, \beta, \gamma$ can be written as:
$$
\hat{R}(\alpha, \beta, \gamma) =
\exp{\left( -i\alpha\hat{J}_{z} \right)} \cdot
\exp{\left( -i\beta\hat{J}_{y} \right)} \cdot
\exp{\left( -i\gamma\hat{J}_{z} \right)}.
$$
Computationally speaking, the matrix exponential $\... |
When a target atom is struck by some kind of radiation (for example, a $\text{MeV}$ proton), electrons from lower shells are kicked off and replaced by electrons from higher shells, which in return emit electromagnetic radiation (photons). Energies of photons emitted during these transitions are specific for every elem... |
Context: I'm working on a space game. I noticed that an unpowered object fired from a strafing spaceship appeared, as the released object moved, to curve in the direction the ship was strafing. This looked wrong, and seems wrong compared against simulated physical reality.
The original code used the firing spaceship's ... |
I have a background in GR and FRW cosmology. I want to learn about primordial magnetogenesis. Could anyone suggest a book?
|
It seems clear that every observable in QM can be represented by some Hermitian operator in Hilbert space.
Does the reverse also hold? That is, for every Hermitian operator $O$ in Hilbert space, is there some observable represented by $O$?
Are there any arguments for or against a particular answer to this question?
|
I'm looking to find experiments that experimentally demonstrate the Idealized greenhouse model.
So far all the experiments I've come across do not quite demonstrate the model, but something else.
There is quite a bit of nuance here, so I will explain. As a brief recap of my understanding, the basic physics model of the... |
I came across with the problem:
A static charge distribution produces a radial eletric field $E=A\frac{e^{−br}}{r}\hat{e}_r$ where $A$ and $b$ are constants. Evaluate the charge density and sketch it.
If the charge distribution is given, we can evaluate the eletric field, the conversely is true? Given the eletric fie... |
I'm going through the derivation LSZ in Coleman's QFT notes. The math is perfectly clear (or at least I don't mind being handwavy about convergence issues), and I'm happy with the idea that \begin{equation*}
\lim_{t \to \pm \infty} \langle \psi | \phi'^f(t) | 0\rangle = \langle \psi | f \rangle.
\end{equation*}
But I'm... |
The prominent justification for ground fault interrupter technology is inability of circuit breaker to trip if intermittent low level arcing is generated as a result of the ground fault, so would you explaining the mechanism that may leads to generation of such low level arcing?
|
I know from the accepted answer to What is the mathematical relationship between the wave functions of QM and the fields in QFT? that "the fields are operator-valued functions of space and time" and that "The fields are operators, so they act on wavefunctions." I've also found several similar threads saying that fiel... |
Specifically, if it turned out the mechanism for quantum entanglement is that all particles are somehow connected to each other via wormholes (assuming that is what the conjecture actually says), it seems like that would explain the correlation without having to invoke any sort of global wavefunction or the like, while... |
It is clear to me that when we are talking about delta function, we should always understand it as a distribution, for example,:
\begin{equation}
\int \delta(x-x') f(x) \, \mathrm{d}x = f(x')
\end{equation}
However, starting from here, I am confused by the following questions:
How do we calculate the integration of a ... |
When two bodies A and B are in thermal equilibrium, I wonder if the entropies of A and B stop changing (ie. stay constant), or their entropies still change but the net change is zero.
What I mean for the latter is that the entropy of body A increases after it receives heat from body B, but after it gives the same amoun... |
In Ward & New (1969), the expression for second harmonic generation (SHG) and third harmonic generation (THG) intensity is derived for the focal volume of a strongly focused gaussian beam (axially thick medium).
The predicted value of the J-integral term in the expression for intensity of SHG under perfect phase matchi... |
The second order correction to the energy of an homogeneous electron gas (jellium) is given rougly by $$E^{(2)}=\frac{Ne^2}{2a_0}(\epsilon_2^r+\epsilon_2^b)$$ with two terms, a direct term
given by $$\epsilon_2^r=-\frac{3}{8\pi^5}\int\text{d}q\frac{1}{q^4}\int_{|\vec{p}+\vec{q}|>1}\text{d}k^3\int_{|\vec{p}+\vec{q}|>1}\... |
Can someone please explain why I'm not getting the known answer, $(2/3)\mu_0M$, using this setup for a uniformly magnetized sphere of radius $b$ and magnetization $M$:
starting with $$dB = \frac{\mu_0I}{4\pi}\frac{(dl \times R)}{R^3}$$
given that volume current density = 0 and a surface current density due to magnetiza... |
The annihilation opertors $\{\hat{a_R}^{(m)}\}_{m=1}^{M}$ of the modes obey the relation
\begin{align}
\label{annihilation}
\hat{a_R}_R^{m}
&= \sqrt{\eta_h} e^{i \phi} \hat{a_S}^{(m)} + \sqrt{1- \eta_h} \hat{a_B}^{(m)}.
\tag{1}
\end{align}
The initial state is
\begin{align}
\vert \Psi \rangle_{IS}
&= \sum_n \sqrt{p_n... |
Consider a sealed jar filled with water and water vapor. Pressure and temperature of the jar is configured in such way that water and vapor coexist with each other (ie. chemical potentials of both phases match).
I wonder which of the following setup is more "stable":
Water vapor fills 1/3 of the jar's total volume whi... |
In the Statistical Mechanics book of Kerson Huang, it is written that "The isotherm in the $p$-$V$ diagram is horizontal during the phase transition, because the gas phase has a smaller density than the liquid phase." I couldn't understand this statement with mathematical equation, can anybody please explain this to me... |
Would frequency of a standing wave in a tube change if the speed of sound was changed? For example, if temperature was increased from 30 degrees Celsius to 20, how would the the frequency of a standing wave in a tube change?
|
On p. 333 in book Quantum Electrodynamics by Walter Greiner, Joachim Reinhardt or other references, they claim that in Bethe–Salpeter equation, we have to use dressed single particle Green's function, including all self interaction with photon.
We want to remark that in principle one should not use the free Feynman pr... |
I’m surveying the relation between quantum and classical mechanics. My interest is how a quantum coherent state approaches a classical state when the wave becomes bigger.
Regarding this, I have a calculation result that a large $\alpha$ coherent state is almost an eigenstate of the creation operator with the eigenvalue... |
When I’ve searched online for the difference between temperature and heat, I’ve seen it defined as:
Heat is the total kinetic energy of an object’s particles, whereas temperature is the average kinetic energy of an object’s particles. But that doesn’t make sense to me, because of two objections I have:
Heat is a form ... |
I am aware that the normal reaction and gravitational force on a body are not action-reaction pairs. However, Newton's Third Law implies that to every action there is an equal and opposite reaction.
My question is:
If we imagine two bodies A and B such that A rests on B, then the weight of B is definitely an action for... |
I am wondering if any wave packet of the form
$$\psi=\int g(\boldsymbol{k}) e^{i(\boldsymbol{k}\boldsymbol{r}-\omega t)}$$
is always a solution to the classical wave equation? In my understanding, this would raise some condition to the amplitude distribution $g(\boldsymbol{k})$. Inserting this into the classical wave e... |
The definition of echo time (TE) in MRI is the time difference between a 90-degree RF signal and the echo peak, which feels like an intrinsic property of the proton.
How can we even control how long does it take for the echo peak to happen?
|
I am dealing with the following problem:
Assume that a charge has been placed on the inner cylinder, and that the entire charge is distributed on the outer surface of the inner cylinder as shown in the figure, giving a surface charge $$σ_1=8.0 \mu C/m^2$$How large will the surface charge be on the inner surface of the ... |
Is it correct to say that the term phase space is valid only in relation to canonically conjugate coordinates and momenta?
Is there a simple/short way to terminologically distinguish the phase space of canonically conjugate coordinates and momenta from the phase space of coordinates and momentum that are not canonicall... |
I'm reading 'Teach Yourself Quantum Mechanics' by Alexandre Zagoskin.
In chapter 2 he introduces Hilbert spaces by starting with the fact that a function may be defined by its Fourier coefficients. There is at this point a diagram implying that a point in Hilbert space may be defined using the coordinates on the axes, ... |
For the ideal gas it is easy to show that $1/T$ is an integrating factor, so
$$\delta Q/T = dS$$
is an exact differential.
So far I haven't found a convincing argument that this should apply in general? Can this be proven in general, or is it just an empirical fact that can only be explained satisfactorily from statist... |
In these three papers, the effect of gravity on anti-kaons, antiprotons, and positrons, is tested by how quickly time moves for them in the presence of Earth's (or the Sun's) gravitational field.
Tests of the Equivalence Principle with neutral kaons: Says that if anti-kaons responded differently to gravity, the kaon/an... |
Introduction to the problem
I computed the absorption by carbon dioxide in earth atmosphere at $14,7$ µm wavelength (absorption band of CO2 where the earth emission is the strongest by far), taking into account the carbon dioxide density decreasing with altitude, the exact solution with hyper geometric series and I fou... |
1.I am trying to understand two-source interference pattern. I am using this simulation for clarity.
As I understand, considering in classic-terms electromagnetic wave has both positive and negative magnitudes, i.e. its electric and magnetic components changes its values from some negative to some positive.
Due to supe... |
i was reading about alternative dark energy models and i stumbled across the concept of quintessence: a scalar field that should generate a dark energy component with a EoS parameter $w$ that varies with the redshift. In particular i wanted to read more about the wcdm model in which $w$ is still a constant but differ... |
Recently I read some literature about how people use the mean-field approximation to solve a particular physical problem. However, I saw people using it in a different way when they dealt with different Hamiltonians. A well-known example would be the BCS theory. People try to perform the Fourier transform on the Hamilt... |
Say I want to solve the eigenvalue problem $$\mathbf{p} \mathrm{u} = p \mathrm{u}$$ where $\mathbf{p}$ is a matrix representation of the momentum operator, $p$ are the eigenvalues and $\mathrm{u}$ the eigenvectors. When I use a central difference scheme to discretize $\mathbf{p}$ I get the Hermitian matrix
$$\begin{bma... |
A regular description of the paradox involves a train travelling through a tunnel which is fitted with doors at either end which can be raised and lowered. In their respective rest frames the length of the train is measured, by an observer on board, at 500 metres and the length of the tunnel is measured, by a ground-ba... |
I have this metallic stickman toy that is able to balance itself. I am curious about its center of mass. Can anyone help me visualize a rough position to where the object's center of mass is with an explanation to it?
|
I know this question has been asked a million times and I have looked at the various questions/answers, but am yet to find a perfect solution. At one of the suggestions here, I picked up the book by Tinkham but it just feels too sloppy to understand what's going on.
I am looking for a textbook on group theory and quant... |
I found an expression that connects the metric tensor and Riemann Tensor in the following way:-
$g_{\mu\nu}~=~\eta_{\mu\nu}~+~\frac{1}{3}R_{\mu\alpha\nu\beta}x^\alpha x^\beta~+~.....$
Is this expression correct? How can one either prove/derive it?
Reference to any source is welcomed.
PS: This is the original question. ... |
It‘s about the following task:
Figure: 2 examples of molar volumes of binary (2 components, i=A,B is the component index).
mixtures. Let V be the total volume of the mixture.
Using binary mixture as an example, explain/ define the molar volumes m, i, and
^E (excess). How can you read these quantities from the graph?
I... |
I am trying to determine the Lyapunov exponent using Gram–Schmidt reorthonormalisation (GSR), for a well-defined dynamical system (I know the differential equations etc). I believe I have implemented it correctly, however I am unsure about the choice of when to renormalise the perturbation vectors. It seems I could pic... |
Given the following scenario, why is the charge per unit area not the same with opposite sign? I am finding it difficult to understand, since the charge per unit area for two parallel plates in a capacitor are related in this manner. How would the two relate in a cylindrical coaxial capacitor?
Sorry if I am not clear, ... |
In derivation of two-neutrino oscillation probability, it was assumed that the mass states have the same momentum. Why is that?
Source: https://www.youtube.com/watch?v=nXzur-2hbkI&t=115s&ab_channel=MITOpenCourseWare
|
If we could split an electron, we would probably find new things. So, why don't we shoot a lot of energy at it, and see what happens? I tried looking up what happens, but I got no good answers.
|
Is there a covariant derivative, $\nabla$, that takes into account torsion, $T^\mu_{\;\;\alpha\beta}$, and covariant derivative of the metric equals zero, $\nabla_\alpha g_{\mu\nu}=0$? If yes, is there a unique for for it?
|
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