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(Context: QFT, spontaneous symmetry breaking):
What I have understood from reading the path integral version of the story is that this "vacuum" is actually the classical solution [i.e. which satisfies the exact, interacting, equations of motion ("on-shell") of the theory] and the perturbations are the "quantum fluctuat... |
Problem of this phenomenon is in title.To describe this, I separate it into 3 phases;
M1 hit airbag, 2) Air moving inside air bag caused by pressure gradient ,
3)M2 flew away caused by air moving to crash it.
So when M1 crash on airbag, its suddenly make pressure under M1 get higher rapidly.This making pressure gradi... |
I am studying spontaneous symmetry breaking of a complex scalar field $\phi(x)$ of a global $U(1)$ symmetry: $\phi(x)\to e^{i\alpha}\phi(x)$, where $\alpha$ is a real constant. I am considering the Lagrangian ($\mu^2<0$):
$$
\mathcal{L}=(\partial_{\mu}\phi)^{\ast}(\partial^{\mu}\phi)-\mu^2\phi^{\ast}\phi-\lambda(\phi^{... |
To see where this question comes from, consider a time independent Hamiltonian $H$ and an initial wave function $\psi(t=0,x)$. We can express time dependant wave function $\psi(t,x) = \sum_j e^{-iE_jt/\hbar} \phi_j(x) c_j$ where $\{\phi_j(x)\}$ is the set of eigen functions of H and $c_j=\int \psi(t=0,y) \phi_j^*(y) d... |
Background
A linear time-invariant (LTI) system (black box) is one described by the system:
\begin{align}
\dot{\xi}(t) & = A\xi(t) + B\omega(t), \; \xi(0) = 0 \label{eq-abc-1}\\
\lambda(t) & = C\xi(t)
\end{align}
where $A \in \mathbb{R}^{n\times n}$ ($n$ is the dimention of the system) and $B \in \mathbb{R}^{n... |
While reading Arnold Arons book Teaching Introductory Physics, I came across this paragraph (Part 1, page 29, emphasis in original):
"An especially important exercise with graphs is one in which students are asked to give verbal interpretations of various lengths in an $s$ versus $t$ diagram. For example, they should ... |
Give the limiting refractive index of a rainbow.
The raindrops are modelled as spherical droplets, with refractive index $n$, with parallel rays from the Sun incident on it. I have a very limited knowledge on this area, so know nothing about Fresnel Coefficients or Snell's Law etc., so I would appreciate an answer whic... |
I'm trying to figure out how one would come up with a case for Kronecker product of diagonal matrices. Suppose we have a $2\times 2$ matrices
$$M_i = \begin{bmatrix}
a_i && 0\\
0 && b_i
\end{bmatrix}.$$
I want to figure out
$$M = \bigotimes_{i=1}^n M_i.$$
What would the diagonal elements of matrix $M$ would be?
|
We will consider an ion is in an harmonic trap. The ion has two internal states \lvert g\rangle and \lvert s\rangle and it interacts with a laser that induces a state-dependent force. The quantum dynamics is governed by the Hamiltonian
$$H = H_R+H_f$$
$$H_R = \Omega (\lvert s\rangle\langle g\rvert+\lvert g\rangle\langl... |
I'm an IT developer and recently I created a project where I tried to send signals between two threads in a slowing down environment. I simulated two points with their own clocks and tried to send a signal of 1Hz to the other. I programmed clocks to gradually (lineary) slow down (from it's perspective it was still 1Hz ... |
So I just finished watching "dark matter is not a theory". An understanding I gleaned from it is that dark matter is observed from the discrepancy between the amount (or perhaps energy? in terms of spectrum) of light a galaxy is emitting, and its rotational speed. These are both indications of mass, and they should mat... |
I've come across an exercise asking me to calculate:
$$[[A,B],[C,D]]$$
knowing $[A,C]=[B,D]=0$ and $[A,D]=[B,C]=1$
I've already solved it by "brute force", separating the commutator as follows:
$$[[A,B],[C,D]]=[AB,CD]-[AB,DC]-[BA,CD]+[BA,DC]=0$$
However, I've found out there's a more elegant way to do it, and that's wi... |
A few weeks ago, I was presented one-dimensional systems in my QM class, and of course one-dimensional potentials too. Nonetheless, I'm still a bit unclear about the terminology my professor uses. Also, before closing this question as a duplicate of this one, please consider I've already had a look at it and the commen... |
The Schwarzschild solution shows decreasing velocities with larger orbits - and needs help from dark matter or MOND to explain galaxies.
Apparantly no Einstein vacuum solution with flat velocities is known but there seems to be also no proof that there cannot be one.
Regardless of what other oddities or disadvantages s... |
So i will directly to the problem. I am not getting how, when we Wick rotate, the EM action should go to (the correct answer)
$$ S_E = \int -d^4 x\frac{1}{4} F_{\mu \nu} F^{\mu \nu} \underbrace{\rightarrow}_{Wick} S_M = \frac{1}{4} \int d^4 x F_{\mu \nu} F^{\mu \nu}$$
So that $S_E = -S_M$
But mine obtained is not exact... |
I want to understand the relation between the Wilsonian RG and the usual QFT RG approach. Several questions have been asked, such as this and many others, yet I don't find a conceptual answer to what follows.
In the computation of loop integrals in QFT, in order to tame divergences a regulator $\Lambda$ is introduced. ... |
Consider two points (A & B) on one half of an elliptical orbit. Satellite moves from point A to B. I want to calculate the work done by the gravitational force, but I DO NOT WANT to use energy conservation. I want to use
$W=$ Integral (from Ra to Rb) of $F dR .$
This should be a dot product and so, I should be able t... |
To better explain my question, I'll describe the problem that gave me the idea, using that the eletric field for a linear distribution of charge is: $$\vec E = \int_L{\frac{k \cdot \rho_{l} \cdot dl}{|\vec r|^{2}} \hat r}$$
Find the eletric field on the center of a semi-circle (going from $0$ to $\pi$) with radius $a$ ... |
Given that the commutator of a pair of operators shows up explicitly in the lower bound of the Robertson-Schrodinger inequality, I am wondering what, if any, statistical meaning/significance one can attach to the Jacobi identity of three operators containing all their pairwise commutators. Is there any?
|
A wheel is rolling up the street (which is "horizontal", not an incline). The center of mass of the wheel has velocity V in the forward direction, relative to the ground. (Let's ignore air friction).
My understanding is that at any given moment, the point at the top of the wheel
will have velocity V relative to the ca... |
To start we have a single proton. We place are proton in a circular particle accelerator, and bring the proton up to speed of 0.99C. we then accelerate the entire particle accelerator on the horizontal plane up to 0.1C.
What does the movement of the proton look like from a top down observer?
|
Salt is used to lower the melting point of ice. This is often used when making ice cream, as 0°C isn't cold enough to freeze some of the creams and fats present.
I need to transport a frozen item for about 3 hours. I was thinking of ways to keep it below 0° beyond a simple ice cooler. I do not have access to dry ice, s... |
I was trying to do an alternative general expression for Coriolis acceleration to the one explained on Wikipedia which I find not too intuitive and too simple calculation wise.
Supposing the $z$ axis is the instantaneous axis of rotation of the Earth, then $\mathbf\Omega=\Omega\mathbf{\hat k}$. To model the velocity of... |
Suppose we have two ferromagnetic objects constituting two permanent magnets. A classical way to think of the two magnets repelling/attracting each other would be by ascribing bulk and surface currents on the magnets and using the Lorentz force law.
When we have two horizontal loops of wire, with one loop above the oth... |
As far as we know the universe is electrically neutral. An electron-positron pair is easy to create. It is not related to the creation of quarks. So why are there the same number of electrons and protons in our universe? What is the mechanism that generates this?
I have reviewed other questions on this site - but there... |
It is often said how to the health of a battery gets worse as you charge and discharge it through numerous cycles. So, the maximum available cell capacity a battery can have after recharging reduces over time.
I am wondering if there is an equation to quantitatively describe this phenomena. I came across this paper whi... |
I have just begun studying geometrical optics, and there is something mysterious about it.
What I want to know is how to derive the definition of ray from Maxwell's equation.
In vacuum, electromagnetic wave equation as follows.
$ \triangledown E^2 - {1 \over c_0^2}{\partial^2 E \over \partial t^2} = 0$ (where E = elect... |
After a nonlinear crystal there are two photons in HH+VV state. What happens to the state if one of the photons in the pair is rotated? Does the state stay the same or it flips to HV+VH?
|
Time taken for an object to fall is generally given by $$t=\sqrt{\frac{2h}{g}}.$$ But this is only true under the assumption that gravitational acceleration is constant. With variable gravity what would be the formula for time taken for an object to fall a distance of $h$. [I've tried using elliptical orbits and calcul... |
I've seen this a lot in physics so far. For example in the stationary state solution to the Schrodinger equation for hydrogenic atoms, it's commonly approached using $\psi(r,\theta,\phi)=R(r)\Theta(\theta)\Phi(\phi)$. Another example is used in splitting the Schrodinger equation into time-dependent and time-independent... |
I derive the translational equations of motion like the following,
$$\frac{d\vec{P}}{dt} = \frac{d}{dt}\int_v \vec{dp_i} = \frac{d}{dt}\int_v \vec{v_i}dm = \frac{d}{dt}\int_v \vec{v_i}\rho_idV$$
Denoting the relative position vector($\vec{r_i}'$) w.r.t body center($\vec{R}$). Then,
\begin{align}
\frac{d}{dt}\int_v \fra... |
The derivation of Coulombs law from Maxwell's first equation for a point charge assumes that the field is symmetric along a sphere. What happens if this assumption is removed? Could there be other ways to distribute the charge on a point?
According to Griffiths, the charge density is described by the Dirac delta functi... |
On E. T. Jaynes view, thermodynamic entropy of a system is, up to a multiplicative constant, the same as the the information entropy for the predicted distribution with maximum uncertainty conditioned on the expectation values of some state variables. In other words, thermodynamic entropy in a way has to do with the in... |
Have anyone seen something similar like this in the lab?
When I input a left-circularly polarized (LCP) light to a non-polarzing beam splitter and check the chirality of both the transimitted and reflected beam. The transmitted beam are still left-circularly polarized light while the reflected beam seems to be right-c... |
I want to solve numerically the 1D time independent Schrödinger:
$$-\dfrac{\hbar^2}{2m} \dfrac{d^2 \psi(x)}{dx^2} + V(x)\psi(x) = E\psi(x)$$
For starter, lets say we solve the Particle In a Box problem with the following boundary conditions:
$$V(x) = 0, \psi(-L/2) = \psi(L/2) = 0, \psi'(-L/2) = 1$$
Where Energy $E$ is ... |
Destructive interferences are interesting for a physics student, specifically when checking the Energy Conservation. In the case of destructive EM waves or String waves it is easy to understand where the energy goes. However, it is not clear to me where it goes in the case of two Gravitational Waves’ destructive interf... |
I'm doing an exercise where $J$ is a 1-form on a manifold $M$ of dimension $N$.
The exercise ask me to calculate $J∧(*J)$ with $J=dx^0+2dx^1$ in a minkowski space with metric =(-1,1,1,1) where $*J$ is the Hodge dual of $J$. And then recalculate in a rotated basis $x^{(\alpha')}=\frac{\partial x^{\alpha'}}{\partial x^\b... |
I have a question on my Quantum Mechanics homework where we consider protons and neutrons to be manifestations of the same particle -- a nucleon. We think of the proton as the "isospin up state", and the neutron as the "isospin down state" are asked to consider a two-particle state as a tensor product of orbital angula... |
So is this always 0?( Where $dJ$ is the exterior derivative and $V$ a vectorial field)
\begin{align}
dJ(V,V)=\partial_jJ_i(dx^j\wedge dx^i)(V,V)=\\
\partial_j J_i (v^kdx^j(\partial_k)v^ldx^i(\partial_l)-v^ldx^j(\partial_l)v^kdx^i(\partial_k).
\end{align}
If $dx^j(\partial_k)=\delta^j_k$ then it is equal to 0 but this r... |
When trying to find $\alpha (t)$ , I have $F_{mg}=mg(\cos{\alpha}\hat r + \sin{\alpha}\hat\theta)$. Using the assumption the rope remains the same length, I get the ODE (from the equation of acceleration in polar coordinates):
$mg\sin{\alpha}=mL \ddot\alpha$ which gives $\alpha (t)=c_1e^{\frac{t}{\sqrt{g/L}}}+c_2e^{... |
How to derive the following equation in quantum mechanics？
$$u\cdot\nabla\psi=-\frac{\hbar}{2m}i\Delta\psi-\frac{1}{2}(\nabla\cdot u)\psi+\frac{\hbar}{4m\rho}\left(2|\nabla\psi|^{2}i\psi-\frac{\psi}{\rho}\nabla\rho\cdot\nabla s+\psi\Delta s\right)$$
where
$$u\equiv\frac{\boldsymbol{J}}{\boldsymbol{\rho}}=\frac{\hbar}{2... |
Recently I came across a video were the origin of inertia was attributed to Sciama’s paper (1953).
I have seen only a couple of questions regarding this topic on Stack Physics. Both of them are showing some level of confusion, e.g., it is not clear why Sciama used G=1 at times, but not at other times, or that it predic... |
Let us say we have a cylinder rolling with an angular velocity 'w'. Now it splits into two parts of the same radius from middle without the application of any external torque. So how do I determine the angular velocity of the two parts?
|
Permanent magnets are a result of quantum mechanics, i.e. quantum spin of electrons inside the magnet aligning.
Quantum spin follows the uncertainty principle. If I measure the spin orientation first in the X axis, then the Y axis, the second measurement would have 50/50 chance of being Y+/Y- (the Stern–Gerlach experim... |
Normally, we have the $z$-component Pauli matrix $\begin{pmatrix} 1 & 0 \\ 0 & -1\end{pmatrix}$.
For the graphene with a magnetic field, the Hamiltonian is
\begin{align}
\hat{H} = v_{F} \left(\mathbf{P}-e \mathbf{A}\right) \cdot \boldsymbol{\sigma},
\end{align}
it has the following commutation relations
\begin{align}
... |
Why has $^1D$ configuration lower energy than $^1S$ ?
Hund's second rule says that for two configurations with
the same multiplicity, the configuration with the highest total orbital angular momentum $L$ has the lowest energy.
But how do I calculate total angular momentum $L$?
I assume that the states in the pictures f... |
Hi everyone we are working on a battery project and have the following question. What is the influence of stacking battery cells next to each other in a battery module on the resulting pressure exerted on the two walls clamping the cells?
The cells will want to expand when charging but are restricted by fixed walls, th... |
There must be a particle for changing Left-handed to Right-handed particles:
$$e_l + Z^0_T \to e_r$$
Where $Z^0_T$ has Weak Isospin = 1/2 and Spin = 1, and no other quantum numbers.
|
I understand that the consensus view is that the dilaton field has been ruled out by solar system experiments like the time-delay measurements of the Cassini probe.
But surely that assumes the rest of the universe doesn’t interfere with the results of the experiment?
I would have thought that the sum of all interaction... |
It is known that a decrease in the grain size of a polycrystalline metal to 1 micron is accompanied by an increase in its strength by several orders of magnitude (super-strength)
almost to the theoretical limit (about 1 GPa) - the Hall-Petch law.
With a further decrease in size (below 10 nm), this super-strength is rep... |
Let's introduce a quark $SU(2)$ doublet. We are in the $m_u \approx m_d$ limit. So we have
$$
q = \begin{pmatrix}
u\\
d
\end{pmatrix}.
$$
Then we can construct the Nucleonic field
$$
N := q q q = \begin{pmatrix}
p\\
n
\end{pmatrix}.
$$
I expect this to transform as a $SU(2)$ doublet, which corresponds to the Isospin li... |
In the $t$-$V$ model, the Hamiltonian is defined as:
\begin{equation}
\hat H = -t \displaystyle \sum_{\langle i,j\rangle} ( \hat c_i^{\dagger} \hat c_j + \hat c_j^{\dagger} \hat c_i) + V \sum_{\langle i, j \rangle} \hat n_i \hat n_j.
\end{equation}
Here, $t$ denotes the electron hopping parameter, and $V$ represents th... |
really naive question here, i don't know anything about physics, in a professional sense.
Light is a electromagnetic wave, and itself requires 3 dimensions to propagate, then how can a one-dimensional or 2 dimensional being even perceive anything ?
AND
If the existence of these lower " dimensions " are questionable , h... |
This paper is based on a question by Puk asked Jun 28, 2020 on the Stack Exchange Physics site, Newton's 2nd law for rolling motion with changing moment of inertia, about a long, hollow, rigid but infinitely thin cylinder with a point-like mass in the form of a rod with mass m attached to its wall as shown in the drawi... |
I have an equation which looks like this:
$${j^2} \frac{\rho_e}{c'} t=\Delta T$$
where $j$ is current's density, $\rho_e$ is conductor's electrical resistivity, $c'$ is heat capacity of conductor at constant volume, $t$ is time passed and $\Delta T$ is the change in conductor's temperature due electric current passing ... |
Is there an existing model or theory that shows there is nothing outside of the universe that interacts with anything inside the universe? Or to put it in other words, is there a model or theory showing that everything happening inside the universe including the expansion of the universe itself is caused by forces and... |
I'm trying to simulate electromagnetic fields. At the moment I'm exploring only magnetic fields (I know you can't have it without electric charge).
Anyway, I created a current carrying wire (just a line of moving particles) that generates a circular magnetic filed around it. I placed a particle near this wire with an i... |
So basically I have two Fierz identities involving spinors:
$$\psi^a \psi^b = -\frac{1}{2} \epsilon^{ab} \psi \psi$$
And
$$\overline{\psi}^{\dot{a}} \overline{\psi}^{\dot{b}} = \frac{1}{2} \epsilon^{\dot{a} \dot{b}} \overline{\psi} \overline{\psi}$$
The first one is immediate to solve it: The expression is antisymmetri... |
When one creates a hemispherical laser cavity, using one flat and one concave mirror, does the beam image invert each time it makes a round trip? I know when passing through the focus of a lens/mirror, such as in a 4f image relay telescope, an image inversion occurs. If you were to look at the "unfolded" diagram of the... |
I cannot come across a good definition of what "quenched" means in the context of spin glass problems. I see such use as "quenched connectivity", "quenched data set", "quenched disorder"... It seems like the term is overloaded. Is there a good definition of quenched in this context and what does it apply to: data, conn... |
Are there any trends in linear thermal expansion coefficient in transition elements?
By thermal expansion theorem, I mean.
$$\alpha = \dfrac{1}{L}\dfrac{\Delta L}{\Delta T}$$
What are the contributing factors that change $\alpha$, such as charge or atomic mass number?
|
The general function of a heat gun is to increase the temperature of ambient air to a set temperature. My broken heat gun is rated at 1100 F.
I have successfully melted a soda bottle in a campfire and annealed it without breaking the glass. But the result is messy, leaving ash and debris imprints in the bottle. So I ne... |
When performing path integral in gauge theory, we naively want to compute
$$
Z = \int DA \exp(iS[A])
$$
But we noticed, that because the action is the same for gauge equivalent conditions, we should actually divide it by the volume of the gauge group:
$$
\begin{aligned}
Z =& \frac{1}{\text{Vol(Gauge)}}\int DA \exp(iS[A... |
The surface current density of a wire with radius $R$ is given by $K = \frac{I}{2\pi R}$ but what if the bounded area is infinitesimally small, for example when the current only goes through the surface of the wire but not the inside. What would $K$ be then?
|
I came across the concept in a book wherein a real object is classified as a body that emits diverging beams of light; whereas the virtual objects are a point or a collection of point where the light rays appear to meet (a set of converging beams). Let us consider a set of converging beam incident on a plane mirror(whi... |
I would like to know if an exact solution for the surface gravity force components of an oblate spheroid has been published and if not can anyone derive it here?
Assume an ideal rigid oblate sphere of uniform homogenous density, that is not rotating. We can always add in centripetal forces later if required.
The place ... |
How do you find the magnification of a microscope given the focal lengths of the objective and eyepiece? What else can you find given this information? If finding the magnification is not feasible with just the focal lengths, what other information do you need?
|
I am looking for a textbook(s) that discusses differential geometry, smooth manifolds etc. More precisely, I have been trying to find a textbook that covers the following topics:
Differential geometry ( vector fields, forms, manifolds, mappings between manifolds, bundles, etc)
Fibre bundle application to physics
Lie t... |
I am having trouble calculating the Noether charges of a charged particle in a curved background.
To be more precise, I am considering a charged massive particle in a given coordinate system of the hyperbolic space, with action
\begin{equation}
S[x,y] = \int ds \left( \frac{1}{2 \sin^2(x)} \left[ \left( \frac{dx}{ds} ... |
I can't seem to find my mistake in this problem and I think it stems from not understanding how to correctly form constraints and the meaning behind the Lagrangian multiplier.
So first of all I learned in class a nice problem and how to solve it using Holonomic Constraints.
Q. Consider a mass starting at the top of a ... |
In Introduction to Quantum Mechanics by Griffiths and Schroeter, they derive the Uncertainty principle in the following way:
First, they define
$$f=\left(\hat A-\langle A\rangle\right)|\Psi\rangle$$
$$g=\left(\hat B-\langle B\rangle\right)|\Psi\rangle$$
Where $\hat A, \hat B$ are two Hermitian Operators.
Then they use ... |
The Schrodinger equation is given by:
$$i \hbar \frac{d}{dt}|\psi(t)\rangle = H(t)|\psi(t)\rangle.$$
Sometimes, physicists set $\hbar=1$. I suppose that they achieve this by changing the scaling and dimensions of units.
I figured that one way of achieving $\hbar =1$ and dimensionless Schrodinger equation is defining di... |
Consider the one-dimensional quantum XXZ model defined by the Hamiltonian:
$$
H = J \sum_{i} \left (X_i X_{i+1} + Y_i Y_{i+1} + \Delta Z_i Z_{i+1} \right).
$$
First, let us focus at zero temperatures, $T = 0$. For $\Delta >1$, the ground state is a Néel antiferromagnet; this phase spontaneously breaks a $\mathbb{Z}... |
I am reading N. D. Mermin, Bringing home the atomic world: Quantum mysteries for anybody
. The main part of the article is pretty clear to me. But I am not sure how quantum mechanics described in Appendix generates Cases (a) and (b) on p.941. Can someone explicate in mathematical details?
|
Suppose you have a surface charge density $\sigma$ on a conducting plane $z=0$. The region $z<0$ is filled with a dielectric of permittivity $\varepsilon$. What is the field everywhere?
I tried taking a limit of a setup where we have a 'slab' conductor of thickness $t$ (so the region $0\leq z\le t$ is conducting) and... |
I'm writing a simulator, and I've found I need greater accuracy than can be afforded by the typical magnetic field equation like given here. So I'm converting my script to integrate over the wire's length, like in this derivation. But I'm still left without a good estimate of the magnetic field strength at a point, bec... |
A recent spacetime video about Kerr's objection to the existence of singularities has made want to clear up something about geodesics towards the origin in the Schwarzschild solution.
It is said that null geodesics of this kind always terminate at the singularity - but what about the worldlines of free-falling objects?... |
Is there a way to use the distances of the two opposite apsides to determine the eccentricity of an orbit? The ratio between the distances (i.e. perihelion & aphelion) seem like they'd have a straightforward relationship with the eccentricity of the orbit.
|
I came across a question which says-
"Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on one of the blocks pulling it away from the other as shown in figure. Find the position of centre of mass at time t... |
Given $\vert\psi(0)\rangle=\vert 0 \rangle$,
$ H =\hbar\omega(\vert 0\rangle \langle 1 \vert+\vert 1\rangle \langle 0 \vert) $,
$p=\vert 0\rangle \langle 0\vert$,
ask for $\langle \psi(t)\vert p \vert \psi(t)\rangle$.
What should I do? I have no idea.
|
Does anyone know any good books for adaptive optics? It should at least include decomposition into Zernike polynomials. It is for PhD level, but any level is welcome.
|
Usually, when we think of inflation we think of it happening at high energy scales, close to the bound set by CMB polarization measurements (with a Hubble scale of $H_I\sim 10^{14}$ GeV). However, many times in the literature we encounter low-scale inflation models where $H\sim 10^{-24}$ GeV, corresponding to $T\sim 10... |
I am given a homogenous volume $F$ of isotropic conductor with resistivity $\rho$. I need to allow current to flow from Point A to B which are a distance $L$ away from each other. I can shape the conductor anyway I like.
Let's assume the conductor lies along the $x$-axis. We can assume the conductor has some longish sh... |
The only formula we learned for work is $W=\int pdV$. In stage 2 of Carnot cycle, there is no heat transfer but the volume increases, pressure decreases, internal energy decreases and temperature too.
So even if we plug ideal gas equation, the integral is not solvable because the temperature is changing (we didn't lear... |
I have found a statement online saying that there must be an eigenvalue of the Hamiltonian inside the range $(E-\Delta H,E+\Delta H)$. Where the mean value and variance are defined for a random (normalized) wave function $| \psi \rangle $, so $E \equiv \langle \psi |H|\psi \rangle$ and $\Delta H \equiv \sqrt{\langle \p... |
I have obtained a numerical solution to the Einstein's equations using the isotropic metric ansatz
$$ds^2=-e^{f(r)}\,dt^2+e^{g(r)}\left(dr^2+r^2\,d\Omega^2\right).$$
The associated energy density function is always positive in the interval $\left(M_{BH}/2, \infty\right)$ and I have imposed the condition that it vanishe... |
I'm attempting to make a simple physics engine but chat gpt for the most part has been unreliable.
I have a 2d space (vacumm).
For simplicity I would like to model collisions between extended circular objects that take changes in angular and linear velocity (and kinetic energy) into account. I would like help with phys... |
I have a basic question about projective representations in quantum mechanics. In projective representation we identify the class of normalized states in Hilbert space as the same physical state as follows :
\begin{equation}
\psi_1\sim \psi_2~~~iff~~~\psi_1=e^{i\lambda}\psi_2,~~~\lambda\in\mathbb{R}
\end{equation}
to m... |
I am a software developer running this simulation and have some trouble understanding the underlying physical problem. My description of the problem is therefore probably not perfect, but I hope understandable. I am working on a simulation that consists of an inverted pendulum actuated through 2 linear actuators to the... |
Generally, a hydrogen balloon would float when released in air, but what will happen when that hydrogen balloon has a mass of 10kg. Is it the density that decides whether an object floats in air or the mass (inertia)?
|
I have been learning about light reflection and refraction and was thinking about objects reflecting only certain wave-lengths.
Why doesn't a red object with a green light shone on it appear black?
I know that some extra light would get in from surounding sources ans the colors might not be perfect opposites, but theo... |
Not the smartest question but when you have a series circuit and it says that the current in R is something, isnt the current the same throughout the circuit? Or if you look at only the things that are happening to the electrons from one end of the resistor to the other its slightly different? and when we talk about cu... |
Why are macroscopic objects, for example, a wine glass, never found in a superposition of a position eigenstate localized at $A$ and another localized at $B$? Why does it never exist in a state $|\Psi\rangle$: $$|\Psi\rangle=c_A|\vec{x}_A\rangle+c_B|\vec{x}_B\rangle, \quad c_A,c_B\in\mathbb{C}$$ where $|\vec{x}_A,|\vec... |
I have a doubt about the conservation of magnetic flux in astrophysical plasmas, in particular in the presence of turbulent motions and vorticity (surely due to poor understanding of vector identities).
If vorticity is always conserved in the absence of viscosity (Kelvin's theorem):
$\frac{\partial\vec{\Omega}}{\partia... |
While reading lecture notes for the course on thermodynamics I have encountered some tiny details that seem extremely important for the understanding of the topic. However, something seems amiss so, I was wondering if there are any underlying intricacies to these concepts or is it just levity of the language used in th... |
A common convention for the definition of the covariant derivative in the SM is
$$
D_\mu = \partial_\mu - i g_s \frac{\lambda^a}{2}G^a_\mu - \cdots
$$
where $\lambda^a$ are the Gell-Mann matrices. In this definition, we have chosen out SU(3) generators to be
$$
T^a_{\bf{3}} = \frac{\lambda^a}{2}
$$
and therefore it has... |
Does it make any sense to talk about energy of any one particle in an interacting system? For example if we talk about a system of two coupled quantum harmonic oscillators of same mass and frequency, the Hamiltonian of the system is:
\begin{align*}
\hat{H}= & \frac{\hat{P}_{1}^{2}}{2m}+\frac{\hat{P}_{2}^{2}}{2m}+\frac{... |
The Question:
According to Prof. Brian Cox in the first 30 seconds of this YouTube video from 4 years ago, we do not know whether the universe had a beginning. Is it still the case that we do not know?
Thoughts:
I know about the Big Bang, that, strictly speaking, it is not the point at which the universe "began", if ... |
More than a dozen Earth-like planets have been discovered around nearby stars based on observations of changes in the brightness of their sun as they pass across its disk (transit events). If an Earth-like planet has a satellite like our Moon, its trajectory is slightly perturbed. Is this disturbance enough to reliably... |
Can someone point me to the derivation of the non-relativistic limit of the time-dependent Dirac equation? I'm presuming that the limit is nothing but the time-dependent Schrodinger equation.
I flipped a few books but couldn't find it.
Update: Also, is there a closed form relationship between the non-relativistic and r... |
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