instruction stringlengths 31 24.3k |
|---|
I'm currently studying Electromagnetic Optics, and I don't quite understand the (classical) process through which we perceive an object with a given color. From my understanding, I'd make a distinction between transparent and absorbent mediums:
Transparent mediums: we see the light that goes through them, and the rest... |
I have recently come to realise that many of the most fundamental theorems can be reduced to a continuity equation. Doing some research on the topic of said equations, I have found out they have stronger implications than just the conservation of a given magnitude, since they also impose locality. I am specially intere... |
Basically in a circuit there is a cell with a positive and negative end, and current flows through it - electrons are pushed by negative electrode and attracted to the positive electrode. But if say a ring rotates about its diameter and say there is an applied magnetic field and as the ring rotates, there is a flux cha... |
Does there exist a proof/conjecture/counterexample, to the statement that the fermionic ground state, of the many-electron Schrödinger operator (including spin-orbit interaction) with spherically symmetric external potential, is unique modulo phase (think isolated atom in Born-Oppenheimer approximation).
Edit: Modified... |
I am trying to know whether it would be possible to do an undergraduate laboratory experiment to measure absorption lines produced by a gas. The idea is to have a background source of light with a continuous spectrum (either sunlight or an incandescent light bulb), a spectrometer, and some gas in between. I thought hel... |
I recently had a CT scan with IV contrast liquid. I was warned it might make me feel warm and that this is normal.
I had an amazing sensation of heat moving down my body.
All my searches tell me that this can happen and that it is perfectly normal.
I'm more interested in the physics about why this happens. No site seem... |
I would like to validate my understanding of angular velocity as a vector.
Suppose we have a particle $P$ moving around in $3D$ space in some arbitrary way. At any given point in time, we would like to know its current angular velocity $\vec\omega$ around a specific point $O$ in space. $\vec\omega$ is a vector (with $3... |
I am a first year PhD student and I am going to work in Quantum Optics ahead in my PhD. I am right now undergoing my coursework and I want to read the subject from the scratch to build a good theoretical background required for my research ahead. I am confused among various books to start with like Christropher Gerry &... |
I am studying Hawking's area theorem from the book the large scale structure of spacetime by Hawking and Ellis. At the end of page#318, it said: null geodesic generators of future infinity have no future end-points. I just don't understand why is that ? Please give some explanation.
|
How to get a sense of $\rm eV$? I mean when I know how much a metre is or a second is, but how to "visualize" when it is said atomic reactions are in order of $\rm eV$ and nuclear reactions are in order of $\rm MeV$? Should I just remember it?
|
I was deriving the von Mises maximum distortion energy criterion:
$${\displaystyle \sigma _{\text{v}}={\sqrt {{\frac {1}{2}}\left[(\sigma _{1}-\sigma _{2})^{2}+(\sigma _{2}-\sigma _{3})^{2}+(\sigma _{3}-\sigma _{1})^{2}\right]}}}\tag1$$
I did the following steps:
Define the Cauchy stress tensor $\sigma_{ij}$
Calculate... |
Suppose we have a complex system changing in state but without order parameter jump. Is there possible that during this change particular dynamic of system chsnges enough to name this phase change, but without entropy growth? Any example? Topological PT? Subtle changes in liquid crystals? Some subtle collective quantum... |
I'm aware of the fact that Feynman said something along the lines of "If you don't think QM is weird then you don't understand QM". So I'm pretty sure he is right and I am wrong :)
Still, when I think of the double-slit experiment I see no paradox.
When a particle (e.g. a photon) is allowed to behave and "be" freely th... |
One of the successes of theory of inflation is its explanation for the flatness of the Universe at the start of the Big Bang. Simply stated, in the Friedmann equation, the inflation field energy density, $\rho$, in the term $8\pi G\rho/3$, is constant and as the scale length increases exponentially, the curvature ter... |
I am an A-level student.
We have traditionally been taught that different types of EM waves exist only between certain ranges of wavelengths and frequencies.
However, I learned that electromagnetic waves of all kinds can exist in different wavelengths, not just the ones within the range they are typically associated wi... |
Inflation guy Andrei Linde says it like this:
… "In that microscopic time interval ($10^{-35}$ sec), the size of the cosmos grew dramatically, going from a diameter of $10^{-33}$ centimeters — the Planck length, that is the smallest size endowed with physical meaning — to one of tens of orders of magnitude greater tha... |
A figure in a 23 Nov 2023 article on Optics.org shows that more energy was produced than delivered. That is, the area or the red region seems to represent the energy produced.
But a similar figure in another article on the Lawrence Livermore National Labs (LLNL) website could be interpreted as meaning that the measure... |
In Mathematical Methods of Classical Mechanics, Arnold states the following theorem without proof in pages 75-76:
Let $\gamma$ be a smooth plane curve, and let $q_1, q_2$ be local coordinates where
$q_1$ parameterises the curve and $q_2$ is the coordinate in the orthogonal direction to the curve. Consider the system w... |
Why cornering wind tunnel
rotate, why is not just curved?
A curved wind tunnel has a radial pressure gradient, but this pressure gradient doesn't exist in a real turn, so how do you get zero pressure gradient in a tunnel section?
In real life P1=P2, but in curved wind tunnel section P2 > P1 , so how get same pressures... |
From this thread How the current actually flows in a circuit?, I know that between 2 points in a conducting wire, the potential difference isn't necessary to maintain the current between them (if we suppose that the wire has nearly zero resistence).
I got a beautiful schema from @Bob D about the wiring of AC current fr... |
Take an inviscid, incompressible fluid, ignore external forces for the sake of simplicity.
The Lagrangian density is
$$
\mathcal{L} = \frac{\rho}{2} {\vec v}\cdot \vec v
$$
I'm trying to solve Euler-Lagrange like so:
$$
\frac{\partial \mathcal{L}}{\partial \vec v} = \partial_\mu \left( \frac{\partial \mathcal{L}}{\part... |
While reading Introduction to Electrodynamics by David J. Griffiths, I have encountered some issue with the notation of the directional derivative of the vector field and I was wondering if there are any simple terms to put it.
The problem is the following notation:
$$(\mathbf{A}\cdot\nabla)\mathbf{B}=\mathbf{A}\cdot\n... |
How do we know the hypothetical graviton must have spin 2? What does that even mean? I can comprehend spin 1/2 fermions and spin 1 bosons, but I don't know what spin 2 would even apply. How was that value for the graviton calculated?
For that matter, how was spin 0 for the Higgs boson calculated?
|
I understand why the warping of spacetime affects moving objects, but why would it affect stationary ones if it even does? Would two completely stationary objects not move closer together because they aren't moving in space therefore wouldn't start bending space towards each other? And if they do, why would they move t... |
Why can't the zero value of gravitational potential energy be set at a different point instead of infinite distance?
I quoted it from: https://ned.ipac.caltech.edu/level5/Guth/Guth3.html
|
From
http://www.damtp.cam.ac.uk/user/tong/statphys/sp.pdf
page 89 (95/191 in the pdf file),
We can see that by looking again at the expressions (3.30) and (3.31), which tell us
$$
z = \left( 1+ \frac{1}{n_0} \right)^{-1} = \left( 1 + \frac{1}{N} \frac{1}{ 1 - (T/T_c)^{3/2} } \right)^{-1}
$$
the author then analyzed $... |
Given a stationary observer and a moving one. One would see the particle in a system of gas moving faster than the other would. Does that mean the particles have more kinetic energy and thus higher temperature? If so what does that say about entropy in different frames of references?
|
In many books, e.g., Sakurai's modern quantum mechanics revised edition Chap 2 p73 & Chap 5 p 326 (though he said Chap 2 similar to Chap 5 from what I understood), Peskin and Schroeder's introduction to QFT 4.2 Perturbation Expansion of Correlation Functions, p 88, Eq. (4.22), it is claimed the Dyson series is perturba... |
From what i understand string theory usually lives in a Minkowski Spacetime or AdS spacetime.
In Minkowski Spacetime conservation of energy is usually very straightforward, is this also the case in string theory?
For AdS space correct me if im wrong but Energy conservation can discussed in the context of AdS/CFT corres... |
Ions have three dimensions in solution and can be estimated as spheres. If ions have dimensions they can experience some degree of capacitance, e.g. an electrostatic potential which increases linearly with distance according to Ohm's law given the fixed charge of individual ions. This capacitance would influence an ion... |
I have tried reading related questions on here, but I have not found what I perceive to be my question nor the answer I seek. Every place I look (textbooks, here, Quora, etc...) indicates that $E_0/B_0 = \omega/k = E/B = c$. Since $E_0$ and $B_0$ are the amplitudes, they are not zero. Since $\omega = 2 \pi f$ and $k = ... |
according to a crude (classical) model of the drift velocity as given in my high school textbook, using an example of cylindrical conductor, we derived ohm's law as
$j=\sigma E$
where $\sigma $
is the conductivity and is given as
$\sigma=\frac{ne^2\tau}{m}$
now we treat $\sigma $ as infinity.
Questions:
(a) why do we t... |
Here is a (practically infeasible) method to determine whether you are in a non-inertial frame of reference:
Look around you, and calculate all of the forces acting on you. The piece of lint on the floor five metres away exerts a gravitational force on you, the chair you're sitting on exerts an electrostatic force on y... |
I am trying to read through these notes on CFT, and author reaches a point in chapter $2$ saying:
$$\Big(\eta_{\mu\nu}\square + (d-2)\partial_{\mu}\partial_{\nu}\Big)(\partial\cdot\epsilon) = 0\tag{2.8}$$
and upon contraction with $\eta^{\mu\nu}$ reaches
$$(d-1)\square(\partial\cdot \epsilon) = 0.\tag{2.9}$$
where we a... |
Pulley and string are all massless => hence, I consider only the net downward force applied to the pulley by both the masses under gravity.
Why is the normal force on the pulley not equal to the net weight below it?
(considering the fact that it is a ideal pulley-string-mass system)
|
Suppose we know the position, velocity of a charge at time $t=0$ and its rest mass is also known. It is attracted by a (nearly) infinitely massive known opposite charge which is at rest and always be at rest (because no force can move it) in our frame of reference. How can we predict the path of the moving charge? I go... |
Is it possible with applying certain type of coating such that a beam splitter can have different splitting ratio when light ray go through it from opposite side? For example, 50/50 in one way and 100% transmittance in the other. Thank you.
|
In a BSM related paper (in appendix B), the authors use an effective Lagrangian $\mathcal{L}_{EFT}$, and define the following fields:
$$ \mathbf{D} = \frac{\partial\mathcal{L}_{EFT}}{\partial\mathbf{E}}, \quad \mathbf{H} = -\frac{\partial\mathcal{L}_{EFT}}{\partial\mathbf{B}}\tag{B.3}$$
Later, it seems they state that ... |
Water bubbles created at the top of the bottle if the water level is higher:
but water bubbles is not created at the top of the bottle if the water level is lower:
This question is very different from this one and this is how what my drawing look in reality.
Why are water bubbles created at the top of the bottle if t... |
I do have a copy of the book, which seems great. It was written by an Olympiad trainer and a student, which means it is related to Olympiads. But I never saw anyone mention the book. Is it any good for Olympiads?
https://www.worldscientific.com/worldscibooks/10.1142/10817
|
Mark scheme
I don't understand 2.7. I have attatched the relevant part of the question and markscheme and also the links to full versions below.
Apparantely you use the decay constant in 2.5 to find specific points on the graph. (The starting point is just half the original graph. For other points, u can say y1 = ... |
I have a question that what would the world be, if matter de Broglie wavelength was large?
|
From what I understand, the weak isospin part of the symmetry-unbroken electroweak interaction consists of the $\mathfrak{su}(2)$ valued gauge field $\hat W_\mu = \sum_i^3W^i_\mu \hat T^i$, where $\{\hat T^i\}_{i=1,2,3}$ are the weak isospin operators which form a basis of $\mathfrak{su}(2)$ generators and obey the fol... |
In LHCb, how do all the produced particles go in one direction i.e. in the forward direction?
Is the proton beam at rest coming from the opposite direction?
|
I heard that the intrinsic Fermi energy level always remains constant because it is an imaginary level assuming an intrinsic semiconductor.
However, at the same time, the Fermi level must also have a constant value in thermal equilibrium. If so, the following picture seems contradictory.
I know that in this case the F... |
Explanation of light bending in an accelerated frame in a relativistic setting
We know the transformation that takes us from one inertial frame to another. In special relativity, the transformation is a Lorentz transformation. For example, in an inertial frame K' that moves uniformly with velocity $V$ along the positiv... |
I am trying to obtain a representation of the momentum-space wavefunction $<p'|\alpha>$
Its position space wavefunction is given as
$$ <x'|\alpha> = N \exp [-(a+ib)x'^2 +(c+id)x'] $$
where $N,a,b,c,d$ are all real.
I have tried to calculate the following integral using Gaussian integral, or Fourier transform method but... |
Imagine a critical line separating two thermodynamic phases. There is a point on this line splitting the line into two pieces such that on one piece the transition between the two phases is 1st order, on the other piece the phase transition is the 2nd order (continuous transition). Is there a special name for a point l... |
There are two bodies with masses $m_1$ and $m_2$ orbiting around barycenter. Distances to both bodies from barycenter are $r_1$ and $r_2$ . First body has known velocity $v_1$ as on the picture :
My goal is to get properties of trajectories for both bodies. I have a solution for the case when body is orbiting around s... |
ecursively, this implies that changes in the electric field generate the magnetic field, and vice versa, akin to the plane wave solution resulting from specific boundary conditions intentionally imposed on Maxwell's equations. Naturally, there exist other solutions to Maxwell's equations where both fields are not neces... |
I study QKD which relies on the single photon as a qubit, on which information is encoded.
There are many protocols which mainly differ on how information (bit) is encoded on the qubit :
polarization encoding
frequency encoding
time bin encoding
phase encoding
I understand well polarization (or may I say spin/helicit... |
I've defined the origin as the center of rotation for the particle on the pendulum. Then:
$$ x = r\cos{\theta} $$ $$ y = r\sin{\theta} $$ $$z = 0$$
From here, the potential energy is $V = 0$ since $z = 0$, and the kinetic energy is $K = \frac{1}{2}m(r\dot{\theta})^2 = L$.
Putting this into $\frac{\mathrm{d}}{\mathrm{d}... |
Please excuse me if I am completely wrong because I am a 9th grader but I hopefully am able to explain briefly about my problem. I was trying to create a function to calculate the Force of an iron projectile (cylinder) when shot using a coilgun. (The projectile goes through the middle of the solenoid and the solenoid i... |
There are lots of examples of oscillatory phenomena in nature the description of which boils down to simple harmonic behavior, i.e. to Cosine/Sine/Complex Exp. This answer explains that we use sines and cosines because of their convenience and ease of mathematical description of phenomena. For example, complex exponent... |
I can see that the particles are displaced perpendicularly but how is the energy actually moving through these particles? I mean the first particle is moving up and down, and then the second should also move up and down by less than or equal to. But it is actually moving higher than the previous one when we draw a curv... |
I have a 800 W microwave oven and want to dry some silica gel packages (each labeled with 10 g and sealed in paper mantling).
The silica gel is colorless and seems to be of the kind of silica gels that does not change its color when getting wet / dry.
I found the quote to have silica gel dried at around 120 °C if using... |
I understand that the Sun undergoes convection and with rotation, the convective cells have a helical motion because of the Coriolis Force. My confusion comes from the fact that via the right-hand rule, wouldn't the magnetic field lines in the southern hemisphere cancel the ones from the northern hemisphere? Essential... |
How does Hawking radiation help in information conservation? Doesn't it create a paradox, as the particle-antiparticle pair created at the event horizon has nothing to do with the matter that has already fallen into the black hole thousands of years ago? How does it prove that information is not being destroyed by blac... |
This is not a homework problem. I have a bigger, more conceptual doubt behind it.
Applying linear momentum conservation: We get velocity of disc is v (towards right)
Now, friction will also apply a torque which will rotate the disc. I solved the question by two methods:
Method 1: Impulse (Force related)
In the above ... |
I have come across a lot of problems that revolve around finding equivalent resistance/capacity/inductivity. But, I can never learn the "tricks" for solving that kind of question. I just can't see those symmetries and how you can "relapse this with that because it is so obvious". Again, I'm asking if there are some bro... |
I am familiar with Gauss's law, how it can be derived and, and how it can be applied (when in integral form)
$$\nabla \cdot \mathbf{E}=\frac{1}{\epsilon_0} \rho$$
But I do not feel I really understand what is meant by $\rho$, to me the definition of charge density only makes sense when you are given a volume, and charg... |
While reading Introduction to Electrodynamics by David J. Griffiths I encountered a problem regarding the time derivative of the electric dipole moment. I wanted to find the conditions when the time derivative of dipole moment is $0$. I concluded that one of the conditions is the magneto-static condition i.e. $\nabla \... |
I just saw the announcement "Breakthrough in melting point prediction: over 100-year-old physics problem solved by Queen Mary Professor", which says that
Professor Trachenko ... demonstrates that melting lines [in a substance's phase diagram] can be described by a simple parabolic equation. This not only offers a prac... |
In a paramagnetic substance like Rubidium (due to its unpaired valence electron), under the influence of a DC magnetic field, the degenerate electronic energy states split into Zeeman states. Let's consider four such states, with #1 being the highest energy and #4 the lowest, for our previous degenerate excited state. ... |
The question starts with why Poisson brackets (in constrained systems) gives different relation if we substitute the constraints before or after expanding the bracket, and why this difference in relations cause a problem. More clearly speaking why do we care that "if we substitute constraints before expanding the brack... |
I am considering $U(1)$ global cosmic string.
In the case of wine-bottle potential with real field ($\phi$), it is known that there exists a static solution that corresponds to cosmic string (or vortices). If you calculate the stress-energy tensor and look at the 00 component ($T^0_0$), the energy is highly concentrate... |
I'm learning about the notation of grounding.
In this post of Wikipedia, https://en.wikipedia.org/wiki/Floating_ground, it is said that
Conductors are also described as having a floating voltage if they are not connected electrically to another non-floating (grounded) conductor. Without such a connection, voltages and... |
I was reading this paper where they calculate the effective potential of a scalar field $\phi$, which is (without any justification)
$$
V_{eff} (\phi) = \dfrac{1}{2} \sum_I (-1)^{F_i} \int \dfrac{d^4 p}{(2\pi)^4} \log \left[ p^2 + M_I^2 (\phi) \right]. \tag{2.1}
$$
Bonus question: Can someone indicate me where to find ... |
This source, The Double Pendulum Fractal provides an image of a flip-time fractal for the rods of a double pendulum. The authors state that it is "not energetically possible for either pendulum to flip [within the solid black curve]".
Can someone explain to me the proof as to why the double pendulum cannot flip in the... |
My research is on radar images and the images are collected in several conical surfaces. These conical surfaces have the same origin, the same maximum length (max flare or max range), but different elevations angles. The images are collected on the surface of the cones only.
I want to determine the velocity field in 3D... |
I stumbled over the "do calculus" in causal modeling https://arxiv.org/abs/1210.4852
and the do-operator which is defined in this post https://stats.stackexchange.com/a/643333/298651 The do-operator defines the Post-Intervention distribution.
Given $\text{do}(X_j=x)$, the key insight is to note that value of $X_j$ is ... |
In an Astrophysics & Cosmology summer programme I attended last summer at UCL we were taught that stars seem to transport matter from the regions near the core to the surface through convective currents, and, if I remember correctly, these currents also take place near the surface. Nonetheless, we were also told there ... |
I am new to special relativity and with still little experience in Physics. I would like to know why a privileged frame of reference that determines absolute rest is not possible. I want you to explain to me what is wrong in the following thought experiment.
An empty universe in which there are only two bodies of the s... |
What if the reason why instantaneous state information is able be transmitted between entangled particles through an EPR bridge is that the metric that this is conveyed in is invariant under all conditions including displacement in the regular universe, and that's the reason it seems to travel faster than light? What a... |
After solving the Schrödinger equation for the charged particle in a constant and homogeneous magnetic field, using the symmetric gauge $\vec{A} = \frac{B}{2} (-y, x, 0)$, we could find the Landau energy levels as the following expression (notice the absolute values, depending on the particle's charge: $q \gtrless 0$):... |
There are so many elementary and composite particles out there, but only a few that are stable and isolatible - namely protons, electrons, photons and neutrinos (oscillating in the three flavors). These compromise most of the particles we interact with day-to-day, with the exception of the neutron, which has a proper d... |
My question occurred when I was reading Introduction to Elementary Particles by David J. Griffiths. In chapter 8, part 8.5, he is calculating the colour factor of quark-antiquark annihilation.
My question relies in the derivation of three formulas, from (8.82) to (8.84), which read:
$$\mathcal{f}=\frac{1}{2 \sqrt{3}} a... |
I'm trying to figure out how to calculate the jumping distance of a person or animal based on body weight and initial speed, but I can't seem to find any relevant information online about this. Is there any formula that can be used to figure this out?
|
I see this statement from time to time.
But when I look at scattering in QED or phi-4 theory, I don't understand how classical calculation can reproduce these amplitudes.
To what extent is this statement valid?
|
I emphasize that the proceeding is purely classical physics. Consider the Grassmann-valued field (where $\mathcal{N}$ is a Grassmann number), which is a solution to the Dirac equation, given by
$$\psi(x) = \mathcal{N}\begin{pmatrix} \sqrt{\omega - k} \\ 0 \\ \sqrt{\omega + k} \\ 0 \end{pmatrix} e^{-i\omega x^0 + ikx^3}... |
From Gauss's theorem, a closed, hollow conductor shields its interior from fields due to charges outside, but does not shield its exterior from the fields due to charges placed inside it. So my opinion is in the elevator, i.e. a Faraday cage, cell phones cannot receive message from outside correspondent but can send me... |
According to this answer on Aviation Stack Exchange, when propelling an airplane it is more efficient to accelerate a bigger amount of air a little than to accelerate a small amount of air a lot. Why is that?
So, because of the v^2, you obviously get more force for your energy input if you accelerate a lot of air by v... |
If we have a current carrying loop with center at a point o, and i have a point P in this plane where im supposed to calculate magnetic field, if i consider an amperian loop with center at o and passing through P, by symmetry at all points on this amperian loop, the magnetic field should be same
and since current enclo... |
Is it possible?
Can I break a rock with eggs if I get great speed of egg almost like a Jet and using millions eggs. there is no air resistance and we can accelerate the egg slowly to be like a Jet speed with low acceleration. we can use enough energy. I don't care about egg is broken after break the rock.
|
If we assume a normal double-slit experiment with two speakers that produce identical sound waves, is the $n=0$ antinodal line going to have a consistent loudness wherever point on it?
As the crest and trough (antinodal) are the loudest points in a longitudinal graph and the nodal points are the quietest points, wouldn... |
Let's say that we have a lattice with particles sitting on the nodes. Each particle $n$ has neighbors $\bar n$:
$$\dfrac{d^2\boldsymbol u_n}{dt^2}=-K\sum_{\bar n}\boldsymbol u_{\bar n}\tag{1}$$
The term in the RHS corresponds to one definition of a discrete laplacian on the lattice considered.
In Fourier space with per... |
The question starts with why Poisson brackets (in constrained systems) gives different relation if we substitute the constraints before or after expanding the bracket, and why this difference in relations cause a problem. More clearly speaking why do we care that "if we substitute constraints before expanding the brac... |
I understand that too short a half-life and flash point, becomes kind of meaningless, if the element generates too much heat, so this only applies to longer half-lives.
Also, as I understand it, flash point is a process of neutrons and the density of the atomic nucleuses in the material, so adding more of the radioacti... |
In classical Lagrangian mechanics, the mass $M$ is a Riemannian metric on the configuration space $Q$.
Does the "arc length" of a path $\gamma : [0, 1] \to Q$,
$$
\int_0^1 {\lVert{\gamma'(t)}\rVert}_{M}\,dt
$$
have a physical meaning?
When there's just one particle, this arc length is just the distance that the particl... |
How do I draw the curl meter on the electric field lines, I know none of them are physically possible, but do these violate faraday's or grass law?
I think an and d violate faraday and b and c violate guass because of the formulas -
|
I am self-studying QFT on "A modern introduction to quantum filed theory" by Maggiore, and on page 95 he states: "For the free Dirac action, one immediately sees that C,P and T are indeed symmetry operation", but I am having an hard time to realize what seems to be immediate.
Also in Peskin&Schroeder's book "Introducti... |
I have seen people deriving:
$$\ddot{\delta} + 2 H \dot{\delta} - 4 \pi G \rho \delta=0 \ ,$$
from combining Continuity, Poisson and Euler equations. I wanted to derive it from the perturbed $00$ and trace components of Einstein's equation (within Newtonian gauge).
Here they are:
\begin{align*}
\text{Poisson equation} ... |
I have struggled with the following steps in finding the expectation value of the momentum operator $\hat{p}$.
$$\left \langle \hat{p} \right \rangle=\int_{-\infty}^{\infty}\psi^{*}(x)\hat{p}\psi{x}dx=\int_{-\infty}^{\infty}\psi^{*}(x)\left(-i\hbar\frac{\partial}{\partial x}\right)\psi(x) dx\tag{1}$$
$$\left \langle \h... |
There is an article in the newspaper today entitled "Northern lights predicted in US and UK on Monday night in wake of solar storms".
I assume that the reason that someone can make this prediction is because 2 different things are ejected by the sun:
The first thing to arrive at the earth must be travelling more quick... |
In the derivation of the BGV theorem paper:
https://arxiv.org/abs/2307.10958
There is the following relation (numbered (8)):
$\dfrac{d}{d s}\left[a^2(t) \dfrac{d \mathbf{x}}{d s}\right]=0$
It's very likely dumb but i don't see how they get that start from the FLWR metric and geodesic equation...
If anyone can help.
|
This is a question my professor gave us in the test.
Consider the spin-$\frac{1}{2}$. Alice measured the system along the $z$ direction, and she observed the outcome as $+1$.
After Alice's measurement, Bob measured the system again along the direction $\vec{n} = (\cos\phi,\sin\phi,0)$. The corresponding matrix represen... |
I was reading this paper on the work of Count Rumford in developing the modern view of heat as a form of energy and not some kind of fluid. In that I encountered this experiment.
Say you had two cylinders B(say at temp. 44°C) and A(at 0°C). Now you place a thermoscope (which was at 22°C) in the middle.
The paper say... |
In a system in which we want to obtain the excitonic ground state. One may use the 1s excitonic wave function which appears in momentum-space as:
$$ \phi(\vec{k})_{1s}=\frac{\sqrt{8 \pi} \beta^2}{(\beta^2+|\vec{k}|^2 )^{3/2}}$$
which for a zero-exciton momentum state appears in the eigenvalue equation as follows:
$$ E_... |
what exactly are transverse waves? other than the commonly repeated answer that propagation is perpendicular to direction of travel / oscillations
my answer to this was D, which was the most encompassing in my opinion, so why is it wrong?
|
How are Lyapunov exponents of dynamical systems used as a measure of chaos? If I have the double pendulum, a chaotic system, then using the equation for the Lyapunov exponent (Wikipedia's article "Lyapunov exponent" viewed on 25/03/24):
$$\lambda =\lim _{t\to \infty }\lim _{|\delta \mathbf {Z} _{0}|\to 0}{\frac {1}{t}}... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.