question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>Let's have the solution for vector boson Lagrangian in form of 4-vector field:
$$
A_{\mu } (x) = \int \sum_{n = 1}^{3} e^{n}_{\mu}(\mathbf p) \left( a_{n}(\mathbf {p})e^{-ipx} + b_{n}^{+} (\mathbf p )e^{ipx}\right)\frac{d^{3}\mathbf {p }}{\sqrt{(2 \pi )^{3}2 \epsilon_{\mathbf p}} },
$$
$$A^{+}_{\mu } (x) = \int \s... | g15179 | [
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<p>Do charge coupled devices as found in telescopes use the photoelectric effect if not what eles librates the electons. Also what is charge intergration in reation to CCD's.</p> | g15180 | [
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<p>This is an expansion of two previous questions I had before (I am very confused by it). I am now encountering a problem with an integral. We want a general expression for the probability of finding E. We have the expression for the wave function for the particle in a box:</p>
<p>$$\psi(x)=x\sin(\frac{\pi x}{a})$$</... | g15181 | [
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<p>I have done some drawings of the magnetic fields of cone shaped solenoid electromagnets. I based this on the work of Tesla and some explanations of
Bashar, known as the Bashar Cones.</p>
<p>I found very strange patterns. </p>
<p><img src="http://i.stack.imgur.com/jMAun.png" alt="enter image description here">
<i... | g15182 | [
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<p>Which one true in First law of thermodynamics: </p>
<ol>
<li><p>$Q = \Delta U \pm W = \Delta U \pm p\Delta V$? (where $\Delta U$ is change of internal energy, $W$ work made by system and $Q=cm\Delta T $ heat made by system.) </p></li>
<li><p>or $\Delta U= \Delta Q + \Delta W $? (where $\Delta U$ is change of inte... | g15183 | [
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<p>I have $n$ points, each of these have a set of coordinates and a mass; what I want to do is calculate the resultant force they induce on an object whose coordinates I also know.</p>
<p>I can do that simply by calculating the separate force for each of the points and adding them together, but this is a bit too slow ... | g15184 | [
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<p>Assuming we develop the capability to send a robot to study Gliese 518, or any of the Earth-like planets discovered in the neighbourhood; the spacecraft would need to travel through the Solar System where it would initially be subject to the Solar furnace, and then further out extreme cold (approaching 0K). It would... | g15185 | [
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<p>The EM field has two possible polarizations, which is caused by spin-one nature of field (leads to the Lorenz gauge) and massless of the field. Really, the Klein-Gordon equations for the EM field
$$
\square A^{\mu} = 0
$$
does not leave a $A^{\mu}$ uniquely determined:
$$
A^{\mu} \to A^{\mu}{'} = A^{\mu} + \partial... | g15186 | [
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<p>Assume there are two ideal gases. The first is made of a light particle, and the second is made of a heavy particle. The two are of the same amount, in the same volume container, and at the same temperature. Assuming the two gases are ideal, both are therefore at the same pressure.</p>
<p>Since the temperatures are... | g15187 | [
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<p>$H = -\sum\limits_{i,j} A_{ij} c_i^{\dagger} c_j + \frac{U}{2} \sum\limits_i(c_i^\dagger c_i)(c_i^\dagger c_i -1)$ is defined to be a Hamiltonian for modeling quantum random walk of identical particles on a graph (Hubbard Model). A particle can make transition from one vertex to another if there is an edge between ... | g15188 | [
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<p>In high-school level textbooks* one encounters often the principles of independence of motion and that of composition (or superpositions) of motions. In this context this is used as "independence of <em>velocities</em>" and superposition of <em>velocities</em> (not of forces).</p>
<p>This is often illustrated by th... | g15189 | [
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<p>Assume the particles generates the magnetic field with their own spin. No motions except spin.(they have their intrinsic angular momentum.) Then which one generates stronger magnetic force?</p>
<p>I've seen the formula which represents the magnetic moment of the 1/2 spin particles with charge $q$, mass $m$, $\vec{\... | g15190 | [
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<p>I was fooling around with string diagrams in a monoidal category and I was thinking about them in terms of chemical reactions. I wondered about bending a wire around and attaching it to the input of the box it came out of. I realized that what I was looking at was a catalyst. I then drew a box with many inputs bu... | g15191 | [
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<p>Recently in my AP Physics class I did a lab in which I measured k for a spring by setting up an oscillating system with it, and timing the period, repeating for different masses. Since $T=2\pi\sqrt{\frac mk}$, we were supposed to relate $T^2=\frac{4\pi^2}km=Cm$ for some $C$. This is a proportionality equation in $T... | g15192 | [
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<p>A <a href="http://electronics.stackexchange.com/questions/98114/why-are-there-only-four-passive-elements">question</a> was asked over at EE.SE recently which I tried to answer, but much of my answer was speculative. I'm hoping someone here can help my ignorance.</p>
<p>In electronics design, there are four physical... | g15193 | [
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<p>A thought experiment has been bothering me. Assume an enclosed box free-falling in a constant gravity field. The box contains a person and a bowling ball at the top end. The person throws the bowling ball down (in the direction the system is falling/the direction gravity is pulling). Obviously, being a closed system... | g15194 | [
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<p>Hello I am working on a project that involves the constraints. I checkout the paper of Dirac about the constraints as well as some other resources. But still confuse about the first class and second class constraints.</p>
<p>Suppose, from the Lagrangian, I found two primary constraints $\Phi_a$ and $\Phi_b$.
Let $\... | g15195 | [
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<p>For free field theory, it seems the solutions of a field equation are used to give a representation of Poincare group, and the field equation is still satisfied after quantization. However for an interacting theory, such as QED, the field equation:</p>
<p>$$\partial_\nu F^{\nu \mu} ~=~ e \bar{\psi} \gamma^\mu \psi.... | g15196 | [
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<p>Work done by a magnetic force(even over an infinitesimally short displacement)=0</p>
<p><em>Net Force</em> on a current loop in an external magnetic field is given by: $$\vec{F}=\nabla(\vec{\mu_m } \cdot \vec{B})$$</p>
<p>How does one prove: $$dW=\nabla(\vec{\mu_m} \cdot \vec{B})\cdot\vec{dr}=0$$</p>
<p>$\vec{\mu... | g15197 | [
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<p>"An electron that is accelerated from rest through an electric potential difference of $V$ has a de Broglie wavelength of $\lambda$. Investigate the relationship between $V$ and $\lambda$." I had two arguments that led to two significantly distinct results.</p>
<p>The first argument: $\lambda \propto \frac{1}{V}$. ... | g15198 | [
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<p>I've been wondering about relativity for a while now.</p>
<ul>
<li>We seem to measure time by using the <a href="https://en.wikipedia.org/wiki/Speed_of_light" rel="nofollow">speed of light</a>.</li>
<li>Light can be slowed down <a href="http://www.newscientist.com/article/dn23925-light-completely-stopped-for-a-reco... | g15199 | [
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<p>What are the detailed steps involved in the emissions of a photon, for example, when an electron drops to a lower energy level? How well do we understand the production of the photon in this example? Any good reference material I can study?</p> | g472 | [
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<ol>
<li><p>Are there any connection between <a href="http://en.wikipedia.org/wiki/Loop_quantum_gravity" rel="nofollow">Loop Quantum Gravity</a> and <a href="http://en.wikipedia.org/wiki/Gauge_theory" rel="nofollow">Gauge theory</a>? If so, how does the gauge theory is described?</p></li>
<li><p>When exactly does the s... | g15200 | [
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<p>If Higgs ($\phi$) is a complex doublet:</p>
<p>$ \phi_{1}+i\phi_{2}$</p>
<p>$\phi_{3}+i\phi_{4}$</p>
<p>how do I show that $\phi_3$ has a vev but the others do not?</p>
<p>$V(\phi)=\mu^{2}(\phi^{\dagger}\phi)+\lambda(\phi^{\dagger}\phi)^{2}$ where $\phi^{\dagger}=1/\sqrt{2}(\phi_{1}-i\phi_{2})$</p>
<p>How do I ... | g15201 | [
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<p>Yes, it's a physics related question. Read on.</p>
<p>I know from general knowledge that in order to produce a decent wine, you must keep it in a dark place. Therefore, from my knowledge of physics I guess that the process of wine making doesn't need much energy (I mean the reactions etc). Also I presume it gets th... | g15202 | [
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<p>Electrons move from higher potential to lower potential. When a conductor is connected to battery, electron move from negative terminal to positive terminal.</p>
<p>But the battery itself forms a Electric field like below
<img src="http://i.stack.imgur.com/xXLBL.jpg" alt="enter image description here">
If a free el... | g15203 | [
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<p>In space, would it be possible to have an object generating such a huge gravitational force so it would be possible for an observer (not affected directly by gravitational force and the space time distortion) to see some visual distortions (bending) on another small object placed near it ? </p>
<p>(eg : a building ... | g15204 | [
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<p>Consider the the following problem:
<img src="http://i.stack.imgur.com/utK3P.png" alt="enter image description here"></p>
<p>Here is a force diagram showing the situation:
<img src="http://i.stack.imgur.com/eHwGx.png" alt="enter image description here"></p>
<p>For part (i) Taking moments about $B$ for $BC$ gives</... | g15205 | [
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<p>In classical mechanics, when talking about the principle of virtual work, what is difference between $\delta r$ and $dr$? e.g. $W=\int \overrightarrow{F} \cdot \delta \overrightarrow{r} $ and $W=\int \overrightarrow{F} \cdot d \overrightarrow{r} $ .</p>
<p>Why can one exchange the place of $d\delta$ and $d$ in ... | g15206 | [
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<p>HJE for nonrelativistic charged particle in an electromagnetic field is</p>
<p>$$\frac{1}{2m}\left(\nabla S - q\mathbf{A}\right)^2 + q\phi + \frac{\partial S}{\partial t} = 0.$$</p>
<p>For a uniform magnetic field $\mathbf{B} = B_0 \hat{\mathbf{z}}$ and a particular choice of gauge this becomes something like:</p>... | g15207 | [
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<blockquote>
<p>A particle is thrown up vertically with initial speed, reaches a maximum height and falls back to ground. Show that the Coriolis deflection when it again reaches the ground is opposite in direction, and four times greater in magnitude, than the Coriolis deflection when it is dropped at rest from the s... | g15208 | [
0.09505347907543182,
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0.017848268151283264,
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0.00715212244540453,
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<p>What shape does the viewer in a reference frame with $v=0$ perceive? I suppose that since the sphere moves in one direction only (oX only, not oY) its section would change into an ellipse, where the horizontal diameter would be shorter.</p>
<p>However, my textbook says that the viewer still perceives a regular sph... | g525 | [
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<p>A classical computer composed of '0' or '1' transistors stores $2^n$ states.</p>
<p>Is it true that a quantum computer composed of '0' or '1' or '0 & 1' qubits stores $3^n$ states? </p> | g15209 | [
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<p>In 2D and 3D quibit models, string-net condensation can happen. In 3D or higher models, is it possible for surfaces (instead of just strings) to condense?</p> | g15210 | [
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<p>I was confused as to how the equation 10 on page 7 or equation 21 on page 8 of this paper <a href="http://arxiv.org/abs/1211.1866">http://arxiv.org/abs/1211.1866</a> was derived. Can someone explain from where does this come and what do the "weird" arrows in Figure 1 on page 7 mean (..it doesn't look like a normal F... | g15211 | [
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<p>I am a bit confused about when to use the method of images in E&M? For example, in Griffith's <em>Electrodynamics</em> Example 3.2, the problem reads:</p>
<blockquote>
<p>A point charge $q$ is situated a distance $a$ from the center of a grounded conducting sphere of radius $R$. Find the potential outside the... | g15212 | [
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<p>Kip S Thorne's "Black Holes & Time Warps", 1994 paperback, p.443, just above Figure 12.5:</p>
<blockquote>
<p>Surprisingly, from the accelerated viewpoint, the vacuum fluctuations consist not of virtual particles flashing in and out of existence, but rather of real particles with positive energies and long li... | g15213 | [
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0.0... |
<p>When I attempted to calculate the following by hand $$\bar{r}\times(\bar{\nabla}\times\bar{F}) - \bar{\nabla}\times(\bar{r}\times\bar{F}),$$ I noticed some of the terms I extracted looked similar to the terms that appear in the oribtal anglar momentum operator $$\bar{L} = -i\hbar(\bar{r}\times\bar{\nabla}).$$ Is the... | g15214 | [
0.02979537658393383,
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<p>Gauge invariance of the electromagnetic field implies local charge conservation. If the gauge is no longer invariant, then the electromagnetic field must no longer conserve charge locally. Is it possible either physically or mathematically, to break local charge conservation, but still enforce global charge conserva... | g15215 | [
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<p>I am trying to solve for the Spherical harmonics $Y^m_{l=1}$ with a second axis at an angle $\alpha$ with respect to the z axis. Then this can be used to find the probability that a particle with projection m onto one axis has m' onto the other.</p>
<p>I have seen the rotation operator, which takes f($\phi$) and r... | g15216 | [
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<p>(A friend at work kindly loaned me loaned me his copy of Kip S Thorne's "Black Holes & Time Warps". This may have been ill-advised... :)</p>
<p>BH&TW 1994 paperback p.410 Figure 11.5:</p>
<blockquote>
<p>... all positive charge that enters the horizon from the outside Universe becomes attached to the ho... | g15217 | [
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0.... |
<p>I don't get how time dilation affects the half-life of muons? Time is just a tool that is used by humans how does that affect the internal clocks of elementary particles?</p> | g15218 | [
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<p>This has bothered me for a while. I've been taught that the formula for determining the perceived velocity on an object from another moving object's reference frame under special relativity is:</p>
<p>$$v = \frac{w - u}{1 - wu/c^2}.$$</p>
<p>If two objects travel from earth at $c$ in exactly opposite directions, w... | g15219 | [
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<p>I'm currently writing a 3D $n$-body simulator (similar to what you <a href="http://www.youtube.com/watch?v=qkMXQS0QytA" rel="nofollow">see here</a> to simulate the evolution of a system of n particles under the force of gravity.</p>
<p>It works fine for "smaller" scale simulations (small galaxies and other random s... | g15220 | [
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<p>Consider the diagram bellow, a massive string hanging in equilibrium</p>
<p><img src="http://i.stack.imgur.com/Vdwh2.png" alt="enter image description here"></p>
<p>My question is this: Can we take any 2 random point on the rope, say A and B and then use $\sum F=0$ on the rope between them: i.e. say that $$T_0 \si... | g15221 | [
0.01810886524617672,
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0.028218358755111694,
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<p>Einstein said that it is impossible to distinguish between the effect of gravity and acceleration (so if you stand in an accelerating elevator in space it would not feel any different than if you were in a gravitational field). My question is, can the same logic apply to the perceived expansion of the universe and t... | g15222 | [
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0.0... |
<p>If the mass of an object or system is a measure of its energy content, multiplied by speed of light squared, does it mean that the total potential energy of the rest mass of object or entire system can only be realized when velocity is similar to speed of light?</p>
<p>What I am looking for is a clear and simple ex... | g15223 | [
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... |
<p>The magnetic field for to a moving charge depend on its velocity (Biot Savart's law). My question is that is it then not frame dependent? If it is, it means if a man is walking and other is standing magnetic field at same point to both will be different. But magnetic field at that point can have only on "constant va... | g15224 | [
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<p>See <a href="http://physics.stackexchange.com/q/38005">What are cosmological "firewalls"?</a>.</p>
<p>Alice is in freefall in her spacecraft just above the horizon of a gigantic black hole. She measures whether or not the near modes of the horizon contain a firewall. The computer settings of the computer ... | g15225 | [
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<p>Please help me check my understanding related to the rotational motion of a 3D rigid body after reading some Physics textbooks and googling for some more materials (e.g., <a href="http://en.wikipedia.org/wiki/Torque" rel="nofollow">Wikipedia's Torque</a>, <a href="http://en.wikipedia.org/wiki/Moment_of_inertia" rel=... | g15226 | [
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<p>I posted this elsewhere also and just found this place so copied it down but yeah. I've always wondered this cause I like wondering bout things but I wanna know and it's simple so I should. I got an idea of it I think, from what I understand particles are points of interaction? Kinda like how light is a wave and a p... | g15227 | [
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<p>In relation to atmospheric spectroscopy and some other gaseous spectroscopy applications where organic molecules are present in the vapor, does anyone know of any papers or resources on pressure broadening due to hydrocarbons or other organic molecules in the vapor?</p>
<p>Broadening due to noble gases seems to hav... | g15228 | [
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<p>Is there a way to take a moving source already into account when one derives the wave equation for sound waves and derive from that using only math the Doppler effect for moving sources?</p> | g15229 | [
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<p>I was solving the following problem and the explanation to it confused me.</p>
<blockquote>
<p><em>There are two objects with mass $m$ and $M$, respectively. The object with mass $m$ has a velocity of $\sqrt{2gl}$ and collides with the other object that is initially at rest. If the collision is elastic, what is t... | g15230 | [
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-0.0454... |
<p>What is the Definition of <a href="http://en.wikipedia.org/wiki/Static_electricity" rel="nofollow">Static Electricity</a>?</p>
<p>My grade nine textbook states: </p>
<blockquote>
<p><em>Static electricity is the imbalance of
positive and negative charges.</em></p>
</blockquote>
<p>What exactly does this mean?... | g15231 | [
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0.0011432821629568934,
-0.01186... |
<p>a fight from east to west, (e.g. Australia melbourne to perth) takes longer than travel backwards. (west to east).</p>
<p>What's the reason? </p> | g15232 | [
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<p>I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question:</p>
<p>While we have Heisenberg uncertainty principle on measuring coupled observables, can we express it using somehow a more fundamental/abstract concept like Information uncertainty (especially ... | g15233 | [
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<p>Are there any nonlinear variations of Dirac's Equation analogous to the Nonlinear Schrodinger Equation, that have been studied and published in any mainstream journals or books? </p>
<p>Perhaps such a thing as a NDE would apply to non-quantum situations the way NSE applies to optics or hydrodynamics, but where r... | g15234 | [
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<p>I am consistently getting this wrong. To me, in the picture below, it would make sense that the structure would be pulling downward, and the cable BD would be pulling upward - thus the system is in equilibrium. I took point D - point B to get line DB.</p>
<p><img src="http://i.stack.imgur.com/wIOUN.jpg" alt="enter ... | g15235 | [
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<p>For nonabelian Yang-Mills in the Coulomb phase, can soft gluons render the charge orientation of charged particles indefinite? Let's say the gauge group is a nonabelian simple Lie group G. Suppose there is a charged particle in the nontrivial irreducible representation r. It might appear the particle can take on a d... | g15236 | [
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<p><a href="http://en.wikipedia.org/wiki/Deuterium#Approximated_wavefunction_of_the_deuteron" rel="nofollow">Wikipedia article on deuterium</a> says this:</p>
<blockquote>
<p>The deuteron wavefunction must be
antisymmetric if the isospin
representation is used (since a proton
and a neutron are not identical
... | g15237 | [
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<p>Say I have Argon gas in an area such as a cube with pressure around pressure between 10-5 and 10-3 Torr (pressure) at 25 degrees at 320 Kelvins . How do I find the amount of atoms in that cube? Any formulas?</p> | g15238 | [
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-0.0012493992689996958,
0.012863808311522007,
0.022048262879252434,
-0.08386723697185516,
-0.0022933681029826403,
-0.005047105252742767,
0.021588416770100594,
0.002869942458346486... |
<p>So the set of solutions for the particle in a box is given by
$$\psi_n(x) = \sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L}).$$</p>
<p>In Dirac notation $<\psi_i|\psi_j>=\delta_{ij}$ assuming $|\psi_i>$ is orthonormal. My question is, are $\psi_i$ and $\psi_j$ simply corresponding to different values of $n$ for t... | g15239 | [
0.02113444171845913,
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<p>I keep wondering how a Rubbia thorium reactor would handle a natural disaster of Fukushima level intensity. As I understand it the nuclear chain reaction would stop instantly if the power is cut, but nasty waste products such as Uranium-233 would still require substantial cooling and hence it would seem that this re... | g15240 | [
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<p>I've just been learning about Einstein, relativity, and the equivalence principle in Physics. I'm fascinated with the idea of being inside a free-falling enclosed environment (such as, e.g., rocket, airplane, Einstein elevator, etc.) and weightlessness, but I'm having trouble understanding the difference between bei... | g15241 | [
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0.011346151120960712,
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<p>Are there fundamental big questions in physics that most scientists encounter no matter what they're working on, or are most questions details of smaller subtopics? What are the great unknowns of our day?</p>
<p>Sorry in advance if my question is too general. I told my kid that there are some things science still d... | g15242 | [
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0.07467969506978989,
0.018227046355605125,
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0.021619107574224472,
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0.016338340938091278,
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<p>Assuming wormholes exist and you put some matter into one, how long would it take to reach the other end versus how far apart the two ends are? Basically, by how much does a wormhole stretch spacetime?</p> | g15243 | [
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<p>The professor in my class of mathematical physics introduces the definition of groups and said that group theory is the mathematics of symmetry. </p>
<p>He gave also some examples of groups such as the set of all real numbers under addition. </p>
<p>My question is what symmetry are we talking about here when we co... | g15244 | [
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0... |
<p>Assume a photon enters the event horizon of a black hole. The gravity of the black hole will draw the photon into the singularity eventually. Doesn't the photon come to rest and therefore lose it's mass?</p> | g15245 | [
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<p>Are there already photon detectors that can resolve the shape of photons in the time domaine if it looks like below where the two humps are separated by a time of the order of femtoseconds? </p>
<p>What I know is that there are photon detectors that can resolve in the picosecond regime (see <a href="http://scitatio... | g15246 | [
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<p>I reformulate the question a little bit because I feel that
I was misunderstood.
There are cosmic observations that tell us the universe seems to expand.
It also seems to expand always faster (accelerating).
I am missing the step of reasoning that, from the collected data, leads to
the conclusion that it is certainl... | g15247 | [
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<p>While I was watching <a href="http://www.youtube.com/watch?v=isVO9AAAhxM">this beautiful video</a>, the absence of air friction pushed me to ask myself: While standing on the surface of the moon, what is the initial velocity by which you can fire a bullet to put it into orbit around the moon so it will hit you in yo... | g15248 | [
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<p>Is there a way to transfer heat from a rotating object made of iron into a suitable heat sink using a magnetic field as a transfer medium?</p> | g15249 | [
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<p>Consider a space ship which is not under any force. Being inside the space ship, I will make a robotic fly from the platform to crawl inside using my remote. For simplicity assume that space ship will be drifting at uniform speed only under forward direction with respect to me, or else it will be under rest. The fol... | g15250 | [
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<p>I've been thinking about Newton's third law lately because I couldn't understand a few things and I think I actually answered my own question. Could someone confirm if my reasoning is right or show me my mistakes? </p>
<p>So the question is: If force and reaction force are always the same, and less mass means great... | g15251 | [
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<p>I have very little background in physics, so I apologize if this question is painfully naive.</p>
<p>Consider the following thought experiment: an observer is in a closed room whose walls, floor, and ceiling are made entirely of mirrors, with a single light source in the middle of the room. When the light is on, th... | g15252 | [
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<p>This question was inspired by: <a href="http://physics.stackexchange.com/questions/13500/how-are-photons-consumed">How are photons "consumed"?</a></p>
<p>Imagine I have some number of photons, $N$, each of frequency $\nu$, moving randomly in a spherical "wrap-around" universe of volume $V$. To clarify wh... | g15253 | [
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0.0443563275039196,
0.07248633354902267,
0.... |
<p>On the scale of a galaxy, can vacuum-based pairs of virtual particles be noticed gravitationally? Even though they are short-lived, shouldn't their mass and numbers be enough to be measured/felt?</p> | g15254 | [
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<p>I have learned so many concepts under astrophysics and unfortunately, I have muddled everything together... Let me try to illustrate my problem:</p>
<ol>
<li><p>When a star is in main sequence, it fuses hydrogen to produce helium and energy that is mostly given off as light (This is what I learned from watching a f... | g15255 | [
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0.05931122228503227,
0.03... |
<p>A canon is fired Horizontal to the ground 80 meters above ground The canon ball is fired a $T=0$ and hits the ground at $T_g$. Calculate the height at the time $T_g/2$
So far I have calculated time. which gives me the equation
$$y=y_i+v_{iy}(4.05) - (0.5)(9.82)(4.05^2)$$
Now my problem is that when I try to calculat... | g15256 | [
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0.0011897728545591235,
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0.041917674243450165,
0.014257073402404785,
0.012... |
<p>Just confused my self again :(. Transition radiation is the radiation produced when a charge crosses a boundary between two dielectric materials (<a href="http://en.wikipedia.org/wiki/Transition_radiation" rel="nofollow">http://en.wikipedia.org/wiki/Transition_radiation</a>). As Jackson (chp 13) states, it is the ac... | g15257 | [
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<p>In the area of random tilings, there are many results that fall under the term "Arctic Circle Theorems." This roughly means that if one chooses a tiling of a specific region uniformly at random, then there will generally be a boundary region outside which the tiles are "frozen" in a fixed configuration. Here are som... | g15258 | [
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<p><img src="http://i.stack.imgur.com/EAN0s.jpg" alt="diamgram of my problem"></p>
<p>Where $\theta=45^\circ$, $d_1=200\:\mathrm{m}$, and $d_2=150\:\mathrm{m}$.
I do not know how to combine the following equations:
$$\begin{align}
t&=\frac{d_1}{v_s\cos(45^\circ)}\\
t&=\frac{d_2}{v_r-v_s \sin(45^\circ)}
\end{al... | g15259 | [
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0.0734953060746193,
0.02294212579727173,
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<p>The uncertainty principle states: $\Delta_x\Delta_p>ħ/4$</p>
<p>We know the photon has a 0 rest mass but we are say that it's momentum is always the same $e=pc$ </p>
<p>And more we are certain about the momentum, more we are not certain about the position, however since we are 100% sure about photons momentum t... | g15260 | [
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0.00878753513097763,
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<p>I'm searching for an at least semi-rigorous Statistical Mechanics description/treatment of a (spatially resolved) chemical reaction process of a macroscopic portion of at least two different species along the lines of
$$A_1+A_2\longrightarrow A_3,$$
(with $A_3=A_1A_2$, necessarily) or
$$A_3\longrightarrow A_1+A_2.$$... | g15261 | [
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0.011601649224758148,
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0.045163173228502274,
0.00562860444188118,
0.0519166998565197,
-0.... |
<p>[ Cross-posted to the Computational Science Stack Exchange: <a href="http://scicomp.stackexchange.com/questions/1297/why-does-iteratively-solving-the-hartree-fock-equations-result-in-convergence">http://scicomp.stackexchange.com/questions/1297/why-does-iteratively-solving-the-hartree-fock-equations-result-in-converg... | g15262 | [
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<p>What's the most efficient way to place your hands under the hand dryer? </p>
<p>Let's assume that dryer creates simple downward flow of hot air.</p>
<p>Here are some examples:</p>
<p><img src="http://i.stack.imgur.com/g44iL.png" alt="positions"></p> | g15263 | [
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0.005602025426924229,
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0.0... |
<pre><code> /\
/ \
| |
| m |
| |
------ <--- floor (Rocket A)
</code></pre>
<p>This rocket is accelerated (g) upwards then mass(m) falls on the floor. </p>
<pre><code>------ <--- floor
| |
| m |
| |
\ /
\ /
\/ (Rocket B)
</code></pre>
<p>This rocket is accelerated (g) downwards t... | g15264 | [
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0.000048797399358591065,
0.0010475252056494355,
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0.06... |
<p>Here are some informations I found on the magnetic field strength (also called "magnetic flux density" or "magnetic induction", commonly denoted as B and expressed in tesla or in gauss) of an average neodymium-iron-boron rare earth magnet.</p>
<p>"A modern neodymium-iron-boron (NIB) rare earth magnet has a strength... | g15265 | [
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0.014586208388209343,
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-... |
<p>I am going through <a href="http://arxiv.org/abs/0809.4266" rel="nofollow">Kerr/CFT correspondence paper</a> again, and I am at the section where authors specify <a href="http://en.wikipedia.org/wiki/Killing_vector_field" rel="nofollow">Killing vectors</a> for near horizon extreme Kerr metric (shortly NHEK).</p>
<p... | g15266 | [
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-... |
<p>The Earth is billions of years old, yet its core has not yet cooled down and become solid. Will this happen in the foreseeable future?</p> | g15267 | [
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<p>I want to calculate the escape velocity of a rocket, standing on the surface of Ganymede (moon of Jupiter) and trying to leave Ganymede.</p>
<p>My thinking was, the kinetic energy $E_{\text{KIN}}$ must be equal or bigger then the potential energy $E_{\text{POT}}$. So $E_{\text{KIN}}\geq E_{\text{POT}}$</p>
<p>Assu... | g15268 | [
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0.04734626039862633,
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0.... |
<p>While it is fairly established that both fast movement and the presence of gravity make time pass slower as compared to a system at rest / free of gravity, does that mean that there is no way for time to pass <em>faster</em> than in vacuum, or does general relativity also have "faster" metrics?</p>
<p>To be more pr... | g15269 | [
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<p>I would like to know whether there has been an experimental detection of advanced radiation. I seem to recall reading about such an experiment but I can't find any reference to it on the interwebs so I'm starting to wonder whether I imagined the whole episode. IIRC the experiment was roughly like this:-</p>
<p>Li... | g15270 | [
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<p>I am having problems with this excercise.</p>
<p>We look at a system where the total angular momentum is given by an electron with $l=1$ and $s=\frac{1}{2}$.</p>
<p>Now I am supposed to calculate the eigenfunctions $|\frac{3}{2},m_j\rangle, |\frac{1}{2},m_j\rangle$ with respect to $J^2 $ and $J_z$, where $J=L^{(1)... | g15271 | [
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0.0... |
<p>A long time ago I was told that the universe is finite. The provided "proof" (or reasoning), known as <a href="http://en.wikipedia.org/wiki/Olbers%27_paradox" rel="nofollow">Olbers' paradox</a>, was that on infinite universe there would be an infinite number of stars, and that an infinite number of stars in night sk... | g15272 | [
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... |
<p><a href="http://en.wikipedia.org/wiki/Refraction" rel="nofollow">Refraction</a> is the bending of a wave when it enters a medium where its speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media.
My que... | g298 | [
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<p>Can a detuned laser can excite an atom? If so, how is this possible? </p> | g15273 | [
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<p>With "Geographic coordinate system" we only get the location, no rotations or anything. Translated into <em>latitude</em> and <em>longitude</em>.</p>
<p>Where with "Spherical coordinate system", we should be able to get the exact position, including rotations.</p>
<blockquote>
<p>The spherical coordinates of a p... | g15274 | [
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<p>This question is about the domain of validity of Lorentz symmetry.</p>
<p>As far as I know, general relativity is a generalization of special relativity. Does that mean that Lorentz symmetry is violated on cosmological distances, i.e in curved spacetime?</p>
<p>I am just curious, since people and the media are cra... | g15275 | [
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... |
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