question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>It's always nice to point out the structural similarieties between (semi-)Riemannian geometry and gauge field theories alla Classical yang Mills theories. Nevertheless, I feel the relation between the gauge group and the gauge bosons "$A_{\mu}\times T^i_{\ j}$" are much simpler than the relation betreen the diffeomo... | g9353 | [
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<p>Now, humanity can <a href="http://www.engadget.com/2012/07/07/wireless-power-through-4-inch-concrete/" rel="nofollow">beam 50-60 watts power through 10 centimeter-thick concrete block</a>. Can such wireless power transfer harm us by anyways?</p> | g9354 | [
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<p>I want to be expert to understand physics behind whirlpool, tornado, hurricane. Which topics are needed for this?</p> | g9355 | [
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<p>How would I normalize the wave function:
$ \psi (x)$ = $Ce^{i\rho_0x/\hbar}e^{-|x|/2\Delta x}$?
I squared it, which got rid of the imaginary part-Then I considered breaking up the absolute value-but this didn't seem to be integrable. I considered also using one of the exponential integrals from negative infinity to... | g9356 | [
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<p>I've searched for it but I only found contradicting answers from "scientists":</p>
<p>Dr. David Balson, Ph.D. states: "<a href="http://www.physlink.com/education/askexperts/ae380.cfm" rel="nofollow">entropy in a system can never be equal to zero</a>".</p>
<p>Sam Bowen does not refutes the following affirmation: "<... | g9357 | [
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<p>Gravitation force is always attractive.</p>
<p>Now assume(not a practical one): I took our Earth in my hand and started shaking up and down. This will create a disturbance in space-time warp and it moves like a wave outward direction. So when the crest part of this disturbance comes in touch with another mass, it s... | g9358 | [
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<p>I'm making a tea bag experiment (Make a hollow cylindrical tube from light paper e.g. from an empty tea bag. When the top end of the cylinder is lit, it takes off.) I need to know how hot air is moving so please help me if you have thermal imaging camera or with out it write your opinion</p> | g9359 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/296/is-energy-really-conserved">Is energy really conserved?</a><br>
<a href="http://physics.stackexchange.com/questions/19216/why-cant-energy-be-created-or-destroyed">Why can’t energy be created or destroy... | g307 | [
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<p>In David J. Griffiths' <em>Introduction to Electrodynamics</em>, he claims that the superposition principle is not obvious but has always been found to be consistent with the experiments. So I was wondering have we found some physics quantities which do not follow superposition principle? If we have not till now why... | g9360 | [
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<p>I want to build a geyser attached to a pump with copper tubing running into an oil tank. This is done because the oil solidifies at a temperature below 15 degrees Celsius. I have done a few calculations to determine the amount of time it would take to heat the oil, but i am not sure if they are correct.</p>
<p>Pump... | g9361 | [
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<p>Suppose I have two batteries one inside the laptop with 2.5 AH giving a backup for around 2 hours. The battery is external inside a UPS system with 7.5 AH. Since it has thrice the capacity of the previous one, can I conclude it will give backup for 6 hours?</p> | g9362 | [
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<p>In this video a single flick of a finger tips 116000 dominos. </p>
<p><a href="http://www.youtube.com/watch?v=3bxk-6GEK6w" rel="nofollow">Domino video</a></p>
<p>I understand the work that needs to be done to move 116000 pieces (at least 100 kilos) of plastic is greater then that expended by flick of a finger. How... | g9363 | [
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<p>Say a red colour with 400nm mixes with blue colour with 700nm, but out of phase by a little. What would be the resultant colour?</p>
<p>I would know how to represent the resulting wave mathematically, but what colour is it? Is the colour only determined by the resulting wavelength?</p> | g308 | [
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<p><a href="http://en.wikipedia.org/wiki/Gauss%27s_law_for_gravity" rel="nofollow">Gauss's law for Gravitation</a>:</p>
<p>$$\int g\cdot \mathrm{d}S=4\pi GM$$</p>
<p>where $g$ is the gravitational field and $S$ is the surface area.</p>
<p>Am I correct?</p> | g9364 | [
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<p>When and where on earth do we get the best view of the <a href="http://en.wikipedia.org/wiki/Milky_Way">Milky Way</a>?</p>
<p>I believe it helps</p>
<ul>
<li>if it is night</li>
<li>if it is winter</li>
<li>to look in the direction of the galaxy center</li>
</ul>
<p>I think that this information from wikipedia:</... | g9365 | [
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<p>let be the 2-loop integral...</p>
<p>$$ \int d^{d}l\int d^{d}k \frac{1}{k^{4}(k+p)^{2}(k+l)^{2}}=I(p)$$</p>
<p>dimensional regularization over the variable 'l0 to evaluate</p>
<p>$$ \int d^{d}l\frac{1}{(k+l)^{2}}=G(k,d)$$</p>
<p>this is the regularizñation of the subdivergence assumed to exist by dimensional rgu... | g9366 | [
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<p>I'm studying for a test in electrostatics and I'm always failing on putting up the correct integrals.</p>
<p>In one problem I have the surface of a sphere with radius $a$ and an opening angle of $2\theta$. There is a total charge $Q$ evenly distributed on the surface. I want to calculate the potential.</p>
<p>In o... | g9367 | [
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<p>Consider an electric dipole and its electric field lines. </p>
<p>There will be many field lines that do not extend to or originate from infinity, but rather begin at the positive charge and loop back around to terminate at the negative charge. </p>
<p>However, the field lines exactly on the dipole axis will ext... | g9368 | [
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<p>Can thermal radiation from a cooler object (B, which emits longer wavelength radiation) ever ADD to the overall thermal energy level of a warmer object (A, which emits shorter wavelength radiation)? Subsidiary question: What exactly happens - at the molecular level - to the longer wavelength radiation from B as it ... | g9369 | [
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<p>I have found from <a href="http://en.wikipedia.org/wiki/Parity_%28physics%29" rel="nofollow">Wikipedia</a> that
"a parity transformation is the flip in the sign of spatial coordinates".</p>
<p>Now when we operate parity operator, does that mean we are taking any physical entity at ${\bf x}$ to $-{\bf x}$. Or we ar... | g9370 | [
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<p>Suppose I have knowledge of a system's dispersion relation $f(\omega,k)$. Is it possible to recover the underlying PDE describing the system? Can I simply use the replacement $k=-i\nabla$, $\omega=i\frac{d}{dt}$ to go back?</p>
<p>I came across one source which claimed that the original PDE could only be recovered ... | g9371 | [
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<p>In Polchinski's textbook String Theory, section 2.8, the author argues that the unit operator $1$ corresponds to the vacuum state, and $\partial X^\mu$ is holomorphic inside couture $Q$ in figure 2.6(b), so operators $\alpha_m^\mu$ with $m>=0$ vanishes.</p>
<p>I am a bit confused about why $\partial X^\mu$ has n... | g9372 | [
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<p>This problem is on Di Francesco's book I. It's exercise 7.1:
Calculate the norm of the following vector, where $\lvert h\rangle$ is the state of highest weight.</p>
<p>$$L_{-1}^n\lvert h\rangle$$ </p>
<p>I have just tried to use the commutation relations of the $L$ operators and the fact that $L_1$ acts on $\lver... | g9373 | [
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<p>My understanding of algebraic topology and Riemannian geometry come from Nakahara's <em>Geometry, Topology, and Physics,</em> which I do not think is sufficient. I am first year PhD student, and I want to do string theory at my university. Can you recommend me any other really nice books that I should read over the ... | g185 | [
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<p>Can anyone tell me very basically how the <a href="http://www.google.com/search?as_epq=Euler+Poincare+equation" rel="nofollow">Euler-Poincare equation</a> generalises the <a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation" rel="nofollow">Euler-Lagrange equation</a>? Further does anyone know if the... | g9374 | [
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<p>Since a polarization of the wave is described by complex numbers, we can try to give that mathematical formalism geometrical meaning. With having two different axes, one imaginary and other real, it is possible to represent the motion of the wave in three dimensions as the motion of 2 waves in two planes. These two ... | g9375 | [
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<p>Apparently the plane mirror makes virtual images, and virtual images cannot be projected onto a screen. If you look below, it is?</p>
<p><img src="http://i.stack.imgur.com/vg05N.png" alt="Virtual Image projection"></p>
<p>If the eye is basically a screen of rods and cones, then everything is a real image?</p>
<p>... | g9376 | [
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<p>Does my question make any sense?</p>
<hr>
<p><strong>Context</strong>: The capacitor is charged with charge $Q_0$. There is a magnetic field $B=B_0 \hat{z}$ perpendicular to the monitor's screen. The length of the (AB) wire is $\ell$. There is no friction.</p>
<p><img src="http://i.stack.imgur.com/kfsS5.png" alt=... | g9377 | [
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<p>I am just trying to wade through literature on classical mechanics and I really don't know where to start, everything is Fibre bundle this or manifold that, and doesn't really ease you in to the topic. I'm sure this is a common question but I would like help with a couple of specific points:</p>
<ul>
<li>What would... | g9378 | [
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<p>If every body emits radiation at a given frequency and temperature exactly as well as it absorbs the same radiation, how do objects heat up?</p> | g9379 | [
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<p>The three Mandelstam-variables are defined as:
$$s=(p_A+p_B)^2=(p_C+p_D)^2,$$$$t=(p_A-p_C)^2=(p_B-p_D)^2$$$$u=(p_A-p_D)^2=(p_B-p_C)^2.$$ Where A and B are the incoming particles and C and D are the outgoing particles, and the second equation follows from the conservation of 4-momentum.</p>
<p>The Mandelstam-variabl... | g9380 | [
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<p>What is preventing $Δ^{++}$ and $Δ^-$ baryons from going to a lower-energy state with spin 1/2 similar to that of protons and neutrons? I don't think the Pauli exclusion principle can prevent it because the quarks have different colors. The whole purpose of the quark color is to allow more than one quark to be in ... | g9381 | [
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<p>i heard that a tear drop shap is the most aerodynamic shape possible or the best is this true? If this isn't true what is since i need to make a fast ROV? Also since i need to have a propeller to propel it should it be on the front or back to produce the most thrust and the best hydrodynamcics?</p> | g9382 | [
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<p>I'm a bit confused with some notation I encounter in physics calculus. Consider this:
<img src="http://i.stack.imgur.com/rAssQ.png" alt="enter image description here"></p>
<p>Taken from <a href="http://en.wikipedia.org/wiki/Impulse_(physics)" rel="nofollow">here</a>.
Integration operates on functions, correct? Wha... | g9383 | [
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<p>As I understand, photons are considered mass-less, which is a necessary condition for moving at the speed of light. However, does that mean their density is 0, as they will occupy some volume. If their density is zero, that means there is no matter inside a photon. Thus, shouldn't a photon be able to pass through ma... | g9384 | [
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<p>I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting vector. I can't really understand how the momentum conservation laws apply to the situations in which there is a magnet(cur... | g9385 | [
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<p>Is this correct? </p>
<p><a href="http://en.wikipedia.org/wiki/Tensor" rel="nofollow">Tensors</a> are linear mappings between two coordinate systems on a manifold. The elements of that mapping (which include the different changes of bases at each point of the manifold) are governed by the components of the <a href... | g9386 | [
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<p>I was reading this question: <a href="http://physics.stackexchange.com/questions/108470/was-titanics-captains-decision-correct">Was Titanic's captain's decision correct?</a> @oakad commented about a Russian vessel keeping itself afloat by going in reverse, using hydrodynamic pressure to keep its damaged bow ... | g9387 | [
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<p>Suppose I start with a basis of states for a two spin-1/2 particle system, namely, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, \left|\uparrow\downarrow\right\rangle, \left|\downarrow\uparrow\right\rangle \} $, and then I apply a Hamiltonian that gives me the new basis, $\{\left|\... | g9388 | [
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0.01518209557980299,
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<p>I know that the rotation period of the moon equals its revolution period. It's just so astonishing that these 2 values have such a small difference. I mean, what is the probability of these 2 values to be practically the same? I don't believe this to be a coincidence. It's just too much for a coincidence. What could... | g263 | [
0.06405382603406906,
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<p>As a homework assignment, we have to find $U_a(\omega)$, that is the voltage that drops over the right resistor in relation to the frequency $\omega$ of the input AC voltage $U_e$.</p>
<p><img src="http://wstaw.org/m/2012/07/01/blindleistung3.png" alt=""></p>
<p>For the two extreme cases, $\omega \to 0$ and $\omeg... | g9389 | [
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<p>In cartoons we can see, how vehicles brake by rotating wheels reverse.</p>
<p>Will this be helpful sometimes in real situations? I know that the main tactics of ABS is to maintain tractive contact. But may be it will be better sometimes, at some speeds, friction and so on -- to rotate back?</p>
<p>Does current ABS... | g9390 | [
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<p>If we have a solenoid and a magnetic field passes through it, a DC voltage will be produced in the wire. If we want to calculate the power, we find out the current using Ohm's law.</p>
<p>I know there is power loss due to the resistance (joule effect). But what about the magnetic field due to current (lenz's law), ... | g9391 | [
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<p>Question goes as</p>
<blockquote>
<p>Show that the solutions to the <a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations" rel="nofollow">Maxwell's equations</a>
$$ \nabla \times \vec H = \frac 1 c \frac{\partial \vec E}{\partial t}+\frac {4\pi} c \vec J, \hspace{ 2 mm} \nabla \times \vec E = -\frac 1 c ... | g9392 | [
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<p>I read somewhere that stress-energy tensor density is a symmetric tensor. But if I take the Dirac Field tensor:</p>
<p>$$T^{\mu \nu}=i \psi^\dagger \gamma^0 \gamma^\mu \partial^\nu \psi $$</p>
<p>How could I demonstrate this property?</p> | g9393 | [
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<p>In particle physics, <a href="http://en.wikipedia.org/wiki/Supersymmetry" rel="nofollow">supersymmetry</a> (often abbreviated SUSY) is a symmetry that relates elementary particles...etc.</p>
<ul>
<li><p>what is <a href="http://en.wikipedia.org/wiki/Symmetry_breaking" rel="nofollow">symmetry breaking</a>?</p></li>
<... | g9394 | [
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<p>Is the number of states in the Universe countable? </p>
<p>What framework could be used to answer the question in the title?</p> | g9395 | [
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<p>If I draw a control volume around a single light wave traveling through empty space, is entropy increasing as it goes? How is the degradation of the quality of energy manifested?</p> | g9396 | [
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<p>Let's have the Lagrangian
$$
L = L_{0} + \lambda V , \qquad (1)
$$
where $\lambda$ is constant which is small in the next senses: if $\lambda$ is dimensionless, it means that $\lambda < 1$; if it has dimension $[\lambda ] = l^{-n}$, it means that it is small in compare with characteristic energy of the free state... | g9397 | [
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<p>My questions are based on this paper - <a href="http://arxiv.org/abs/0905.4013" rel="nofollow">http://arxiv.org/abs/0905.4013</a></p>
<ul>
<li><p>Firstly I want to know as to whether some assumptions are needed about the relationship between the systems $A$ and $B$ for the Hilbert space to factor as tensor products... | g9398 | [
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<p>What will happen in young's double slit experiment, when instead of screen I put a black screen with a hole and a second screen behind the black one. Will it still form interference pattern albeit a faint one or no interference pattern will be observed?</p> | g9399 | [
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<p>A wavefunction is inherently a multi-particle function. If you have a container that is perfectly isolated from the external universe (not possible, but just imagine it) and filled with $n$ particles, then the information necessary to perfectly describe everything there is to know about that system would be contain... | g9400 | [
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<p>The no-cloning theorem implies that we cannot use entanglement to send signals faster-than-light. Has anyone proved the contrapositive? That is, if we are given a system for superluminal signalling can we use it to violate the no-cloning theorem?</p> | g9401 | [
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<p>The <a href="http://www.eenews.net/stories/1060004813" rel="nofollow">internet is ablaze</a> with the new nano particle based extraction method of converting water to hydrogen. In 2002/2003 when I was 16 there was a similar craze about a lawn mower motor which supposedly ran on water. Indeed there were even conversi... | g9402 | [
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<p>15th group elements like As, Sb, P can be used for doping whereas N and Bi cannot be used for doping even though they too belong belong to 15th group. Why ?</p> | g9403 | [
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<p>I am taking for granted that when we say that something is conserved it is understood '<em>in its full integrity'.</em> <strong>Energy</strong> is represented by a number (of J, or other) and is usually conserved. </p>
<p>But <strong>momentum</strong> is the product of a number (of Kg) by velocity which is a <em>ve... | g9404 | [
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<p>Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? </p>
<p>Why can it be 0 when spin and linear momentum are parallel?</p>
<p>Like in the example of a scalar field at rest decaying into an electron and a positron via interaction $\frac{1}{2}g\phi \bar{\Psi}\Psi $ </p>
<p>If spi... | g463 | [
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<p>I'm in a mechanical physics class, and I'm having a hard time understanding what the quantity of work represents. How can I understand it conceptually?</p> | g380 | [
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<p>On <a href="http://en.wikipedia.org/wiki/Ampere" rel="nofollow">Wikipedia</a> it says: </p>
<blockquote>
<p>This force is used in the formal definition of the ampere, which states that it is "the constant current that will produce an attractive force of $2 × 10–7$ newton per metre of length between two straight, ... | g9405 | [
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<p>Let's say </p>
<ul>
<li><p>the cylinder has a diameter equal to its height of $25\;\mathrm{cm}$</p></li>
<li><p>the cylinder is sealed at the top and filled with sand</p></li>
<li><p>the cylinder is also buried in the sand at sea at a depth of $10\;\mathrm{m}$ with only its top exposed</p></li>
<li><p>the top has a... | g9406 | [
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<p>There's a common QnA which has amused and inspired many kids:</p>
<blockquote>
<p><strong>There are billions of Stars in the sky. If we combine lights received from all stars, wouldn't it beat Sun? Why is night dark really?</strong><br>
It's because speed of light is finite and lights from most of stars are in ... | g9407 | [
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... |
<p>I have a reptil UVB lamp in my room, and a de-humidifier that uses a UV lamp to clean the air passing through it. Honestly since I got it working (the lamp was dead at first) my room is mold free. </p>
<p>I just read that UV air purifiers were banned, and although the dehumidifier model is not in the ban notice, I ... | g9408 | [
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<p>In the Peltier effect, we consider charge carriers being able to carry heat. As for electrons or ions, this attitude makes sense, since external electric potential drives particles with mass in a direction and effectively transfers heat from one point of material to another.</p>
<p>But for holes, this situation is ... | g9409 | [
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<p>I read in several papers that for a Harmonic Oscillator Hamiltonian in the time dependent Schrödinger equation a Gaussian wave packet remains Gaussian.</p>
<p>Unfortunately I could not find any proof for this statement and trying to verify it myself I did not succeed. If I make a general ansatz with a spherically s... | g9410 | [
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<p>Try this:</p>
<p>Make a cup of tea, add sugar, and stir it. </p>
<p>Now add some milk, while it's still spinning.</p>
<p>What I noticed is that the milk appears to move around a lot quicker in the middle of the cup of tea, than the outside. </p>
<p>This seems to be the opposite of what happens on a vinyl, though... | g9411 | [
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<p>I want to write $F^{\mu \nu}F_{\mu \nu}$ in terms of $F_{\mu \nu}F^{\mu \nu}$. How to do it?</p> | g9412 | [
0.006903911009430885,
0.01847505010664463,
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<p>$\newcommand{\bra}[1]{\left\langle#1\right|}$
$\newcommand{\ket}[1]{\left|#1\right\rangle}$
Suppose I have a beam splitter that will either reflect a photon by 45 degrees, or will allow the photon to pass directly through.</p>
<p>If I send a single photon state through, that is, $\ket{1}_{initial}$, we have:</p>
<... | g9413 | [
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... |
<p>I know that the components of stress energy tensor are: energy density, energy flux, momentum density and momentum flux.</p>
<p>But can I explicitly calculate the form of stress energy tensor in any complicated situation? </p>
<p>Or explicit form is known only for few systems? How do I do it?</p> | g9414 | [
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<p>As far as I know Coulomb's law only works for point charges but what if there are not any point charges? For example, let's imagine there are three rectangles with different sizes. First one is 50 cm, second one is 30 cm and last one ise 10 cm. The distance between first and second triangle is 10 cm and the distance... | g9415 | [
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<p>Firstly, I understand what the Doppler effect is when it comes to sound or light waves.</p>
<p>From everything that I've read, we are told that the universe is constantly expanding since the all the radiation we observed is red-shifted.
Assuming we are observing a distant galaxy/start that is moving away from us, t... | g9416 | [
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<p>As far as I know, a magnetic field can only be produced by a moving electric charge, or from a particle's spin (this is how a permanent magnet works, all the spins are in the same direction)</p>
<p>What is strength and direction of the magnetic field of a stationary electron at the origin with spin oriented straigh... | g9417 | [
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<p>I have two solid objects. Each of them has an arbitary complex surface, which is discribed by set of vertices. The aim is to describe their interaction, result of which is the change in trajectory of one of them.</p>
<p>Example: one object (M1) is stable and fixed. The second object (M2) moves along some certain ax... | g9418 | [
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<p>I have read that the pressure in a water barometer at the top of the water column is around 0.5 psi and at such low pressures water should boil at around ~26°C (Room temperature). <a href="http://www.engineeringtoolbox.com/boiling-point-water-d_926.html" rel="nofollow">[1]</a> <a href="http://www.thermospokenher... | g9419 | [
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<p>Wikipedia: "Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of the original pair are zero."</p>
<p>Is it possible to annihilate a quark-antiquark pair if the antiquark has a color different from the quark?</p>
<p>Eg.: Will red up and anti-green anti-u... | g9420 | [
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<p>As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for solitons in nonlinear wave equation? </p> | g9421 | [
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<p>I have just covered a very brief module on special relativity as a part of my physics course. I have also done some extra reading mostly; Morrin's Classical Mechanics. While I found the book really illuminating in some aspects, I still feel that regardless of how hard I try there is something with relativity that pr... | g9422 | [
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<p>I'm just looking to set up a free body diagram for this scenario and I'm having a bit of trouble understanding what's going on. The problem states, "A rectangular block of mass $m_1$ lies on top of a (larger) rectangular block of mass $m_2$, which lies on a horizontal plane without friction. Between the two blocks t... | g9423 | [
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<p>Let's say we somehow speed up the moon's rotation. (I'm thinking about a big asteroid smashing into it, but I'm open to better ideas.) Here are some questions:</p>
<p>How fast could we get the moon to spin before gravity stopped holding it together? (An answer in revolutions per minute would be nice.) </p>
<p>At h... | g9424 | [
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<p>Imagine an arbitrary object with center of mass at the red dot in the picture, rotational inertia from the point of the hanging: <strong>I</strong>, hanging from a fixed point, what is the energy required to start moving at constant angular velocity of $\ ω=ω_0 $ the object within a small amount of time $\ t=t_1$, f... | g9425 | [
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<p>My textbook states that "Ideally, we would like to have measurements of pressure versus altitude over the specific range for the specific conditions (temperature, reference pressure) for which the pressure is to be determined. However, this type of information is usually not available. Thus, a "standard atmosphere" ... | g9426 | [
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<p>Could you please, explain to me the logic of the folllowing process as you would do to your 8 y/o sister:</p>
<blockquote>
<p>Ubiquitousness and stability of atoms relies on their binding energy,
which means that an atom has a lower energy than an unbound system of
the nucleus and electrons. Where the tempera... | g9427 | [
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<p>Last night, a rather strange noise woke me up around 5 am. It was like if a normal thunder sound had been fed to a reverb/delay box. As I was getting back to sleep afterwards, I could hear the sound of rain.</p>
<p>As I have been producing acid house tracks the whole day (it's just a hobby), using quite a lot of de... | g9428 | [
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<p>I would like to know, how measurements of the speed of light are conducted these days, especially in the context of the invariance of $c$.</p>
<p>Do all the methods involve mirrors to redirect the photons back to the place where they were emitted from?</p>
<p>If not, could somebody, please, describe the method br... | g9429 | [
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<p>I have a problem understanding how to deal with the chemical potential when two thermodynamic systems are in contact. For simplicity, let us consider $T=0\ K$. We have a system that is composed of two parts - I and II - where I occupies a space of fixed volume and II occupies the remaining space (essentially going t... | g9430 | [
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<blockquote>
<p>Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$.</p>
</blockquote>
<p>Where $P=-i\hbar \nabla$.</p>
<p>Here's what I've gotten: $$T_\epsilon\Psi(\mathbf r)= e^{i \mathbf{\epsilon} P/ \hbar}\Psi(\mathbf r)=\sum^\... | g9431 | [
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<p>I have a big confusion. There is a question in my book which basically says that a ball is tied to a string and rotated. and it asks me to tell whether the following statement is true of false. Direction of radial acceleration MAY remain the same.
This statement is true.
Please explain to me a case where this is p... | g9432 | [
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<p>I had a doubt on what kind of transformations can be applied to qubits. I understand that
the transformations need to be reversible , but they also have to preserve the norm thats why
the transformations need to be unitary as $U^{\dagger}U=I$.<br><br>
But then I was reading the paper 'Quantum Mechanics Near closed T... | g9433 | [
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<p>While reading Polchinski's Chapter 1, I encountered the following on page 24,</p>
<p>"For example, the $(D-1)$ dimensional vector representation of $SO(D-1)$ breaks up into an invariant and a $(D-2)$-vector under the $SO(D-2)$ acting on the transverse directions, $$ \vec{v} = (v^1, 0, 0, \dots) + (0. v^2, v^2, \dot... | g9434 | [
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<p>I'm doing a research internship in attosecond physics right now, and one of the really important things in the field is the description of a propagating laser pulse as the combination of a slowly (or not) varying envelope and a carrier frequency.</p>
<p>I was wondering, is this envelope-carrier description complete... | g9435 | [
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<p>Different kinds of white light have a different spectrum.</p>
<p>Light from a white LED will have blue at the peak intensity while white light from a CFL or something else will have a different looking spectrum.</p>
<p>I dont understand how this works. Shouldn't pure white light have a unique spectrum no matter wh... | g9436 | [
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<p>To account for parity violation the weak interaction matrix element is written in the form</p>
<p>$$
M \propto \sum_{i} C_i (\bar u_p O_i u_n) (\bar u_e O_i (1 + {{C'_i}\over{C_i}}\gamma^5)u_\nu)
$$</p>
<p>Why does time reversal invariance imply that the $C_i$ coefficients must be real?</p>
<p>I was thinking that... | g9437 | [
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<p>What is the rigorous definition of the <a href="http://en.wikipedia.org/wiki/Aufbau_principle" rel="nofollow">Aufbau principle</a> and the mathematical model used for its description? </p>
<p>From Wikipedia, we have that the principle postulates a hypothetical process in which an atom is "built up" by progressively... | g9438 | [
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<p>To put it bluntly, weather is described by the Navier-Stokes equation, which in turn exhibits turbulence, so eventually predictions will become unreliable.</p>
<p>I am interested in a derivation of the time-scale where weather predictions become unreliable. Let us call this the critical time-scale for weather on Ea... | g9439 | [
0.04257894679903984,
0.02434140257537365,
-0.00520729273557663,
-0.034075457602739334,
-0.0015605594962835312,
0.02534693107008934,
-0.028866231441497803,
-0.02856452204287052,
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0.02149832434952259,
0.003348497673869133,
-0.009061276912689209,
0.029973013326525688,
0.... |
<p>I've only learned about to use kinematics equation when solving projectile problems but today i came across the following equations. where does they come from?</p>
<ul>
<li>Distance travelled</li>
<li>Time of flight</li>
<li>Angle of reach</li>
</ul> | g9440 | [
0.055953942239284515,
0.01689961925148964,
-0.02086596004664898,
0.019123414531350136,
0.04031606763601303,
0.009860807098448277,
0.019240504130721092,
0.02118575945496559,
0.00604145647957921,
0.014421297237277031,
-0.08461521565914154,
0.03465002402663231,
0.08766315132379532,
-0.0146885... |
<p>The damping of a spring is calculated with:</p>
<p>$$[\zeta] = \frac{[c]}{\sqrt{[m][k]}}$$</p>
<p>Where c is the 'viscous damping coefficient' of the spring, according to Wikipedia. m is the mass, k is the spring constant, and zeta is the damping ratio.</p>
<p>How is the value of c calculated though? Is it a cons... | g9441 | [
0.11084897071123123,
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-0.017304806038737297,
0.032197628170251846,
0.07363514602184296,
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0.10047679394483566,
0.030964627861976624,
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-0.0323491245508194,
-0.0628712847828865,
0.005381674040108919,
0.02038809470832348,
0.05162055... |
<p>As the only way String theory can respect the principles of quantum mechanics and Special theory of relativity, by formulating it in hypothetical nine dimensional space.
You could use string compactification for d number of non compact direction, all it requires to have d non compact direction is to choose an approp... | g9442 | [
0.04230818152427673,
0.03967289626598358,
0.023134734481573105,
-0.08696767687797546,
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0.03532111272215843,
0.015654191374778748,
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0.0016753468662500381,
-0.06497084349393845,
0.016342340037226677,
-0.05271179601550102,
-0.0046722558327019215,
-0.... |
<p>Suppose that the atmosphere is composed of 21% $O_2$ and 78% $Kr$ (instead of $N_2$). Since the density of $Kr$ is greater than the density of $O_2$, the lower atmosphere (where we live) should be deprived of $O_2$. Am I right? I know that diffusion has a role here, but is there a temperature where diffusion can't o... | g9443 | [
0.0641319528222084,
-0.0055102696642279625,
-0.02303900755941868,
0.04754166677594185,
-0.03470196947455406,
0.10569154471158981,
0.043012939393520355,
0.02646208368241787,
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0.004844028968364,
-0.0163333211094141,
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0.024433214217424393,
-0.009926... |
<p>I found this <a href="http://www.matweb.com/search/datasheet.aspx?matguid=638937fc52ca4683bc0c3f18f54f5a24" rel="nofollow">link where it described steel with UTS at 5200 MPa (755kpsi)</a>, is this the strongest steel or just a typo because value is seemed to be unreal?</p> | g9444 | [
0.0449988916516304,
0.03673897311091423,
0.006236376706510782,
0.03137923777103424,
0.015056582167744637,
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0.005492862313985825,
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0.04571995884180069,
0.04896034300327301,
0.02238837070763111,
0.05181803181767464,
-0.053000... |
<p>My question concerns the following definition</p>
<blockquote>
<p><strong>Definition:</strong> The <em>timelike</em> (resp. null) <em>generic condition</em> in GR is fulfilled if
$$u_{[\alpha} R_{\rho]\mu \nu [\sigma}u_{\beta]}u^\mu u^\nu \ne 0$$
at some point of each timelike (resp. null) geodesic with tan... | g9445 | [
0.05250091105699539,
0.011877931654453278,
0.00042402162216603756,
-0.009606856852769852,
0.045158594846725464,
0.060647737234830856,
0.04275355115532875,
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-0.02254360541701317,
-0.01154638733714819,
0.02304663322865963,
0.02760409191250801,
0.02... |
<p>I came across the word "absorption grating" in a review article. I googled it tried to find out what it means but couldn't. Could you explain it to me? </p> | g9446 | [
0.07237213850021362,
0.07796559482812881,
0.0010852321283891797,
-0.05404231697320938,
0.02840454876422882,
0.08235662430524826,
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0.06032603606581688,
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0.0007075248286128044,
0.0036662528291344643,
-0.0028248210437595844,
-0.02... |
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