question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>Say you have a hollow sphere with a uniformly distributed charge on the surface. Why is the electric field everywhere inside the sphere zero?</p>
<p>For the centre, its easy to add the vectors from the surface charges and show they sum to zero because of symmetry. </p>
<p>But can you show me how the field cancels ... | g10009 | [
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<p>Since a quantum mechanical system, even an isolated system containing one particle, can be described by a density matrix, with entropy for the system given by $\langle S\rangle=-k \rho\ln(\rho)$, is not entropy therefore a property of the system like mass or energy?</p> | g10010 | [
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<p>If the universe is expanding, it would make sense that the spaces between particles are getting bigger. If this is so, then the particles which make up atoms are also affected. Does that imply the spaces between the components of an atom will become large for the subatomic forces to hold? Are atoms getting weaker?</... | g56 | [
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<p>Consider a travelling wave produced by vibrating one end of a rope while the other end is made to freely move along a vertical line. Mathematically, the equation of the traveling wave that also represents the equation of motion of each point on the rope is given as follows.</p>
<p>$$y(x,t)=A\sin(kx-\omega t)$$</p>
... | g10011 | [
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<p>I am given that a wave function at time 0 is given as
$$\psi(x,t=0)=\sin^6(\frac{\pi x}{2L})\cos(\frac{\pi x}{2L})$$
I am asked to find this wave function as a function of time. In order to do this, I feel like I need to find the combinations of eigenfunctions that make this function and then I can find how they ea... | g10012 | [
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<p>When a system rejects heat it can be assumed that work is done by the system. So as per law the sign convention must be negative. But my physics textbook says the reverse. So is the question.</p> | g10013 | [
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<p>This is a very basic Lagrangian Field Theory question, it is about a definition convention. It takes much more time to typeset it than answering, but here it is:</p>
<p>Consider a field Lagrangian with only a kinetic term,</p>
<p>$$L = \frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi $$</p>
<p>Consider the very si... | g10014 | [
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<p>Tesla patented a device for gathering energy from light, using the photoelectric effect. (<a href="http://www.google.com/patents/about?id=YitoAAAAEBAJ" rel="nofollow">US 685,957 - Apparatus for the Utilization of Radiant Energy</a>):</p>
<p><img src="http://i.stack.imgur.com/cSGJ1.png" alt="Telsa's photoelectric ef... | g10015 | [
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<p>Consider a conducting wire of 1M and 1000KM. Now if we connect a battery and a bulb to both these wires. Bulb glows instantaneously its because (my guess:) electric filed travels from positive terminal of battery to negative terminal through wire almost instantaneously.</p>
<p>Now, My question is there any speed fo... | g10016 | [
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<p>I'm looking for something that will generate scatter plots comparing different properties of isotopes. Ideally I'd like some web page that lets me select axis and click go but a CSV file with lost of properties would work.</p> | g10017 | [
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<p>I have recently become curious about modeling the repulsion of everyday objects in contact with one another. By repulsion I mean as you attempt to walk through a wall, the pain in your nose suddenly alerts you to the fact that it won't be possible. I've come up with this exercise:</p>
<p>What is the mutual pressu... | g10018 | [
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<p>I have a general question concerning mean-field approaches for condensed matter classical of quantum statistical mechanic systems. Does determining the mean-field by a variational approach <em>always</em> imply that the self-consistency is satisfied ? Moreover are there some cases where it is physically justified to... | g10019 | [
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<p>The <a href="http://en.wikipedia.org/wiki/No-hair_theorem">no hair theorem</a> says that a black hole can be characterized by a small number of parameters that are visible from distance - mass, angular momentum and electric charge.</p>
<p>For me it is puzzling why local quantities are not included, i.e. quantum num... | g10020 | [
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<p>First I will have to explain my question. Look at the image below. This shows doppler shift when an object is moving horizontally to the direction of the wave. Keep the word 'horizontally' in mind. Now this happens because:</p>
<p>I will quote Jim from his answer for <a href="http://physics.stackexchange.com/questi... | g10021 | [
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<p>For evaluating the electric field of some charge distribution one can use $$\phi(r):= \frac{1}{4 \pi \varepsilon_0}\int_{\mathbb{R}^3} \frac{\rho(r')}{||r-r'||_2} dr'.$$</p>
<p>My question is: What symmetry do we need to have that we can write in spherical coordinates $$||r-r'||_2 = \sqrt{||r||_2^2+||r'||_2^2-2||r|... | g10022 | [
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<p>Average velocity, as I have heard, cannot be found simply by finding the average of two numbers. I have a question on average velocity, but am simply unable to proceed:</p>
<blockquote>
<p><em>A particle moving in a straight line covers half the distance with speed of 3m/s. The other half of the distance is cover... | g10023 | [
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<p>I'm trying to figure out how many atoms are decaying spontaneously in a span of 2 seconds. Let's say that the quantum yield is 0.45, and that the lifetime "τ" (tau) is 10 microseconds. </p>
<p>Then I found that the radiative lifetime is 22.2 microseconds. However, at this point I'm stuck. I don't know a relationshi... | g10024 | [
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<p>Quantum mechanics has a peculiar feature, entanglement entropy, allowing the total entropy of a system to be less than the sum of the entropies of the individual subsystems comprising it. Can the entropy of a subsystem exceed the maximum entropy of the system in quantum mechanics?</p>
<p>What I have in mind is eter... | g10025 | [
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<p>I`m looking for a nice introductary reference that explains how the turbulence coefficient or any kind of turbulence parameterization (in view of applications to atmospheric turbulence for example) can be derived from the gravity - fluid dynamics correspondance, such that even I can get it. I mean, if something like... | g10026 | [
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<p>I've been reading through various materials on relativistic quantum mechanics, but I find the lack of simple examples disturbing.</p>
<p>I'm acquainted with the general form the solutions to the Dirac equations have, but I'm having trouble just practically getting any specific example solution.</p>
<p>Since the mo... | g10027 | [
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<p>I decided to dig a tunnel inside the Earth. In equatorial plane. It should be designed in such a way that it follows the Coriolis effect. That means if, say a stone is dropped from rest into the tunnel, then it travels in the tunnel without touching the walls of the tunnel until it reaches the tunnel's lip on the ot... | g10028 | [
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<p>When I was student I was told that time is defined by the requirement that the physical laws are simple. For example, in classical mechanics time can be defined by the requirment that the velocity of an isolated body is constant. One could generalize this approach by assuming that <em>space-time</em> is defined by t... | g10029 | [
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<p>I get confused when I see expressions like "the universe is $x$ years old" or "$10^{-2}$ seconds after the big bang" since it seems to me that relativity shows such statements don't have meaning. Is it assumed or experimentally verified or proved that space-time is equipped with a projection to the real numbers whos... | g10030 | [
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<p>In an electron gun, the heating filament heats the cathode, releasing electrons by thermionic emission. I've read that <em>"electrons are negatively charged particles and the positively charged cylindrical anode develops a strong electric field that exerts a force on the electrons, accelerating them along the tube"<... | g10031 | [
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<p>I'm guessing that when the LHC ramps up to 4000 GeV this means they are increasing the current in the superconducting magnets as RF fields accelerate the beams. Where does this current go when they ramp down? Is it dissipated as heat? Is it fed back into the grid?</p>
<p>P.S.- by 'ramp' I mean the normal increas... | g10032 | [
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<p>I'm reading an article on liquid crystal lasers and they're saying periodicity determines lasing wavelength and cavity geometry determines emission wavelength. What is the difference?</p> | g10033 | [
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<p>Can someone summarize as to what are the problems and/or the open questions with the <a href="http://www.google.com/search?as_q=hayden+preskill" rel="nofollow">Hayden-Preskill circuit</a>? (in the context of understanding black-holes or as a computer science question)It gives a framework to see how the black-hole ca... | g322 | [
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<p>The statistical thermodynamics definition of entropy: $S = kN \ln (W)$ troubles me a lot with the problem of dimenstions. where $S$ is entropy; $k$, the Boltzmann constant; $N$ the number of particles in the system and W the number of microstates corresponding to a given macrostate of the system. </p>
<p>For the eq... | g10034 | [
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<p>Regarding the cosmological selection hypothesis and testable predictions, Lee Smolin asserted the following:</p>
<blockquote>
<p>"Smolin: I did make two predictions which were eminently checkable by
astrophysical and cosmological observations, and both of them could
easily have been falsified by observations ... | g774 | [
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<p>How might one consider a conductor to be an 'obstructor'? </p>
<p>Might the strength of the 'skin effect' of a conductor be in direct relation to conductance?</p>
<p>And how does this relate to insulators, as these material are literal obstructors to energy transfer.. Might electricity flow at full strength along ... | g10035 | [
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<p>Is there any example of a transmission of energy in a medium that does not show wave nature? </p> | g10036 | [
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<p>While i was in high-school i learn't the <strong>Doppler's Effect</strong> which if i remember correctly is:</p>
<ul>
<li>The Apparent change in the frequency of sound caused due the relative motion between the sound and the observer.</li>
</ul>
<p>This phenomenon seems obvious, but what i would like to know is, w... | g10037 | [
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-0.03178092837333679,
-0.027161598205566406,
0.053199402987957,
0.0699729... |
<p>I wanted to know a few things about elliptical motion, that I do not understand so far.</p>
<p>Let's imagine that we have an attractive gravitational two body problem where both bodies carry out elliptical motion around the center of mass. In this case, the center of mass is in one focus of the ellipse, right?
Fur... | g10038 | [
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<p>An object is pulled up a slope at constant speed. I'm trying to find the Tension on the rope.</p>
<p>$$m = 65kg \Rightarrow W=-637$$
$$\mbox{constant speed} \Rightarrow a = 0$$
$$\mbox{angle of slope} = 45^\circ$$
$$T=?$$</p>
<p>I use Newton's first Law to determine that there is no acceleration because of constan... | g10039 | [
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<p>Can space-time singularities be treated as mathematical knots occurring in dimensions greater than four? I just drew an analogy with knots in one-dimensional strings. When a rubber-band is looped over again and again, it ultimately forms a clumped-up ball like structure, having 3 dimensions. Similarly, the fabric of... | g10040 | [
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<p>I am doing this problem:</p>
<blockquote>
<p><em>The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N.</em> </p>
<p><em>What is the magnitude of the acceleration?</em></p>
</blockquote>
<p>This is how I solved it:</p>
<p>$$\sum F = F_1+F_2=N+(-W)=ma$$</p>
<p>I am... | g10041 | [
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<p>I would like to determine the number of energy states two free, distinguishable particles in a box of length $L$ have. I would then like to determine the number of states two free, indistinguishable particles, with spin $3/2$ each, have in that box at the elementary level. Finally, determine the number of states in ... | g10042 | [
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<p>The phase density function is usually denoted as <a href="http://en.wikipedia.org/wiki/Boltzmann_equation" rel="nofollow">$f(\mathbf{x},\mathbf{v},t)$</a> which gives probable number of particles moving with velocity $ \mathbf{v}$ at position $\mathbf{x}$ at time t. Also we assume that position and velocities of par... | g10043 | [
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<p>I am creating a particle in cell simulation that models an electron plasma in a cylindrical container. Part of this process is assigning charge density to grid points based on the position of each particle. My question is this: for the examples of these simulations that I have seen, the charge density is given by th... | g10044 | [
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<p>In general, a sphere with conductivity $\kappa$, heat capacity per unit volume $C$ and radius $R$ obeys the differential equation at time t:</p>
<p>$$C\frac{\partial T}{\partial t} = \kappa \frac{\partial^2 T}{\partial r^2} + \frac{2\kappa}{r}\frac{\partial T}{\partial r}$$</p>
<p>Part (a): A sphere with a cavity ... | g10045 | [
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<p>According to the third law of motion, you van't have an mass move in a particular direction unless there is a proportional opposite mass/acceleration ratio in the opposite direction.</p>
<p>No-one has been able to provide a convincing argument otherwise, but the best one to date is Shawyer's <a href="http://en.wiki... | g10046 | [
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<p>Someone sent me this link to a talk by <a href="http://www.ks.uiuc.edu/~kschulte/" rel="nofollow">Prof. Klaus Schulten</a> from the University of Illinois: (my emphasis)</p>
<blockquote>
<p><strong>Quantum Computing and Animal Navigation</strong></p>
<p>Quantum computing is all the rage nowadays. But this ty... | g10047 | [
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<p>I am reading Ludwig's paper "<a href="http://arxiv.org/abs/1010.0936" rel="nofollow">Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors</a>", and in this paper, although I am clear how they get the descent equation which introduced the relationship between anomaly... | g10048 | [
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<p>I've heard that the strong force doesn't decrease in strength with increasing distance, and that's why quarks must be confined within hadrons. But could there be, say, a single quark out there, so that the universe would be colour neutral without it, but with it, it's not? Would such a quark have a "strong field" th... | g10049 | [
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0.00090... |
<p>In relativity, if two events are simultaneous in a specified frame, they cannot be simultaneous in any other frame. </p>
<p>My question is this: given any two events, is there always a frame in which these two events are simultaneous? For example, if I drop a blue ball on one side of a tennis court, and my friend d... | g10050 | [
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<p>This is a conceptual question as much as an empirical one, but the question is: Does the lift of a wing change when the slats (or any other leading edge device) are deployed? I am stipulating that the angle of attack $(\alpha)$, freestream dynamic pressure $(q_\infty=\frac{\gamma}{2}p_\infty {M_\infty}^2)$, and wing... | g10051 | [
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<p>Consider a system of two entangled harmonic oscillators. The normalised ground state is denoted by $\psi_0(x_1,x_2)$.</p>
<p>I've been taught that a density matrix is constructed as $\rho = \left|\psi\rangle\langle\psi\right|$, so in this basis: $$\rho = \psi_0(x_1,x_2) \psi_0^*(x_1',x_2') \left|x_1,x_2\rangle\lang... | g10052 | [
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<p>We have been discussing whether or not bigger cars are more dangerous to pedestrians. I will reduce it to a simpler question. </p>
<p>Imagine two cars, which are exactly identical in shape, but have different masses. One is 1000kg and the other 2000kg. One person is hit by the light car, and another is hit by the h... | g10053 | [
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<p>Currently I'm taking an introductory course on thermodynamics. I've got a problem with understanding what is the meaning of pressure of a solid body. The question arose when I looked at phase diagram in P, T coordinates. </p>
<p>When we're talking about pressure of gas or liquid, it can be defined thus: it is the f... | g10054 | [
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<p>Simply stated the <a href="http://arxiv.org/abs/1105.4714" rel="nofollow">casimir effect</a> can be observed bringing two plates together microscopically and in vaccum</p>
<p>Is this analogous to the observation of gravity?</p>
<p>Question: What is casimir effect?</p>
<p>Canonical, answers only please no wiki lin... | g10055 | [
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... |
<p>I am reading a paper and saw the author wrote something like, </p>
<p>Because of no-slip wall assumption, so velocity vector $\vec{v}$ is $0$ on the wall, and also the variation of this velocity on the wall is $\delta \vec{v} = 0$. And he also said $\delta \vec{v}_t = 0$.</p>
<p>But it seems his subtext is $\delta... | g10056 | [
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<p>Twin Paradox
Can anyone clarify and or correct the following for me?
A space ship is flying at speed v equal to 0.8 times the speed of light. Within the ship are three stations, a transmitter at station A, station B directly across the ship from station A and station C directly forward of station A. The distance AB... | g10057 | [
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<p>In elementary QM, an electron is typically viewed as a cloud around a proton. The idea is that it's position can only be determined once a measurement is made. The probability that the electron will be found in a certain region is determined by it's wave function. </p>
<p>For background see the question
<a href="h... | g10058 | [
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<p>We know that for constant pressure thermodynamic processes, $dH=dQ_p$. My question is, does it implies that only reversible work is possible in this processes so that $dw=0$ because $dv$ is zero? In addition, does $Q_v$ necessarily be reversible heat transfer in this case? What if the heat transfer is irreversible?<... | g10059 | [
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<p>I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor field and $\Sigma_{ab}$ the Lorentz generators involving gamma matrices). Dirac equation for the massless fermion is ... | g10060 | [
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<p>Are the speeds of the different wavelengths of visible light different or varying in a medium such as air? If so, please inform by how much?</p>
<p>Also, even if the wavelength speeds vary minimally, please inform.</p> | g10061 | [
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<p><a href="http://en.wikipedia.org/wiki/Einstein_field_equations">Einstein's field equation</a>:</p>
<p>$$G_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu} - g_{\mu\nu}\Lambda$$</p>
<p>I'm trying to understand each of the terms in this equation intuitively, but I'm struggling.</p>
<p>Basically, I want to understand how the... | g10062 | [
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<p>Why Our Electricity Flowing in the Sequence of 11kv,33,66,132kv,why not Flow in 10 kv,11,12,13,14 that Sequence.</p> | g10063 | [
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<p>I've been reading a fair amount about quantum chaos, and <a href="http://en.wikipedia.org/wiki/Random_matrix" rel="nofollow">random matrix theory</a> comes up a lot. I get that they're looking at the distribution of eigenvalues from an ensemble of random matrices, but I still don't know what the ensemble of those ma... | g10064 | [
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<p>I have found equation for moment of inertia $(J)$. I'm calculating $J$ for hemisphere, with rotational axis $Z$.</p>
<p>$$ J = \iiint\limits_V r^2 \cdot \rho \cdot dV $$</p>
<p>But if $\rho$ is constant (homogenous), I can do:
$$ J = \rho \cdot \iiint\limits_V r^2 \cdot dV $$</p>
<p>Which is:
$$ J = \rho \cdot V ... | g10065 | [
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<p>Most people can ride 10 km on their bike. However, running 10 km is a lot harder to do. Why?</p>
<p>According to the law of conservation of energy, bicycling should be more intensive because you have to move a higher mass, requiring more kinetic energy to reach a certain speed. But the opposite is true. </p>
<p>So... | g10066 | [
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<p>OK so we've all heard of this from Carl Sagan, Lawrence Krauss and others and we know the argumentation, I don't refute that. There are other examples, for instance I once calculated (this was before I had taken any QM-course) that since there are more particles in a glass of water than there are glasses of water in... | g10067 | [
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<p>In many physical applications, the Heaviside step fuction is defined as $$H(x) = \left\{\begin{eqnarray}
1, \quad x>0 \\
0, \quad x<0
\end{eqnarray}\right.$$
The value $H(0)$ is left undefined. Is there a physically prefered value of $H(0)$ or does it depend on the problem at hand?</p>
<p>For example, due to ... | g10068 | [
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0.0... |
<p>To my understanding the work done on an object is defined mathematically as:
$$W = \vec{F}\cdot\vec{S}=|\vec{F}||\vec{S}|cos\theta$$
This, I understand. My problem is that I don't understand that if the angle $\theta$ is 90 degrees how can the work done by $\vec{F}$ on the object is zero. For example; say you have a... | g10069 | [
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<p>In what ways can a lunar eclipse occur?</p>
<p>Also, on what percentage of the Earth are they usually viewable? </p>
<p>I am aware that there are multiple configurations that constitute a lunar eclipse (umbral, penumbral, partial) and would like more information about each and how they occur.</p> | g10070 | [
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<p>The very highest energy photons, gamma-rays, are too energetic to be detected by standard optical methods. In fact they rarely actually make it to the surface of the Earth at all but interact with molecules in the Earth's atmosphere. The high energy gamma-ray telescopes, such as Veritas and Hess use air Cherenkov te... | g10071 | [
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<p>Well, there is a measure of how a planet could be considered like Earth, called Planetary habitability. Based on this measure, what are the prerequisites needed to consider a planet to be a habitable one?</p> | g10072 | [
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<p>Why it is easy to start the vehicle on hot day than on cold days?
Since on winter days it is diffcult to start than on hot days I thought it is due to the low temperature which in turn affects the chemical reaction in the cell.Since energy is produced in the cell due to reaction.But I don't think it is the correct o... | g10073 | [
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<p>so here's the problem: A simple RC circuit where the capacitor has been charged, and two resistors are in parallel configuration. How does one find the power (as function of time) through any of the two resistors? </p>
<p><img src="http://i.stack.imgur.com/mOGjJ.jpg" alt="enter image description here"></p> | g10074 | [
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<p><img src="http://i.stack.imgur.com/dxSE3.jpg" alt="enter image description here"></p>
<p>![enter image description here][2]</p>
<p>This question is truly annoying, and I have been stuck for an hour on part D, would greatly appreciate if anyone could shed a light on this problem.
Why ans for part c and d are differ... | g10075 | [
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<p>I am working across mathematics, physics and engineering. And I am looking for whether there exists already formally established knowledge in the field.</p>
<p>Given a periodic graph (actually a physical lattice or crystal structure), we want to examine some periodic coloring ( or ordered but not periodic coloring)... | g10076 | [
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<p>In the theory of constrained Hamiltonian systems, one differentiates between primary and secondary constraints, where the former are constraints derived directly from the Hamiltonian in question and the latter are only realized 'on-shell', i.e. once the equations of motion are satisfied. </p>
<p>Further one can dif... | g10077 | [
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<p>According to the definition of angular momentum: </p>
<blockquote>
<p>Angular momentum, moment of momentum, or rotational momentum is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a <strong>particular axis</strong>.[This definition has been extracted f... | g10078 | [
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<p>We just saw parity symmetry and we were told about the experiments to see the non parity symmetry of disintegration, in particular one involving the reaction:</p>
<p>$$^{60}Co\longrightarrow^{60}Ni+ e + \bar \nu$$</p>
<p>Now, we were asked to check that if we prepare the system so that the spin is parallel to the ... | g10079 | [
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<p>Is there a reason to believe that the axial resonances be heavier than the vector resonances in the composite higgs models? </p>
<p>For instance, in <a href="http://arxiv.org/abs/0808.2071">http://arxiv.org/abs/0808.2071</a>, to have zero tree level contributions to S parameter, the constrain on the wave function m... | g10080 | [
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<p>The induced emf in a coil in AC generator is given as:</p>
<p>$$\mathbb E = NAB\omega \sin \theta $$</p>
<p>$\omega = d\theta/dt$</p>
<p>Now, when the angle between the normal of plane and magnetic field is zero degrees, the induced emf is zero i.e.</p>
<p>$$\Bbb E = NAB\omega \sin 0 = 0$$</p>
<p>But we also d... | g10081 | [
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<p>I have confused myself about the following variant of Maxwell's demon and I can't seem to find out where the energy went. </p>
<p>Consider this: You have a chain (one dimension) of spins (up/down) with a nearest-neighbor coupling. Energy is minimized if spins are aligned. Let us say the energy difference between al... | g10082 | [
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<p>Let's say we have an incomplete spacetime A that is globally hyperbolic, does there necessary exist a globally hyperbolic completion?</p>
<p>My guess is no, in which case what further restrictions can be placed on A to ensure that it can always be extended to geodesically-complete globally hyperbolic spacetime?</p> | g10083 | [
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<p>The configuration space of a system of particles $(m_i,x_i)$, $i=1,\dots,n$, subject to constraints $$\Phi (x)=0,\qquad \Phi\colon \mathbb R^{3n}\to \mathbb R ^{3n-k},\qquad x=(x_1,...,x_n),$$
if the constraint is nice enough (i.e. if $0$ is a regular value of $\Phi$), can be described as a $k$-dimensional submanifo... | g10084 | [
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<p>Given a coil initially in the x-y plane, rotating at angular frequency $ \omega $ about the x-axis in a magnetic field in the z-direction. This uniform time varying magnetic field is given by $B_z (t)=B(0)cos(\omega t) $ I am required to show that there is a voltage of frequency $2\omega $ across the loop. Clearly w... | g10085 | [
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<p>A radar transmitter (T) is fixed to a system $S_{2}$ which is moving to the right with speed v relative to system $S_{1}$. A timer in $S_{2}$, having a period $\tau_{0}$ (measured in $S_{2}$) causes transmitter T to emit radar pulses, which travel at the speed of light, and are received by R, a receiver fixed to $S_... | g10086 | [
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<p>I mean look how big is the Cosmos and hof few planets and suns are outthere, compared to the vast "nothingness" between them. </p>
<p>With "nothingness" I mean no standard particles like atoms, electrons etc.</p>
<p>Why is that the ratio is so hugely in favor of "nothingness"?</p> | g10087 | [
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<p>While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian $H(p,q)$ by </p>
<p>$$\hat{H}(\hat{P},\hat{Q}) \equiv \int {dx\over2\pi}\,{dk\over2\pi}\,
e^{ix\hat{P} + ik\hat{Q}} \in... | g10088 | [
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... |
<p>It is stated in many books that analytic closed solutions to the time-independent electronic Schrödinger equation,
$$\hat{H}\Psi = E\Psi, $$
exist for the one-electron problem (e.g. hydrogen atom, assuming separability of nuclear and electronic motion) but that such solutions do not exist for systems with more than... | g10089 | [
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<p>In <a href="http://arxiv.org/abs/quant-ph/0504102" rel="nofollow">arXiv:quant-ph/0504102v1</a>, A.J. Bracken says</p>
<blockquote>
<p>if we think of the phase space formulation of QM as more fundamental,
arising directly from a deformation of classical mechanics in phase
space [12] we can think of the formu... | g10090 | [
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<p>I plan to graduate with an honours (four year) degree in philosophy and a general (three year) degree in mathematics. Are there any physics graduate programs that might admit me if I were to apply?</p>
<p>For context: My plan-A is to work in academic philosophy. A physics education might not appear on the resume of... | g10091 | [
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<p><img src="http://i.stack.imgur.com/rKWj0.jpg" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/w95Zy.jpg" alt="enter image description here"></p>
<p>What i don't understand is why The solution to this problem says that,$$\tan\theta=\frac{m_{l}}{m_{r}}$$, isn't mass a scalar quantity?</... | g10092 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/13325/what-is-the-minimum-amount-of-fissile-mass-required-to-acheive-criticality">What is the minimum amount of fissile mass required to acheive criticality?</a> </p>
</blockquote>
<p>I want to make a re... | g323 | [
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<p>I was reading <a href="http://physics.stackexchange.com/questions/51838/why-do-tuning-forks-have-two-prongs">Why tuning forks have two prongs?</a>. The top answer said the reason was to reduce oscillation through the hand holding the other prong.</p>
<p>So if having 2 prongs will reduce oscillation loss, surely a 3... | g10093 | [
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0.0530314... |
<p>Are there any logical relationship between specific heat capacity and thermal conductivity ?</p>
<p>I was wondering about this when I was reading an article on whether to choose cast iron or aluminium vessels for kitchen.</p>
<p>Aluminium has more thermal conductivity and specific heat than iron ( <a href="http://... | g10094 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/14056/how-does-gravitational-lensing-account-for-einsteins-cross">How does gravitational lensing account for Einstein’s Cross?</a> </p>
</blockquote>
<p><a href="http://en.wikipedia.org/wiki/Einstein_Cro... | g48 | [
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<p>I read an article about phase transitions and I read about thermodynamic processes such as <a href="http://en.wikipedia.org/wiki/Adiabatic_process" rel="nofollow">Adiabatic process</a>, <a href="http://en.wikipedia.org/wiki/Isochoric_process" rel="nofollow">Isochoric process</a>, <a href="http://en.wikipedia.org/wik... | g10095 | [
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0.001... |
<p>So this is the question given in my text book: </p>
<blockquote>
<p><em>A particle of mass m is at rest at the origin at time $t = 0$. It is subjected to a force $F (t) = F_0e^{–bt}$ in the $x$
direction. Its speed $v(t)$ is depicted by which of the following curves? (I am not posting the curve.)</em></p>
</blo... | g10096 | [
0.07556401938199997,
0.010683782398700714,
0.03276730701327324,
-0.02670547366142273,
0.09609237313270569,
0.0070678978227078915,
0.06255335360765457,
0.01947913132607937,
-0.0672350823879242,
0.020214462652802467,
0.01575382612645626,
0.03281146287918091,
0.02588632144033909,
0.0005466050... |
<p>Usually in electrostatics we start by introducing the vector field $\mathbf{E}$ representing the electric field due to some charge distribution. Later when we study fields in materials we consider the electric displacement field $\mathbf{D}=\epsilon_0 \mathbf{E}+\mathbf{P}$ being $\mathbf{P}$ the polarization densit... | g10097 | [
0.06459270417690277,
0.030838703736662865,
-0.047631483525037766,
-0.0007530828006565571,
0.10301195830106735,
0.06009902432560921,
0.05243578925728798,
0.0046433680690824986,
-0.033921536058187485,
-0.03838652744889259,
-0.009129943326115608,
-0.03444448858499527,
0.048886120319366455,
-0... |
<p>In my introductory modern physics class we have examined time-independent solutions to the <a href="http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation" rel="nofollow">Schrödinger equation</a> in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles and step potentials with $V_{\math... | g10098 | [
0.014481770806014538,
0.028013458475470543,
0.002297838218510151,
-0.056864380836486816,
0.03771820291876793,
0.0037896980065852404,
0.058242958039045334,
0.041630521416664124,
-0.01540470402687788,
-0.031058335676789284,
0.01631028950214386,
-0.04485330358147621,
0.03274620696902275,
0.07... |
<p>Biot-Savart law for a linear current distribution is:</p>
<p>$\displaystyle \vec{B}=\frac{\mu I}{4\pi}\int\frac{\vec{dl}\times \vec{r}}{r^{3}}$.</p>
<p>In the book that my professor uses says that if we have current flowing in a wire of very small cross section $S$, in a length $\vec{dl}$ of the wire we have $dV=S... | g10099 | [
0.06644070148468018,
0.05504896491765976,
-0.03274209424853325,
-0.02395705133676529,
0.012196849100291729,
0.03108455054461956,
0.0055361646227538586,
0.005477949045598507,
-0.037421006709337234,
0.03784293681383133,
-0.02572767063975334,
-0.02639201655983925,
0.018906209617853165,
-0.026... |
<p><strong>Question:</strong> How hot is the water in the pot? More precisely speaking, how can I get a temperature of the water as a function of time a priori? </p>
<p><strong>Background & My attempt:</strong> Recently I started spend some time on cooking. And I'm curious about it. I have learned mathematics as a... | g10100 | [
0.030440665781497955,
-0.020268291234970093,
-0.0047637890093028545,
-0.06190262362360954,
-0.01642952673137188,
-0.046490393579006195,
-0.006336130667477846,
0.01949414610862732,
-0.033406008034944534,
0.004484619479626417,
-0.011513704434037209,
0.05033803731203079,
0.06058448553085327,
... |
<p>Consider we have two atoms $a$ and $b$. They are entangled with each other in position and momentum, with some wavefuction describing them in position space that is $\Psi(x_a, x_b)$. This initialization of the entangled state is achieved as described in this paper: <a href="http://arxiv.org/abs/quant-ph/9907049" re... | g10101 | [
-0.038223996758461,
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0.00007895433373050764,
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0.0032511793542653322,
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0.031165892258286476,
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0.04575078934431076,
0.023060649633407593,
0.05067171901464462,
-0.038672298192977905,
0.... |
<p>Well this got me stumbled, because I've been wondering what the "question" is. One of the example examns got the following question (strangely there are no supplied solution books):</p>
<blockquote>
<p>A $0.2 {\rm m^3}$ thermally insulated rigid container is divided into two
equal volumes by only a thin membra... | g10102 | [
0.04351573437452316,
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0.03332854062318802,
0.04743027314543724,
0.008771268650889397,
0.010472990572452545,
0.0238373763859272,
0.03371412679553032,
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0.014597410336136818,
0.004361978266388178,
0.03348265588283539,
0.004906938876956701,
-0.02726633... |
<p>I have been following the methods suggested by members of this site to calculate the solar irradiance outside of the earth's atmosphere, see <a href="http://physics.stackexchange.com/questions/116596/convert-units-for-spectral-irradiance">here</a>.</p>
<p>I now want to calculate the solar irradiance reaching the ea... | g10103 | [
0.026833200827240944,
-0.02733304724097252,
-0.025900427252054214,
-0.03429391607642174,
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0.07648623734712601,
-0.004680941347032785,
0.03138887137174606,
-0.022700240835547447,
-0.02980324998497963,
0.032593484967947006,
0.05054567754268646,
0.05234738439321518,
0.01... |
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