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My five-year old daughter was asking about astronauts the other day and why they float in space. After me showing her a few bits on the kids section on the NASA web site I started explaining about the planets and how the sun was a ball of gas and you couldn't stand on it. I then had to explain to her what a gas was, us... |
I want to solve bound states (in fact only base state is needed) of time-independent Schrodinger equation with a 2D finite rectangular square well
\begin{equation}V(x,y)=\cases{0,&$ |x|\le a \text{ and } |y|\le b$ \\ V_0,&\text{otherwise}}.\tag{1}\end{equation}
$$\Big[-\frac{\hbar^2}{2m}(\partial_x^2+\partial_y^2)+V(x,... |
If I have a cube that is moving at a velocity of $v$ and spinning at an angular velocity of $\omega$, how can I determine the instantaneous velocity vector of one of the vertices of the cube?
What if the cube is accelerating? And what if it had angular acceleration, $\alpha$? Would this change the method of calculation... |
I have a question in reading Polchinski's string theory vol I p 123, about the "old covariant quantization".
It is said
... $\langle 0;k | 0; k' \rangle = ( 2\pi)^D \delta^D (k-k') \tag{4.1.15}$
as follows from momentum conservation. The timelike excitation has a negative norm.
How to see "the timelike excitation h... |
If my phone is charging that means it's mass increasing by this Youtube video.
Now if an current is flowing from the power station to home, does it mean that electron is flowing from house to the power station (on the basis of convectional direction of current)? And the house is losing some amount of mass?
|
http://www.youtube.com/watch?v=gKYrXHZwtPw
In this video it is explained that Land Skin Temperature (LST) are measured by NASA's Aqua and Terra satellites.
It seems it works by collecting the radiation emitted by the earth's surface, and the instrument is Spectroradiometer.
And its a fact that atmosphere warms up by a... |
I'm asking because I have a problem asking me what the diffraction pattern would be if instead of spherical atoms I'd have triangular atoms. I can't find anything about this in my X-ray diffraction book, but I can in my optics book, but I'm having trouble justifying this.
I thought that in a plane of atoms the separati... |
Imagine this:
You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be $\rho(r,\theta,\phi)=e^{-r}$)
Now my question is: What is the most general equation that will give me the potential inside the sphere?-You can use th... |
I have a little question I hope someone could answer.
I'm reading some Solid State Physics and I have come across energy bands and energy gaps.
As far as I understand the energy band is where the electrons are able to occupy space, and the gap is space where there are no states to occupy.
Now, in my book they have exam... |
1. The problem statement, all variables and given/known data
Beam of electrons with energy $10eV$ hits the potential step
($8eV$ high and $0.5nm$ wide). How much of the current is
transmitted?
2. Relevant equations
I know that energy mentioned in the statement is kinetic energy so keep in mind when reading that ... |
Assume we had an elevator shaft long enough for a free-falling elevator to reach terminal velocity.
As I understand it, when the elevator begins to fall a person inside would experiences weightlessness because they would be accelerating downward at the same rate as the elevator. The rate of downward acceleration for t... |
Only because
Rep is unitary, so saves positive-definite norm (for possibility density),
Casimir operators of the group have eigenvalues $m^{2}$ and $m^2s(s + 1)$, so characterizes mass and spin, and
It is the representation of the global group of relativistic symmetry,
yes?
|
What is a good way to block neutrons and what is the mechanism that allows this? It's my understanding that polyethylene is somewhat effective. Why?
|
In quantum mechanics, we talk about (1) vectors, (2) states, and (3) ensembles (e.g., a beam in a particle accelerator). Suppose we want to translate this into mathematical definitions. If I'd never heard of the von Neumann density matrix, I'd approach this problem as follows. Two vectors can represent the same state i... |
I recently came across two nice papers on the foundations of quantum mechancis, Aaronson 2004 and Hardy 2001. Aaronson makes the statement, which was new to me, that nonlinearity in QM leads to superluminal signaling (as well as the solvability of hard problems in computer science by a nonlinear quantum computer). Can ... |
I have put up a question here,
https://mathoverflow.net/questions/139685/proof-of-the-general-expression-for-anomaly-in-a-cft-and-its-partition-function
Here I am putting up a slightly different version of that question,
I think the statement is that for any dimensional CFT the following is true,
$$\langle T^{\mu... |
I completely understand the difficulties of making and storing antimatter, so I am not talking about the mechanism or the way of doing it here, I am just talking about the concept.
As far as I know, nuclear power plants use the heat from the nuclear fission reaction to heat water and use the steam through turbines and ... |
I'm a space physicist. I've been working with a group of school students (aged between around 10 and 12) exploring the Sun, the Earth and the solar system. We've talked about some basics of magnetism and the fact that the Earth's magnetic field is vital in protecting us from the Solar wind. However, one canny student w... |
Suppose two rings are kept facing each other and that one ring have some current which increases constantly. Will the other ring be attracted or repelled? Does this also depend on how they are kept?
|
A few sequential questions:
Is it possible for a nuclear explosion to be small enough to produce a 250-ml (one cup) mushroom cloud?
If so, how much uranium would that take?
How close to the explosion could one be (in normal clothing) not to suffer from burns or excessive radiation exposure?
|
What is the metric tensor?
How can this be a covariant and contravariant tensor, or a mixed tensor, by raising and lowering indices?
How it relates to distance function (metric) and angles?
How does it transport basis vectors from one coordinate system to another?
How is it different from the field tensor, Riemann c... |
A car travels 100 miles in 2 hours, it then completes the return leg of the journey. How fast must it travel on the return leg to average 100mph over the total journey.
My thoughts on this are that it is impossible as if the total average was 100mph then the total time would be 2 hours but that can't be if the first ... |
What does it mean to say that 2 fields are coupled? More generally, what does "coupling" mean?
|
Goodmorning everybody,
I have to run a numerical simulation of a Bose-Einstein condensate on a rotating disc. Now, my problem is that I became suspicious about the equation I'm using, since the final result I obtain is not what I expected. First of all, the Gross-Pitaevskii equation (in a z-axis symmetrical trap) for t... |
I can only boast of my passion for science and not of any credentials. I ask because I am curious, and it is not the type of question one can easily Google! What if the key to discovering and unlocking the secrets of dark matter and energy lie in the Island of Stability? Am I missing a vital reason that outright contra... |
How does $t=0$ transform into $t - vx/c^2 = 0$ if a frame of reference is moving as given in here?
It seems that the relativistic transformation is given by
$$ \begin{bmatrix}
x' \\
ct'
\end{bmatrix}= A\begin{bmatrix}
x \\
ct
\end{bmatrix} = \left(
\begin{array}{cc}
\frac{1}{\sqrt{1-\frac{v^2}{c^2}}} & -\frac{v}{c \... |
In momentum and energy is low enough, we end up with the same number of neutrons, protons and electrons after a collision as before it. This can be considered an approximate conservation law. Shouldn't there be a corresponding (approximate) symmetry corresponding to each of these particle groups?
|
Let's have Pauli-Lubanski operator:
$$
\hat {W}^{\alpha} = \frac{1}{2}\varepsilon^{\alpha \beta \gamma \delta}\hat {J}_{\beta \gamma}\hat {P}_{\delta} = \frac{1}{2}\varepsilon^{\alpha \beta \gamma \delta}\hat {S}_{\beta \gamma}\hat {P}_{\delta},
$$
where $\hat {J}_{\beta \gamma} = \hat {L}_{\beta \gamma} + \hat {S}_{\b... |
Cosmic rays can have energies going into the $10^{20}$ eV domain. Asteroids and meteoroids originating in the solar system are probably limited in their speed because they all started out from the same lump of matter having more or less the same speed, but what about rocks from other galaxies ? Could they reach relativ... |
From the Maxwell's equations we get
$$\frac{\partial E}{\partial x} = -\frac{\partial B}{\partial t}$$
and
$$\frac{\partial B}{\partial x} = -\mu_0\epsilon_0\frac{\partial E}{\partial t}$$
My question is: A change in the electric field causes a change in the magnetic field, while a change in magnetic field is ca... |
I'm really excited by an opportunity to watch Leonard Susskind's course "The Theoretical Minimum". However, I couldn't find any physics problems on the website, and I'm a little bit wary of just watching videos. I want to think on some problems during that.
Maybe there's a good collection of Physics problems on related... |
Why can't we answer this simple question? Where does the magnetic field of a permanent magnet come from? What is different about a magnetizable atom that allows it? Why is it perpetual? Or is it recurrent? Charged particles in motion into wave-flux, then the wave-flux back to charged particles in motion? Primal ... |
I have a question in Polchinski's string theory vol I p 167. It is said
For example,
$$ds^2= \frac{ 4 r^2 dz d \bar{z} }{(1+ z \bar{z})^2} = \frac{ 4 r^2 du d\bar{u}}{ (1+ z \bar{z})^2} \tag{6.1.3}$$
describes a sphere of radius $r$ and curvature $R=2/r^2$.
Why Eq. (6.1.3) describes a sphere of radius $r$ and cur... |
The symmetrisation postulate is known for stating that, in nature, particles have either completely symmetric or completely antisymmetric wave functions. According to these postulate, these states are thought to be sufficient do describe all possible systems of identical particles.
However, in Landau Lifshitz Quantum M... |
When a body is in circular motion, realistically, it experiences only the centripetal force, created by gravitational pull, tension etc., which gives it acceleration towards the centre. Now, assuming we were to fill a bucket with water, and whirl it in the vertical plane. There will be a certain velocity when the water... |
Can someone tell me a reference which proves this? - as to how does the bulk partition function of Chern-Simons' theory get completely determined by the WZW theory (its conformal blocks) on its boundary..
I see that Toshitake Kohno's book seems to do a thorough study of this but its not beginner friendly at all! (...... |
Apart from thermo-nuclear reactions in the Sun, (and in hydrogen bombs and other methods developed by scientists) does nuclear fusion occur naturally in the planets? If not, why?
Also, do the Sun and the Outer planets - Jupiter through Neptune - have rocky cores similar to the Earth (consisting of iron, nickel, silico... |
Suppose we have two radio waveforms each has amplitude of 1, then the total power is 2.
Suppose these two waveforms add up some where constructively, then the amplitude become 2, and the total power is 4, so where is the extra power comes from?
|
EDIT: Apparently this is called reactive molecular dynamics. It seems that the ReaxFF potential function is used for some reactions like this.
I am interested in adding support for reactions to a coarse grained molecular dynamics simulations. On the whole each particle will represent a large biomolecule.
Most of the l... |
I just calculated that if the European extremely large telescope(978 m^2 area) would be pointed at the Andromeda galaxy once it is built, it will only get mere 1.2*10^-6 Watts of power from Andromeda.
And I didn't account for atmospheric factors or the fact that the telescope is only going to read visible and infra red... |
So there I was resting me eyes thinking about rocket drives, and what-not. The thought struck me that, perhaps, even before Mr. Einstein interferes with the increasing velocity of the spacecraft Mr. Newton may have something to say.
Please poke me in the rib if my comprehension is wrong -
A rocket, basically a reactio... |
I have a quick question I hope someone can answer.
Why do you dope a semiconductor ? Is that only to get more carriers to conduct, or is it also to make the energy gap between the valance- and conduction band smaller ? Or is the gap between the hole doped energy level and valence band so small that it doesn't really ma... |
Considering that electrons are highly mobile inside of a metal, why do they have such a tough time getting out at the edge of it and continuing their trip ballistically?
|
I've read a few explanations about why stress concentration occurs at sharp corners but I don't find the explanations intuitive.
Can anyone explain it perhaps using an analogy such as atoms "holding hands" with neighbor atoms or a similar easy to understand analogy?
Most explanations I've shown just show the result of ... |
I'm making several assumptions, not sure if any are correct:
there is a black hole at the center of a galaxy
the black hole is eating the galaxy
Eventually the galaxy will be gone, right?
Has this been observed? Do we know what happens afterwards?
Posting here since astronomy got merged into physics
|
Considering that on the atomic level objects consists of densely spaced positively and negatively charged particles, does not the acceleration of those objects lead to Bremsstrahlung of those particles? And although the monopole field is zero, couldn't higher order multipole radiation escape and cause the inertia? I wo... |
I am trying to calculate the field of an infinite flat sheet of charge
(a plain with uniform charge density $\sigma$) using the superposition
principle.
I know that the field of an infinite line charged with uniform charge
density $\lambda$ is $E(r)=\frac{2\lambda}{r}$.
I want to consider the plain as infinite number o... |
I have stumbled upon a given question I really have a hard time to solve. Basically I need to find an equivalent resistance in some form of "ladder" configuration. Where the chain is an infinite sequence of resistors.
I have really no good idea how to find this equivalent resistance. Trying the old fashioned rule of p... |
I was reading a popular news account of the sun's upcoming magnetic field reversal at http://www.csmonitor.com/Science/2013/0807/Sun-s-magnetic-reversal-means-big-changes-for-the-solar-system-video, and was confused already in the second paragraph:
Data from NASA-supported observatories indicate that the next flip wil... |
Graphene has two atoms in its primitive unit cell. This makes it intuitive to see that the tight binding Hamiltonian can be constructed as a $ 2 \times 2 $ matrix $H$ acting on a spinor $S$ that consists of the wavefunction from an atom in sublattice A and B.
$H_{monolayer}=\gamma \cdot \begin{pmatrix}
0 & k_x-ik_y \\ ... |
An excerpt from this page:
Gases can fill a container of any size or shape. It doesn't even matter how big the container is. The molecules still spread out to fill the whole space equally. That is one of their physical characteristics.
If a fixed quantity of gas is let out in a limited space, will it spread out equa... |
Following Polchinski's book (String Theory 1), we have the $bc$ action:
$$S = \frac{1}{2 \pi}\int~d^2z ~b\bar \partial c,\tag{2.5.4}$$
where $b$ and $c$ have holomorphic weights $\lambda$ and $1- \lambda$.
From this action, it is said, that applying the Noether's theorem, we get the energy-momentum tensor:
$$T(z) = :(... |
I was reading this blog post: https://ianstormtaylor.com/design-tip-never-use-black/
Which phenomenon explains this:
But I must have been thinking the same thing, because one of those days in art class Mrs. Zamula came in with a blue light bulb to prove it. She screwed the bulb into a clamp-light, plugged the light in... |
I am trying to learn the Photoelectron velocity map imaging. While I was going through the article "Chem. Soc. Rev., 2009,38,2169-2177", it is said that the "photoelectron spectrum reflects the energy eigenvalues of the parent atomic or molecular system, while the phtoelectron angular distributions reveal the character... |
It is known that matter and antimatter annihilate each other when they "touch" each other. And as far as I know, the concept of "touching" as our brain gets it is not true on the atomic level since atoms never really touch each other but only get affected by different forces.
If this is true, then when does the annihil... |
This is one of the "fast answer" exercises I've been given to train (should be answerable in around 6-7 minutes). I can only think of a very long-round way to solve this. The question is as following:
Two point charges 2Q and Q are located at the opposite corners of a
square of length l (2Q at the top right corner).... |
On page 92, my still favorite supersymmetry book says, by making the global infinitesimal parameter of a SUSY tranformation space-time dependent (gauging) it forces one to introduce a new gauge field which turns out to have the properties of a graviton and one obtains supergravity. This is analogue to obtaining electro... |
We've got two long straight wires carrying current of 5A and placed along x and y axis respectively current flows in direction of positive axes we have to find magnetic field at a) (1 m,1 m)
b) (-1 m,1 m)
c) (-1 m,-1 m)
d) (1 m,-1 m)
now using ampere's law $$ \oint_{}^{}B.dl=\mu_oi $$ i found magnetic field for infin... |
I guess that these questions were being asked by many people on the Northern Hemisphere during this summer (and other summers) and someone may give a nice, coherent answer. The general question is how many times more slowly one is getting suntan or damages his skin in the evening, relatively to the noon?
The Sun altitu... |
What is the net electric charge (in magnitude and sign) of the Sun and its corona?
|
The earth's rotation around itself (one rotation around Earth's own axis) doesn't take exactly 24 hours. It off by some seconds which becomes somewhere around 6 hours per year and 1 day in 4 years(leap year), which brings the question why didn't we modify the measurement of 1 second ever so slightly so as to avoid leap... |
We know
$$E = q V$$
where $E$ is the energy (in Joules), $V$ is the potential difference (in Volts), and $q$ is the charge. Why is this equation true and how we prove it?
|
I'm trying to do the dimensional analysis of the Lennard-Jones force to work out what units are being used in my MD simulation.
The lennard Jones force is given as the negative derivative of the potential:
$F = 24e/r*[2*(s/r)^{12}-(s/r)^6]$
This article:
http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics... |
This is a theoretical question since we haven't made enough antimatter to try it in reality of course. But I am asking about the physics part in this.
Also, by "useful energy" I mean the energy we are able to use either as a heating source for something like a nuclear reactor, or as energy for an explosion like nuclea... |
For small thicknesses of wire, it's pretty obvious why resistance affects thickness. (The electronics squeeze to get through). But after a certain thickness shouldn't the thickness become irrelevant?
For example if your trying to pour a bucket of water through a straw, the thickness of the straw is obviously gonna be a... |
A picture in my text book shows a three dimensional wave packet dispersing, "resulting from the fact that the phase velocity of the individual waves making up the packet depends on the wavelength of the waves."
Does this mean a particle moving through space has a gradually diminishing probability of being in it's locat... |
I have a measurement method for which I want to study the measurement error by an error budget. Therefore, I listed all possible errors (error sources) (lets say $x_1, x_2, x_3,\ldots$). For each error $x_i$, I have derived an analytical expression from which I can calculate the resulting measurement error $\epsilon_i$... |
I have a little knowledge about ionizing radiation and I have been confused over why nuclear reactors need these massive shields.
So, if I am not mistaken, Alpha and Beta radiation are not that dangerous since they can be shielded with relatively light materials, the main problem is because Gamma and Neutron radiation.... |
I need to do some work with liquid nitrogen at home. The main question is how to store it without buying huge vacuum flask specifically for liquid nitrogen.
I've tried to use usual steel household vacuum bottles, added ~1 cm of extra insulation (some foamy material, multiple layers), wrapped in plastic to protect from ... |
A loop is a 1-sphere that can vibrate in increasingly complex ways as it is embedded in higher dimensional spaces.
Does string theory assume that 1-spheres are the only possible vibrating structures, or does it also look at the vibrations of higher spheres, e.g. (2,3,...,8)-spheres? If only 1-spheres are assumed, what... |
Short version of my question:
Do dipole currents cause fields? I think currents of aligned magnetic dipoles cause an electric field, but I don't know how to calculate this field except in the simplest of cases. I'd like to know how!
Full version of my question:
Suppose I have a wire (or pipe) that carries a steady curr... |
Imagine I have a solenoid connected to a power supply. Solenoid produces an electromagnetic field. Now I take a permanent magnet and place it inside the solenoid. How will the magnet align itself (assuming there is no gravity) inside the solenoid and will it rotate itself around the central axis "aligning" itself?
From... |
Why is geometric optics the low wavelength limit of the wave theory of light? I can't seem to grasp why either a low or high wavelength limit would be necessary.
|
Newton's Third Law states that
Whenever any force is exerted by a body#1 on any other body#2, another force which is equal in magnitude and opposite in direction is exerted on body#1 by body#2.
In theory, suppose a boy is pushing a rock heavier than him on ice. Due to the relative lack of friction, the boy would pro... |
I'm working on a college project for a subject called Motorcycle Engineering, and in this project I'm supposed to do some reverse engineering on a MATLAB program to model the engine of the motorcycle. In this program I just came across the following expression:
$$u=h_f-RT+(c_p-R)(T-T_0)$$
where $u$ is the specific inte... |
Considering the fault of any experimental evidence from LHC for supporting the supersymmetry idea until now, can we say that it is dead? Generally the people who are working on this subject say that MSSM probably is dead but we have some new extensions of it such as NMSSM. This argument seems weird a bit. Sometimes I f... |
We should all fondly remember this basic undergraduate problem: A quantum particle is incident (from the left) upon a potential barrier of height V and width L. Compute the transmission and reflection coefficients.
However, this isn't the full story. To completely solve the potential barrier, we need a complete set o... |
This question is about the generalization of Coulomb's law to continuous bodies of charge. The basic statement of Coulomb's Law involves two discrete charges $q_1$ an $q_2$:
$$\vec{F}_i = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r_{12}} \hat{r}_i $$
Here $i$ represents the charge on which the force is exerted, and $\h... |
Excuse me, I have calculated $a^g$ a lot of times, using the relation between $:\;:$ and ${}^{{}_\circ}_{{}^\circ} \; {}^{{}_\circ}_{{}^\circ}$. But I can't get the same result with the book.
It is not too hard to get
$$
:b(z)c(z'):-{}^{{}_\circ}_{{}^\circ} b(z)c(z'){}^{{}_\circ}_{{}^\circ} =
\frac{\left(\frac{z'}{z}\r... |
If you push a bar magnet inside a solenoid, a current is produced. But why is that? I mean, the wire is being moved along the magnetic field, so taking the cross product:
$\vec{F} = I\vec{V}\times\vec{B} = I|\vec{V}||\vec{B}|\sin\theta\hat{n}$
Here, the angle between the velocity of the charge in the wires and the magn... |
My book starts section 2.2 like this:
Equation 1.1 is this:
$$q_x=-k\frac {\partial T}{\partial x}$$
As you can see in the picture I posted, my book says that one can go from equation 1.1 to equation 2.1 by integration. I don't see how this is done by integration at all.
Thank you
|
Well the following question I really struggle to find an answer
A thin lens creates an image of an object with magnification -3. A
second identical lens is positioned very close to the first lens such
that the distance between the two lenses can be neglected. What is the
magnification with this two lens system a... |
Once day, I talked to my Prof. about Computational Physics and he showed me his work. I'm quite surprised that why Prof. use C++ for computation because C++ quite complicated. I heard he talked about memory talk about pointer. Why didn't he use Python or Java that more easier? no need to manage memory no need to busy w... |
We can define a topological current,
\begin{equation}
J_{top}^u = \frac{1}{2v} \epsilon^{\mu \nu} \partial_\nu \phi
\end{equation}
where $\epsilon^{\mu \nu} = − \epsilon^{\nu \mu}$ and $\epsilon^{01} = 1$. The antisymmetry of $\epsilon^{\mu \nu}$ guarantees that this current is divergenceless. Its normalization has bee... |
Will a helm made entirely of diamond be more protective against bullets than standard steel or kevlar helmlets?
|
I was drinking iced-water from a drinking glass (made of glass) at a restaurant yesterday when I was taking a drink, I noticed that there is very little ice water coming out and then suddenly, the ice water mixture comes crashing down. With my open mouth overfilled with ice water, my shirt gets wet – I hate when this h... |
Relevant diagram is available here.
The circular disk of radius $a$ lies in the $xy$ plane and carries surface charge density of
$\sigma (s, \phi) = s^{2}cos\phi $,
where $(s,\phi)$ are in cylindrical co-ordinates.
The problem is to find potential at a point which is slightly displaced from the $z$ axis at position $ r... |
I've been studying quantum mechanics and quantum field theory for a few years now and one question continues to bother me.
The Schrödinger picture allows for an evolving state, which evolves through a unitary, reversible evolution (Schrödinger’s equation, represented by the Hamiltonian operator) and an irreversible evo... |
By Coulomb's law, say if we have 2 point particles each having a charge of +1C
then by the formula,
$$F = k/d^2$$
if we need to make the distance $d$ between them zero, clearly the formula, we need to have an infinite amount of force.
However, in a real life scenario, we see that if we rub two balloons with our head, t... |
I have a question regarding the magnetic moment of an atom.
If you just have one atom, and you apply an external magnetic field in lets say the z-direction. Then the magnetic moment will precess around the direction of the magnetic field applied, and depending on the quantum numbers it can precess in different quantize... |
If you can could you lists the types of light from the greatest amount to the least amount (Ex: Visible, Infrared, Violet).
|
can someone help me with the following issue. I need a method for transforming mechanical work into electrical energy without using piezoelectricity. I have such kind of mechanical forces (like on the picture in the link) and I want to transform this mechanical force into electrical energy.
mechanical energy
|
Can I decrease a photon's wavelength by a medium or a vacuum? Are there other ways of decreasing the wavelength?
|
The phenomenon I'm talking about is positive feedback, as known from control engineering: when the microphone is too close to its speaker, it can "hear itself", so the signal will be infinitely amplified. This can be very irritating e.g. during a concert.
But I wonder: why do you only hear a high-pitched tone when this... |
Well in a problem I had to calculate the maximum amount of "reflections" in a glass fibre optic pipe (index of refraction = 1.3, width of 20 micrometer and length of 1 meter). I am a bit blocked on how to calculate this.
I considered first the critical angle $sin(\theta_{cr}) = \frac{1}{n}$ Which came out to be 50 degr... |
In a fascinating 30 June 2013 article in Nature Chemistry, researchers from the University of Leeds found that when molecules of hydroxyl (OH, a fairly stable radical) and methanol (CH$_3$OH) are cold enough to adhere to each other in deep space instead of bouncing apart, they combine to form methoxy molecules (CH$_3$O... |
From Laundau & Lifshitz "Quantum Mechanics":
If there are two conserved physical quantities $f$ and $g$ whose operators do not commute, then the energy levels of the system are in general degenerate.
Let's consider a 1D free particle. Its wavefunction would be
$$\left<x\middle|\psi\right>=e^{ikx}$$
For all $k>0$ it's... |
My Mechanics textbook claims that the sum of the work by internal forces is not generally zero.
translated to English the paragraph reads:
Notice about the work by internal forces: the work by the internal forces is in general not equal to zero although the sum of the internal forces is always equal to zero. Since the... |
In Polyakov's book, he explains that one possible way to compute the propagator for a point particle is to compute the lattice sum $\sum_{P_{x,x'}}\exp(-m_0L[P_{x,x'}])$, where the sum goes over all paths between $x$ and $x'$. One then needs to compute this sum and choose the bare mass so that there's a good continuum ... |
I am given the feeling that there exists scenarios when this equality holds.
Can anyone state/refer to the situations?
One case that I hear of is that for $2+1$ CFTs the entanglement entropy across a spatial disk is the same as the free energy of the CFT system on a $S^2 \times S^1$ (or $S^3$?)
What is the exact corr... |
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