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I'm interested in using normal "Reynolds wrap" type aluminum foil as a radiant barrier. What are some measures of how much light and heat this would reflect under ideal and "normal" conditions? Are there significantly better types of foil out there? How much better-performing are the products designed for this purpose,...
The Joule Thomson coefficient for various gases can be found in textbooks, e.g. have I found that hydrogen has $\mu_{jt}=-0,024735$ K/bar and an inversiontemperatur of around 200 K. Not having the background to understand its derivation: Is $\mu_{jt}$ constant for a given gas or is it a function of some parameter (apar...
According to textbooks, the Joule Thomson coefficient requires a isenthalpic process ($H = const.$). I found much related information about the throttling process. But what happens, if a pipe system for not-ideal gas (e.g. hydrogen) at some process pressure has a leakage and the environment is at atmospheric pressure a...
I’m a beginner in general relativity, I start with reading Field Theory written by Landau. There are some confusions arose when I tried to understand the physic logic of general relativity. Let me first conclude how general relativity is built up in this book: Truth: In inertial reference frame, we know a truth of gra...
Which one of the two following descriptions is the correct one: a pendulum clock carried by an astronaut orbiting the earth will not swing because there's no gravity and the pendulum is in free fall. a pendulum clock will swing at a reduced rate: the periodic time will increase because the acceleration due to gravity...
I am trying to get the time evolution for the following initial condition: $$ \Psi(x,0) = \left(\frac{1}{2\pi \sigma^2} \right)^{\frac{1}{4}} e^{- \left(\frac{ x-x_{0}}{2 \sigma}\right)^{2}} e^{i\frac{ p_{0} x}{\hbar}}$$ I have got the Fourier transform of this function, $$\Phi(p) = \left(\frac{2 \sigma^{2}}{\pi \hbar^...
I'm doing a lab for my physics II class in college. We're to watch a video that shows two metal spheres, one sitting on a scale and the other suspended from a string. When the spheres are charged they exert forces on each other. We measure the force on the lower sphere by looking at the scale reading. As we vary the d...
Problem statement: In the given figure, two blocks A and B, each having a mass of 320 grams are connected by a light string passing over a smooth light pulley. The horizontal surface on which block A can slide is smooth. The block A is attached to a spring of spring constant 40$\frac{N}m$ whose other end is fixed to a...
I have started to use thermal imaging cameras more and more and realized that I can see the reflection of my self bouncing off of a glass window through the IR camera. When viewing it on my monitor, I can see a clear and distinct reflection and wondered if it is because I, a human, is producing IR light actively throug...
The Schrodinger equation: -((h^2)/8 pi m)(d^(2)psi(x)/dx^2)+v(x)psi(x)=E psi(x) is just another way of writing : kinetic energy + potential energy = total energy right? (for those of who can't see the image its just an image of the Schrodinger equation) Well in QM conservation of energy is violated right?(nuclear expl...
As you know when we have given substance in an empty container then the substance would evaporate until and equilibrium is attained between the substance and it's vapour phase. In due process the original phase of the substance will decrease in amount. So I was thinking if we have initially $n_o$ moles of substance and...
I have read a lot about (what is the total energy of universe? And Is it zero?) here, such as, Is the total energy of the universe zero? and other sources. I thought decades about a question, not exactly about: What is the total energy of universe? But: Is the total energy of universe, if has any meaning word "total", ...
Recently, I have an interest in Mixed Higgs-$R^2$ inflation and its preheating. However, there are some problems that I faced, one of them is solving the equation of motion in certain papers and producing some plots. In case to make it simple here it is considering the figure. 2 of https://arxiv.org/abs/1812.10099 mus...
Consider this diagram from wikipedia. Now the diagram clearly depicts forces due to three interfaces. But in the derivation of capillary rise, we only consider the force due to Surface Tension of the liquid - air interface. Why don't we consider the forces due to other interfaces in this derivation?
Carrie is in a spaceship that is travelling towards a star in a straight-line at constant velocity as observed by Peter. Peter is at rest relative to the star. Carrie travels at a speed of $0.4c$ relative to Peter. Question: According to Peter, as Carrie passes the star she sends a radio signal. Determine the time, as...
Consider a system composed of two parts $s$ (subsystem) and $R$ (reservoir), and let $\rho$ be the density matrix for some state of the combined system. Show that if subsystem $s$ is in the pure state, $\rho$ must have the form $P_s \otimes \rho_R$ , where $P_s$ is a projection operator on the Hilbert space of $s$. Fro...
during re-coiling of tungsten coil wound with moly mandrel ,the mandrel is breaking in between(the mandrel is annealed before) : we don't know what exactly is causing as some length works fine and in some length it is breaking . we are getting suggestions that this causes by either Lack of plasticity, or it is caused ...
Suppose I have a stationary charge in an area where the magnetic field is constantly changing. Now from my understanding of Faraday's law, the direction of the force it experiences seems to be ambiguous. If I pick a circular loop and the charge is on the point P of the loop, then the rate of change of flux would tell m...
When the heat supplied to system is zero and change in internal energy is brought by work, it is said that $W=P(ext)×dV$ is the work done. Isn't that work done (causing internal energy change) due to change in pressure $P_{ext}-P_{int}$? Isn't it $W=dP×dV$?
I find a small black hole floating in space. It's very small, say 0.001 femtometer diameter. But it weighs about 300 thousand tonnes. It is also quite hot at about 400 trillion degrees and altogether it radiates about 4000 Terawatts of power. Apparently it will take about 70 years to evaporate. [ ref. https://space.ge...
I'm not entirely sure if my question is valid or not but I'll ask it anyway. So my physics porf. told us the Photons are constantly in motion and they never come at rest and the sub-topics relating to it. Now since they never come to rest we cannot possible observe them, but [ There's always a but] if we're able to mov...
Without working with Lagrangian, how can one explain if we are dealing with $s$ or $t$ channel diagrams? For example, for $\rm e^+e^-\to\gamma\gamma$, I thought $s$-channel diagram, but the solutions I have, show a $t$-channel diagram.
I attended a lecture given by Professor Wen Xiaogang. In the lecture, Prof.Wen gave an example of topological excitation: For a state $$(\uparrow\downarrow)(\uparrow\downarrow)(\uparrow\downarrow)(\uparrow\downarrow)(\uparrow\downarrow)(\uparrow\downarrow)(\uparrow\downarrow)(\uparrow\downarrow)(\uparrow\downarrow)(\up...
A charged particle, decelerated by the electric field of another charged particle, typically an atomic nucleus, emits electromagnetic radiation, called Bremsstrahlung. This process typically happens in the matter in the presence of electric fields of the atomic nuclei in the medium. Question The term Bremsstrahlung lit...
Why is there no effect in the mass of the bob on the period of the simple pendulum? I have found out many different explanations. However, I wasn't able to find a scientific explanation for my research proposal.
I am from the USA, just a retired soldier who looks at the sky a lot. This morning 26 SEP 2020 at 1am, the Moon was approximately a quarter Moon. It was bright, the line/shadow on the moon was not straight. I have never in my 58 years saw any Moon that appeared this way. The line of the light on the moon is always a s...
The term 'bremsstrahlung' is usually reserved for the emission of electromagnetic radiation caused by $(1)$ acceleration or deceleration of the charged particle by an electric field and $(2)$ in presence of matter/medium. See section $8.8$ of the book Quantum Field Theory by Mandl and Shaw, and section 11.5.3 of Perkin...
It is well-known, that Veneziano amplitude is the string scattering amplitude for the scattering of four open bosonic strings in their tachyon states. Are some QFT models, in which amplitude is Veneziano amplitude?
Having studied supersymmetry in $d=4$, my understanding is that we count supersymmetries by the number of pair of complex supercharges $$ Q_\alpha^I = \begin{pmatrix} Q_1^I \\ Q_2^I \end{pmatrix}~,~ \bar{Q}_{\dot{\alpha}}^I = \begin{pmatrix} \bar{Q}_{\dot{1}}^I \\ \bar{Q}_{\dot{2}}^I \end{pmatrix} $$ which are Weyl spi...
This is something I got curious about. Let's say I have the Wigner function for an $n$ particle system: $$W \equiv W(x_1,\dots,x_n,;p_1,\dots,p_n) $$ Now, let's say this system obeys has spin. As far as I understand that restricts the allowed eigen-basis (upon interchange of $r_i \leftrightarrow r_j$for bosons its symm...
Why does the Hartree-Fock method for electronic structure work so well for atoms? More specifically, why is the "correlation energy" a relatively small component of an atom's (ground state) energy? I might also ask why electron-electron interaction appears to be so small compared to electron-nucleus. For example: The ...
Consider a pendulum doing vertical circular motion and having velocity with magnitude $v$, mass $m$ and length of string $l$ starting from horizontal (inextensible rope, the given velocity is at horizontal position). Using force balance at top most point (and considering tension is 0), $$ \frac{mv_{tngt}^2}{r} = mg$$...
The condition for diffraction is that the effects of diffraction become more noticeable when the width of aperture is comparable to the wavelength, and from that we can say the spacing of fringes become more significant when $d \approx \lambda$. Now taking the equation : $$\lambda=\frac{d\sin\theta}{n}$$ where : $d \t...
Given a pure state $|\psi\rangle$ with position wavefunction $x\mapsto\psi(x)$, define its Wigner function as $$f_\psi(x,p) = \frac{1}{2\pi} \int dy e^{-iyp} \psi(x+y/2)\psi^*(x-y/2) \equiv \frac{1}{2\pi}\int dy e^{-iyp}\tilde f_\psi(x,y),$$ where the last expression highlights that this is the Fourier transform of $\t...
I have found that the Coulomb force in two dimension varies with $\frac 1 r$: \begin{equation}\tag{2}F=\frac{1}{2\pi\epsilon}\cdot\frac{q_1q_2}{r}\end{equation} But I was not able to prove it. I think it can be proved using the Laplace equation and other further modifications. One question related to this topic is answ...
Do the green charged particles produce a different electromagnetic field than the red charges? They seemingly produce the same motion. Imagine the case to be a line charge. Here they are discretized into particles for easier illustration of the problem. Red particles are moving straight with uniform speed and emerge an...
Title basically says it all. I'm not a physicist by any stretch. I'm an IT professional with slightly more than a passing interest in mechanics. I got to thinking the other day how much power is generated when a manned rocket is launched to go to the moon (or ISS, etc etc). Wouldn't it be possible to set up the hydroge...
I was reading Cambridge lecture notes on Statistical physics, and I came across this equation where they used some technique of expansion which honestly I couldn't understand how. So my question is how they found the last equation from the second one. Thank you.
Assuming a QFT description of a second-order phase transition. From the free theory, one obtains some critical exponents and one performs an $\epsilon$-expansion below the upper critical dimension. There are some cases, where one finds that $\Sigma=G_0^{-1}-G^{-1}$ the self-energy is zero in all orders in the perturbat...
I've been reading "L. D. Landau, E.M. Lifshitz - Mechanics (Volume 1)" and he justifies the fact that the Lagrangian is a function of $v^2$ with the fact that space is isotropic - that is, direction does not matter. My question is: could we choose $L$ to be a function of $|v|$ or $v^4$? I know that, if we choose $v^2$ ...
OK, the topic of my post is General Relativity, and first I try to present my train of thought. GR says that gravity is geometry, and what we may experience as a gravity force is in fact objects moving in curved geometry and following straight lines in that geometry. I imagine a curved geometry like this: let's take a ...
In HBO's Chernobyl series, after reactor no. 4's meltdown, soldiers (Chernobyl's liquidators) splash a light-brown liquid onto the ground, both streets and forest, and for washing vehicles; for this operation they used a variety of means (manned pumps, trucks, helicopters). Here are some screenshots: What is the reas...
After the plum-pudding model failed, physicists concluded that atoms had nuclei that were relatively dense and positively charged. But the rejection of the plum-pudding model posed many conceptual challenges for physicists of the early 20th century because it was hard to reconcile alternative models of the atom with cl...
My understanding is this: angular momentum of a body about a point cannot be in two directions at once, which is why a wheel already rotating about its axle, cannot also rotate about its diameter at the same time; it tilts sideways. However this doesn't seem to be the case for points of reference outside the body? For ...
I was using Jefimenko's equations to solve a problem our Electrodynamics teacher sent us involving a infinite wire with current $$I(t) = q_0 \delta(t).$$ So we have to obtain electric, $\vec{E}(\vec{r}, t),$ and magnetic, $\vec{B}(\vec{r}, t),$ fields produced by that current. That make me find a situation with which I...
It is a well known fact in the field of non-equilibrium statistical physics that in order to maintain a system far from equilbrium, you need to drive it via an external energy source. The system uses that energy to go to a non-equilibrium state and then disspates some of that energy in the form of a heat to go back to ...
I'm building a game prototype where you control a 2D spaceship by activating it's thrusters. Below is an schema of my thruster. It applies a force in the direction of the arrow, with a variable and controlled intensity. Now let's assume I have the following blue spaceship, with 6 attached thrusters: Currently I can f...
You know the angular momentum equation that makes keplers second law work L=rmv where L is angular momentum is r radius, m is mass and v is velocity. Well according to that equation if we decrease the radius then either the mass or the velocity would have to increase (sort of how keplers second law works) right? Well ...
I'd like to model some simple molecules using VSEPR. With what functions should I approximate the sigma and pi bond orbitals? A simple Gauss would do it? I'd like to have a good precision. Thanks in advance
Consider the following question which was asked in JEE Advanced 2016: Consider the first option(which is the third option here) In the video linked above, Tibees takes $L_{com}=L_1+L_2$ where $L_1$ & $L_2$ are the angular momenta caused by the rotation of the two discs about the line joining them. My question is this-...
I don't think it's just a matter of reorienting maps and recalibrating compasses. In any case, how long does a inversion last? hours, days, weeks, years? If it lasts days or more.... would Sun fry Earth surface?
In Topological Insulators and Topological Superconductors (Bernevig & Hughes) a limit of an insulating Hamiltonian, the flat-band limit is used to compute the Hall conductance. For the fist we define the adiabatic deformation of the bands (the chemical potential is located between $\varepsilon_{p}$ and $\varepsilon_{p+...
Given a circular wire connected to a battery with a potential difference of v across the wire. And given the fact that resistance in the wire is zero. If a constant potential difference is applied across the wire then the electric field does work on the electrons causing them to accelerate. In a wire with resistance th...
Can anyone prove the time-reversal invariance of the following scalar field theory? $$ \mathcal{L}=\frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi-\frac{\mu^{2}}{2} \phi^{2}-g\phi\psi^*\psi+\partial_{\mu} \psi \partial^{\mu} \psi^*-m^2\psi^*\psi$$
In special relativity, the spacetime interval between the same two events measured by two different inertial observers are numerically the same: $$c^2dt^2-|d\vec{x}|^2=c^2dt^{'2}-|\vec{dx'}|^{2}.$$ In general relativity, does the same thing remain true i.e. if two arbitrary observers measure the same two events, does t...
Here the purple represents the disc, red represents the axis of rotation of the disc, and green represents the direction of rotation. It is said that by applying right hand thumb rule we can find the direction of angular displacement of the disc, and the direction of thumb points or tells us the direction of the angul...
I have heard of the fact (see e.g. here) that there exists no everywhere-regular Hadamard (vacuum) state for quantum field in Kerr spacetime. My understanding is that the Hadamard condition provides "good" short-distance (UV) property which is to some extent universal, and related to the fact that locally spacetime is ...
In the last chapter of W. Greiner's book, Relativistic Quantum Mechanics, orthogonal transformations are defined as follows : $$ x^{\prime\mu}=a^{\mu}{}_{\nu}x^{\nu} $$ When proceeding to find $a^{\mu}{}_{\nu}$'s components, he says that the equation defining the length : $$ s=\sqrt {g_{\mu}{}_{\nu}x^{\mu}x^{\nu}}, $$ ...
This question is somehow related to Newton's bucket and absolute rotation concepts, but applied to a simple, tangible scenario. Let's suppose I could hover over the North Pole, and "detach" from Earth's rotation. In this scenario : From my point of view, the Earth is spinning below my feet For an Earth observer, I am ...
If we have a larger pinhole, would it produce a larger image? I know the size of the opening will affect the brightness and sharpness of the image, but what about its size? If you think about it, a wider opening will make the light rays more spread out and therefore consequently produce a bigger (and also blurrier) im...
I can't wrap my head around this problem. Let there be two masses $m$ attached vertically to springs of elastic constant $k$, each mass is also attached to an end of a catenary of mass $m_c$ e length $l$, so that $m_c = \mu l$. Let $l_1,l_2$ be the partial length of the catenary between the mass and the minimum point a...
I have read for a couple weeks now about a universe from nothing. I understand that the gluon field supports quarks in a proton. I understand that the universe has zero total energy. I'm confused about the beginning of the universe, and terminology. When Dr. Lawrence Krauss debated Hamza Tzortzis, Krauss told Tzortzis ...
Applying Wick's theorem to a string of four field operators, $\phi_a\equiv\phi(x_a)$: $$T(\phi_1\phi_2\phi_3\phi_4)=\{...\}, \tag{1}$$ we obtain several terms, three of which are fully contracted fields: $$\phi_1^{\bullet}\phi_2^{\bullet}\phi_3^{\bullet\bullet}\phi_4^{\bullet\bullet},\quad \phi_1^{\bullet}\phi_2^{\bull...
We are given a unit cell with $a=4$ angstroms, $b = 6$ angstroms, and $c=8$ angstroms. $\alpha=\beta= 90^{\circ}$, $\gamma= 120^{\circ}$. I would like to find $\mathbf{a}^*$, $\mathbf{b}^{*}$, and $\mathbf{c}^*$ for the reciprocal cell. I am not quite certain how to determine this from the information given. I know tha...
Could one explain this? Technically a kilogram (kg) is now defined: […] by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10–34 when expressed in the unit J s, which is equal to kg m2 s–1, where the metre and the second are defined in terms of c and ΔνCs. Does that mean that 1 kg = 1 ...
In a lot of literature the notion of different Hilbert spaces has been mentioned. In QFT, for non-interacting theories the Hilbert space is a called a 'Fock space', this is different from the interacting theory 'Physical Hilbert Space'. When the notion of Hilbert spaces was introduced to me it was described as the spac...
In many books, a truth of gravitation field has been stated in the following way: "No matter what mass does matter have, all objects will follow exactly the same trajectory under the action done by gravitation field if they start with the same initial conditions." But we know, if we state a truth of physics, we must sa...
So I want to measure the resistance of an unknown resistor. My setup is shown with the circuit diagram and I use the variable resistor to collect a range of readings of current $I$ through and potential difference $V$ across the unknown resistor. I get my table of values of $V$ and $I$. Then there are two options: plo...
So I have a small confusion when normalising an infinite well wave-function. The wave-function for my problem is $$Ψ(x) = Ae^{i(kx-wt)}+Be^{-i(kx-wt)}+Ce^{i(kx-wt)}+De^{-i(kx-wt)}.\tag{1}$$ Applying the boundary conditions at $x = 0$ and at $x = L$, considering the quantised energy formulae for the function's arguments...
A thin sheet of magnitude A has uniform charge Q> 0, and is closely placed near a conductor of width d. The conductor has net charge of zero. In terms of the given quantities and fundamental constants, find the charge density on both the near and far surfaces of the conductor, and the electric field strength in each of...
Imagine we have a panel of lasers in a truly dark vacuum, together with a panel of sensors, facing each other, some distance apart. Further, imagine that the number of lasers within the light-panel is exactly the number of sensors in the sensor-panel, and that each laser points directly at exactly one sensor. There is,...
My understanding of Hawking Radiation is that it is a pair of virtual particles that pop into existence at the edge of an even horizon. The anti-particle falls into the event horizon thus slightly reducing the holes mass. My question is this: The anti particle will fall in 50% of the time... Wouldn't that mean that ...
In classical physics: If momentum is doubled, KE increases by a factor of 4. Classical: $ \frac{1}{2} m(2v)^{2} = $ $ \frac{1}{2}4mv^{2} = $ $KE = 2mv^{2} $ In Modern Physics, that is not the case Modern: $E = \sqrt{p^{2}c^{2}-(m_{o}c^{2})^{2}}$ $KE_{rel} = E - (m_{o}c^{2})^{2}$ $KE_{rel}/KE_{classical} \neq 1$ Hence,...
My question is about mathematics in the context of physics Imagine a series of quantum states of a single particle: In the first state the particle has a certain position but an uncertain momentum In the last state the particle has an uncertain position but a certain momentum Also imagine all other possible (obeying th...
I am having a really hard time wrapping my head around component notation for tensor fields. For example, I do not know exactly what the following expression means $$\partial_\mu\partial^\nu \phi, \tag{$\#$}$$ where $\phi$ is a scalar field. On the one hand $\partial^\nu=g^{\lambda\nu}\partial_\lambda$ where $g_{\mu\nu...
I am a bit confused on how to compute the Euler Lagrange equation for the action \begin{align} S(\phi, \bar\phi) = \int d^2xdt\ \left\{|\nabla \phi(t, x)|^2-|\partial_t \phi(t, x)|^2+\phi_1(t, x)^2\phi_2(t, -x)\right\} \end{align} where $\phi = \phi_1+i\phi_2$, i.e. $\phi_i$ are real-valued functions. The Euler-Lagrang...
There is a classic example that a spinning skater pulls his arms back. The angular momentum is conserved, the moment of inertia decreases. And therefore, it's angular velocity increases, so the rotational kinetic energy will increase. But what will happen if the skate pushes his arms outward? The rotational kinetic ene...
The Bose-Einstein probability distribution (see below from Statistical Optics, Goodman) for $K=0$ is simply $P = \frac{1}{1+\bar K}$. But this does not integrate to one as all PDFs should. The integral from Zero to Inf does not converge so it cannot be normalized? Is this the correct distribution function (PDF)? $$ P...
A non-trivial result from studying the classical mechanics of an extended object shows that rotation about an axis whose moment of inertia is between the largest and smallest moment-of-inertia axes is unstable. This is known as the "tennis racket" theorem, as described on the Wikipedia page. In essence, there are two a...
Can Newton's first law of motion be considered merely as a special case of second law of motion with $a=0$? If so, the first law really needed? Why does the acceleration of a freely falling body not depend on the mass of the object?
I am working through an exercise in QED from Halzen and Martin's textbook Quarks and Leptons. For the QED scattering process $e^-(k)\mu^-(p)\to e^-(k')\mu^-(p')$, the absolute square of the Feynman amplitude averaged over the electron and muon spins can be expressed in short as $$\overline{|\mathcal{M}|}^2=\frac{e^4}{q...
I am having a really hard time wrapping my head around component notation for tensor fields. For example, I do not know exactly what the following expression means $$\partial_\mu\partial^\nu \phi, \tag{$\#$}$$ where $\phi$ is a scalar field. On the one hand $\partial^\nu=g^{\lambda\nu}\partial_\lambda$ and hence we cou...
Considering a bosonic $\phi^4$-theory: If I know that a certain connected Feynman diagram has a vanishing contribution. Does this imply that all larger connected diagrams containing this diagram are also vanishing in the general case? In my specific problem, all diagrams contributing to the self-energy are zero. Is the...
We work with Maxwell's equations in the frequency domain. Let's consider a bounded open domain $ V $ with boundary $ \partial V $. The equivalence theorem tells me that if the field sources in $ V $ are assigned and if the fields in the points of $ \partial V $ are assigned, then I can compute the field in each point ...
In the ideal gas equation $PV=nRT$, $V$ is defined as free space available to the gas. In an open vessel in which temperature is maintained constant, shouldn't the volume $V$ of the gas be the volume of the whole universe? I know this sounds stupid but I've read everywhere that the volume of gas will be the same as th...
The observer is at rest at point O. At once, he shots two bullets with equal masses $m$ in the opposite directions. Their velocities are equal by modulo $v=v_1=-v_2$. Now, he wants to calculate the total invariant mass of such a system. The bullet's four-momentums are $$p^{\mu}_1=\left(\frac{mc}{\sqrt{1-\frac{v^2}{c^2}...
As We know that light shoaws dual nature or I would rather say that Sometime we can explain some phenomenon using wave analogy and other with particle nature(photon analogy). Phenomena like the photoelectric effect, Compton effect, etc can be understood using photon analogy and phenomena like interference, diffraction,...
In this Wikipedia article, it is said that the inversion of ammines happens due to tunnelling effects and superposition of states and gives Feynman lectures as citation. I have not done a quantum course but out of curiosity I opened the specific lecture which was linked (this) and in it he has not mentioned the word 't...
An electron-hole is just a free electron state in a quantum system. Is this right? For example, let's say that there are 2 electrons with opposite spins in the fundamental state of a quantum well. If one electron with spin up is excited to the first excited state now you have a free spin up spot at the fundamental leve...
Suppose we need to convert $18\text{ km/h}$ speed into $\text{m/s}$. The answer is $5\text{ m/s}$. But $5\text{ m/s}$ has only one significant figure only whereas the $18\text{ km/h}$ has two. My question is, should not the number of significant figures remain same when we convert units? And then suppose we were to cov...
Fermat's principle is a boundary value problem which gives possible paths as it's answer. And I understand how it's applied to give possible paths between two arbitrary points. And following from the definition of a parabolic surface it could be easily shown that the focus point can only receive rays that are parallel ...
An echo sounder is simply a device that is used to help sailors determine the depth of water at different locations in the sea. There is a transducer that is attached to the hull of the ship that produces sound waves directed at the seabed. Various sources say that the principle is simple: time taken for the sound wave...
It is a known fact that $$ \gamma (1\pm\beta) = \sqrt\frac{1\pm\beta}{1\mp\beta} $$ is an eigenvalue of the Lorentz transformation (which is a linear transformation). This is also (as stated in the linked SE question) the relativistic Doppler shift. I know how to show that this is both the eigenvalue and the relativist...
Doesn't zero conductivity mean infinite resistance which would lead to infinite loss.
I know that electron-positron pairs can be produced within a uniform electric field with electric field strength above $10^{18}V$. Electric field of such strength can be found near atomic nuclei. So if one has an atomic nucleus free of its electrons, can electron-positron pairs be produced at it's surface?
I'm trying to make a 2d top down driving game, and I want to be able to drift with handbrake. To make calculations easier and faster, the car has only two wheels. If I can solve the following problem, I know how to compute the rest: The car is standing still, and there is some force F and torque T acting on it. What fo...
stackexchange, Upon reading in Modern Quantum Mechanics by Sakurai & Napolitano, I fell upon a calculation of the expectation value of the annihilation/creation operators squared, with respect to some basis. This was in relation to the Simple Harmonic Oscillator. Here, using the simple relation $a^{\dagger}|n> = \sqrt{...
I believe that at the boundary of Brilluoin Zone i.e, at -π/a,π/a. Taking k=π/a we have k=2π/λ so λ=2a. Making the group velocity zero. Does it point to Braggs law? What does it really signify?
In Walter Greiner's book, "Relativistic Quantum Mechanics", when discussing infinitesimal tranformations: $$x^{\prime\nu}=a^{\nu}{}_{\mu}x^{\mu},$$ where the $a^{\nu}{}_{\mu}$ is are infinitesimal elements of $SO(4)$: $$a^{\nu}{}_{\mu}=\delta^{\nu}{}_{\mu}+\epsilon^{\nu}{}_{\mu}.$$ He establishes the group generators a...
A colleague wanted to understand the notation for X-ray transitions. The main query is about the labeling of alpha, beta and gamma, with K, L, M etc. What is the main distinguishing criterion to label a transition as K, L, M along with the Greek letters alpha, beta and gamma. One of the websites she found said that alp...