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The wave equation is an example of an equation for which there are simple transparent boundary conditions. We can factorize the wave operator
$$\partial_t^2 -\partial_x^2 = (\partial_t - \partial_x)(\partial_t + \partial_x)\,.$$
The physical interpretation of this operator is that each factor is responsible for propaga... |
I understand that P4mm belongs to Tetragonal system. But how do we decide along which axis should we perform these symmetry operations?
According to my professor the axis along which we should do the operations is determined by which crystal system we are dealing with. According to him, for tetragonal system we should ... |
In my introductory condensed matter course, my teacher wrote the following for a 2-band model with eigenstates $|m\rangle,|n\rangle$. The dots indicate derivatives with respect to some arbitrary Hamiltonian parameter. However, I think there's a mistake.
$$
\langle\dot{m}|\dot{n}\rangle=\Sigma_p \langle\dot{m}|p\rangle\... |
The Seeback Effect is a thermoelectric effect, where two different alloy wires are attached in a loop. One conjunction is heated while the other is cooled, creating a temprature gradient. As the wires have different electic & heat conductivities, one overpowers the other and pushes electrons in a loop.
Heres a diagram ... |
Can the De Broglie wavelength of a composite system (like a molecule) be derived as opposed to being calculated from the composite mass?
EDIT:
@Dr jh, interesting relation you have derived. However, that is a rewrite of the original DeBroglie equation albeit using the λ variables. De Broglie guessed his solution by se... |
We have some evidence of excess heat being generated by Pons & Fleischmann type experiments. Ultimately, I want to understand why the orthodoxy put down the muon theory & shut down the entire line of inquiry. Is Eric Weinstein right? Have physicists become corrupt? Or were Pons & Fleischmann just frauds?
#geometric-uni... |
I'd like to know whether the blood flow is pulsatile in small capillaries present in tissues that lie away from the heart.
From the literature, I understand that the Womersley number can be computed to find out if the flow profile will be pulsatile. Also, at small values of Womersley number, the flow becomes Poiseuille... |
This question of mine is regarding some general observation. From ray diagrams it can easily be concluded that using a real object, we cannot get a real image from a plane mirror. But, if we shine a torch on the mirror we see a real image on the wall. Why does a real image form despite ray diagrams showing they do not ... |
Let us say we have a simple purely resistive DC circuit. When we flip the switch a current starts flowing which after some time becomes constant. Now, I know that the electric field across difference components (wire and resistance in this case) is different and results in a net uniform current across the circuit. My q... |
It is easy to see how light propagating in a dense medium destructively interferes laterally and constructively interferes in the forward direction. This is why light will travel forward in such a medium but wont scatter laterally. This phenomenon is usually shown using a diagram like this one
or this one
However in ... |
A wire carrying a current $I$ is placed in a region of uniform magnetic field B, as shown in the diagram.
The direction of the field B is out of the page and the length of the wire is L. What is correct about the direction and magnitude of the force acting on the wire?
As you can see I chose B as my answer due to the... |
Sorry if this is a simple question, I did my research and couldn't find much.
The equation for thermal diffusivity is: $a = \frac{k}{pc_p}$
Where $k$ is thermal conductivity, $p$ is density, and $c_p$ is specific heat capacity.
The title pretty much says it all; Why does SHC have any effect on heat transfer? Say you ha... |
While studying the book Heat and Thermodynamics by Zemansky and RH Dittman, in the topic 'equation for a hydrostatic system' (page no. 88) it was given
in equation 4.12, when we take Pressure P constant, how the dv/dt (marked in red sqaure) got converted into partial derivative? (marked in red square)
|
How can I relate the eigenvalues of $H=\hbar\omega(a^\dagger a+1/2)$ to the eigenfunctions of $H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2 x^2$, with $p=-i\hbar\nabla$? I mean, how the analytical approach to the solution of this problem can be related to the algebraic one, obtaining a 1:1 correspondence between the solutions... |
Why do electrons form shells/clouds around nucleus? If electron is negative charge and protons in nucleus are positive they should attract each other and as a end result stick in one place?
Second question (an I think it's related) is about ionic bonding. I think this is most popular example:
But why does the electron... |
Definition according to lecture note:
Positive work means that the surroundings do work to the system
If heat enters the system, then it is positive
Consider the following heat engine diagram:
My understand is that
$q_1>0$ because heat enters the system (the cycle).
But why $q_2<0 \Rightarrow -q_2 >0$? Heat should ... |
I started with the Hamiltonian of coupled oscillators in a circular lattice(with $m=\hbar=1$ and $x_{a+N}=x_{a}$)
$$H=\frac{1}{2}\sum_{a=0}^{N-1}\left[p_a^2+\omega^2 x_a^2+\Omega^2\left(x_a-a_{a+1}\right)\right]$$
Then I used the normal-modes
$$\tilde{x}_k\equiv\frac{1}{\sqrt{N}}\sum_{a=0}^{N-1}\exp\left(-\frac{2\pi i... |
In his his book "Gauge Fields and Strings" Polyakov introduces the compact QED on a cubic lattice in 3D Euclidean space as:
$$ S\left[ \left\{ A_{\mathbf{r},\mathbf{\alpha}}\right\} \right]=\frac{1}{2g^2}\sum_{\mathbf{r},\mathbf{\alpha},\mathbf{\beta}}(1-\cos{F_{\mathbf{r},\mathbf{\alpha}\mathbf{\beta}}}) $$
Where $F$ ... |
1. Defining TFTs
Let $n$ be a positive integer and $\mathbb k$ be a field.
In my lecture I was introduced to TFTs using the following definition going back to Atiyah (around 1988):
A $n$-dimensional, oriented TFT is a symmetric monoidal functor $$Z: Cob_n \rightarrow vect(\mathbb k).$$
The cobordism category $C=Cob_n... |
I'm searching particle accelerators. I couldn't see focusing magnets in Linear accelerators. When we need focusing magnets in Linacs? I'm sharing some photos of what ı found.
|
In Introduction to Solid state physics 8th edition by Charles Kittel. The scattering amplitude is defined as, $$F=\int dV n_G exp[i(\bf{G-\Delta k}).\bf{r}]$$ where G is the reciprocal lattice vector and $\Delta k$ is the scattering vector. It goes on to state that when $\Delta k \neq G $ the integral goes to zero. Can... |
Lasers are coherent beams so they can be totaly cancelled out if applied a source out of phase of 180 degrees. So the question is simple... do two different coherent lasers of same luminosity when pointed at a point sometimes produce a more destructive and sometimes a more constructive interference depending just on ti... |
I've been trying to establish for a while whether the angular distribution of scattered energy from a small sphere (relative to the wavelength) is azimuthally symmetrical about the $E$-vector of the impinging photon/wave.
People often offer a $\sin^2\theta$ dependence, but I understand that this refers to the angle bet... |
I have just learnt quantum physics in school and learnt the concept of wave-particle duality.
But I still have trouble understanding what the de Broglie wavelength is. What does it mean for a particle to have wavelike properties? If everything is a wave then why don't we just phase through one another?
There's also a q... |
I was learning about spherical abberation and in my book
it is written that when parallel rays pass through lens marginal rays (which are far from principal axis) are bent more than paraxial rays(closer to principal axis)
(considering only thin spherical
lenses)
i am not able to find any explanation of this, and i feel... |
I am reading Wayne Hu's short lecture on cosmology mathematical infrastructure (https://arxiv.org/abs/astro-ph/0402060), and have several questions.
Some background for us lazy people that don't want to open the link:
Wayne basically shows us how to quickly count the number of degrees of freedom, using a couple of meth... |
This might be a stupid question, but why is the normalization of the Gell-Mann matrices (basis of the $\mathrm{su}(3)$ Lie algebra) chosen to be
$$\mathrm{trace}(\lambda_i\lambda_j)=2\delta_{ij}$$
instead of just $\delta_{ij}$ without the factor $2$? In most of linear-algebra, basis vectors are normalized to $1$ (or no... |
I'm reading Fetter Walecka on many body theory (Chapter 7). We have established the from of the many body green function
\begin{equation}
G(xt,x't')=\langle T \psi(xt)\, \psi^{\dagger}(x't')\rangle
\end{equation}
in the Lehmann representation
\begin{equation}
G(k,\omega)=\int_0^{\infty}dE \, \frac{A(k,E)}{\omeg... |
I refer to LF Abbott's "Introduction to the background field method". The background field generating functional is
$$ \tilde{Z}[J,\phi] = \int \mathcal{D}Q \exp i[S[Q+\phi] + J.Q], \text{ where } J.Q := \int d^{d}x J(x) Q(x).$$
The generator of connected diagrams is:
$$ \tilde{W}[J, \phi] = -i \log \tilde{Z}[J,\phi]$... |
Context:
I'm creating a simulated VR billiard game and trying to get the physics as realistic as possible. I have a cue ball being hit with a cue across a surface with accurate friction values calculated from real-world trials.
Question:
According to this source:
Angular velocity equals of a moving ball:
$$w = \frac{5... |
Let's consider a case where observer AB (let's suppose 'you') are standing on the radius of curvature of a concave mirror . The point A is your eye (as shown in the figure) and with the help of the ray diagram we can see that the image A' of the eye is formed exactly below the point A and at the same distance from the... |
Let's say there is a spacecraft flying near a planet. It just flies near without orbiting the planet. Its trajectory changes as a result of planet's gravitational pull.
Does the planet do any work?
|
I spent the last 2 hours reading up on Feynman's path integral formalism of quantum mechanics. Now, I have a few questions, which are rather very simple, but since unconventional (or maybe silly) are not present in any text that I could find online.
Define the propagator of a quantum system between two spacetime points... |
I have read this question:
Why do turbine engines work?
The compressor generates a certain volume of air at a high pressure. In the combustion chamber, this air is heated - this leads to a much larger volume of air.
Looking at a section of the turbine (tapering to smaller section as compressor stage approaches combust... |
If I understand the relativistic explanation of gravitation - that it is curvature of spacetime - then a particle left alone will travel along that curved spacetime in a path that depends on the local curvature at each instant in time (right?). If so, then the orbit of a small body without significant effects on that ... |
why the deflection(why there is change in direction) increases with increased current in a straight metal conductor ?
in figure 2 , the magnetic fields are closely packed due to high current but still the deflection would remain the same. But why do we say that the compass deflection is by more angle
|
I have a question following the derivation of the Klein-Gordon equation from a lagrangian. From
Eq. (13d), where does $\delta^\mu_\nu$ come from? I guess it's a conversion factor of some sort.
|
Fermat's principle states that light always takes the path for which the optical length is stationary.
\begin{align}
\delta\int n(\vec{r}) \:\mathrm ds = 0.
\end{align}
Furthermore, it is equivalent to Huygens' principle. Huygens' principle states that each point on a wavefront is the source of a new spherical wave. Hu... |
In the Double Slit Experiment for electrons could be possible the use of an appropriate laser pointer at one slit aiming up so when an electron passes through that distinct slit it get scattered up so its picture on the screen will show up in the upper part. The question that arises: will the electron path probability ... |
I'm standing at a safe distance from a black hole and I'm in an Earthlike time frame of reference. Through my telescope I see a man starts to fall towards the black hole. I have looked at this question but it doesn't quite get to what I'm looking for.
I watch him accelerate towards the black hole until I know that he ... |
Kinematic theory and dynamical theory of x-ray (or electron) diffraction. Why such names are given to scattering theories ? Does it have any connection to Kinematics (of Galileo) and Dynamics (of Newton) of general physics?
|
The heart of my question is below in bold. The rest is clarifying information or additional points of discussion - in case my assumptions are the heart of my misunderstanding.
In a two body attractive quantum mechanical system (namely the simplified Hydrogen atom - ignoring spin etc.), it can be shown that this reduces... |
I know from my OL chemistry and physics classes that the reading of a liquid volume should always be taken from the bottom of the meniscus, but isn't this an underestimation of the real volume. I mean there's some water sticking upward to the surface of the container and, say, if these water fell and made a flat surfac... |
For something like the hydrogen atom $V(r)\propto{r^{-1}}$. And there are energy levels described by the equation
$$E_n=-\frac{m_ee^4}{8\epsilon_0^2h^2n^2}$$
that indicate where orbitals are allowed. As understand it $V(r)\propto{r^{-1}}$ for any pair of electric charges, not just for the hydrogen atom.
I was wonderi... |
If $\nabla\times\nabla\times \mathbf{F} = 0$, then can we say that $\nabla\times \mathbf{F} = 0$?
If yes, then how to prove it?
|
Let's say that an ideal gas does work on a piston, thus increasing the volume of the gas in its insulated cylinder. The pressure of the gas is assumed to be constant; therefore, by the ideal gas law, $PV =nRT$, the temperature of the ideal gas should increase.
Now let's look at this problem from the angle of the First ... |
This has puzzled me quite a bit . To illustrate my doubt we can take a situation where I take a block and an ideal spring and hang them in a vertical line the spring attached to the ceiling .(the spring is in its natural state initially)
Now if I were asked to find the maximum elongation of this spring.
My initial app... |
If I consider a fluid which rotates as a rigid body, then the curl of the velocity field is $2\vec\omega$ where $\vec\omega$ is the angular velocity of the rigid body, but let us assume that we are considering a fluid which does not rotate like a rigid body. According to my book, $\nabla\times\vec{v} = 2\vec\omega$ is ... |
I have seen in several sources that by invoking Lie groups, $$e^{\alpha_1 g_1+\alpha_2 g_2 + \dots} = e^{\beta_1 g_1}e^{\beta_2 g_2}\dots $$ where $g_i$ are elements of a Lie algbera.
For example, take the two-mode squeeze operator in quantum optics:
$$e^{-\xi\hat{a}\hat{b}+\xi^*\hat{a}^\dagger\hat{b}^\dagger} = e^{-\f... |
My understanding of renormalizability is that a theory is renormalizable if it the divergences in its amplitudes can be cancelled out by finitely many terms. I see that by adding counterterm (in the MS-bar scheme)
$$L_{ct}=-\frac{g^2}{12\pi^2}\left(\frac{2}{\epsilon}-\gamma+\ln4\pi\right),$$
the one-loop divergence of ... |
Hoping this is a quick question. But lets say two blocks traveling equal and opposite directions, equal speeds and mass, were to make contact and slide past each other. Lets say they were long enough or slow enough that this would cause them to stop.
All the kinetic energy would become heat I know. But looking at this ... |
The following Lagrangian density describes a charged scalar field. Determine the global U(1) symmetry. Make this global symmetry local and give the Lagrangian density. The Lagrangian density is given by: $$L = \partial_\mu \psi \partial^\mu \psi^* - \frac{1}{2}m^2|\psi|^2 - \frac{1}{4}\lambda|\psi|^2.$$
My first idea... |
I'm curious how would one calculate the shape of the orbit around irregular objects (let's call them asteroids).
How do you tackle this problem? How do you write down basic equations?
In classical mechanics we only mention very simplified problems and the force is always central. But what happens if the asteroid is not... |
Consider the free Maxwell Lagrangian density:
\begin{align*}
\mathcal{L} = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu} + \frac{m^2}{2}A^{\mu}A_{\mu}
\end{align*}
Where we added a mass contribution $m$. And sign convention $(+,-,-,-).$ Now my question is:
How can one find all the values of the mass $m$ for which this Lagrangian d... |
Given two disks D1 and D2. Their radii, positions, and velocities are known. How can I predict whether they will collide or not? For a head-on collision, the angles that the directions of motion make with the x-axis add up to 180 degrees. But I don't know what is the condition for an oblique collision. Any help would b... |
Related questions..
How does the Sun's gravity extend out millions of miles to influence the far reaches of our solar system?
Reference: movie - "Interstellar", 2014 Nolan) / How does a ship avoid strong gravitational effects of a supermassive blackhole while orbiting a planet that is within range of those effects. Sce... |
Could a transparent slab coated with photosensitive film be placed inside a pinhole camera nearly paralel to the path of the light emitted by a source of light(star) to produce a picture wich due to the explained position of the slab looks very elongated along one its dimension.Ofcourse it would be ideal to have enough... |
The helicity is defined as:
$$h=\frac{\vec{S}.\vec{p}}{||\vec{p}||}$$ where $$S= \frac{\hbar}{2} \zeta$$ and $\zeta$ equals
\begin{pmatrix}
\vec{\sigma} & 0\\
0 & \vec{\sigma}
\end{pmatrix}
where $\sigma$ is equal to the Pauli-matrices.
I have to prove that $h$ is conserved, the way I wanted to do this is by showing th... |
This is not a question per se -- I am trying to recall an example from a lecture long ago about the inconsistencies that arise when you try to use QFT with Newtonian gravity.
It involves an electron-positron pair falling side-by-side in a uniform gravitational field, and from QED we have the $e^+e^- \rightarrow 2\gamma... |
Consider the astronaut as floating in the middle of the "Kibo" (ISS module) without him having any initial motion. The module has a diameter of 4.2 m (inner), and the goal is to reach any of the module's walls by only blowing air through his mouth. Is it possible for him to reach any wall? If it is, how long would it t... |
It seems like, as a flow becomes more turbulent, there should be more possible states in the fluid. Shouldn't that correspond to an increase in entropy? Steam tables seem to only depend on temperature and pressure and not Reynolds number.
|
I'm trying to consider relativistic multi-body dynamics in special relativity. In classical mechanics, it's easy to write a simple $n$-body system with arbitrary potential $V$:
\begin{equation}
m \ddot{x}_ i=\sum_ j - \nabla_ {x_ i} V(|x_ i-x_ j|). \tag{1}
\label{1}
\end{equation}
In special relativity, it's tempting t... |
I have been reading up on time evolution methods using matrix product states. Reading from Schollwoeck's notes on the density matrix renormalization group, (https://arxiv.org/abs/1008.3477), I looked at the tDMRG and TEBD methods, and the comparison thereof (section 7.3.3). It is noted that tDMRG advances the two activ... |
I know there are a lot of similar question but I don't believe this to be a copy. I understand that if two people lived far away they could not transfer information through quantum entangled particles because forcing a particle into a particular spin breaks the entanglement and simply observing the particle to collapse... |
For rigid bodies, all the particles can have different linear velocities but the same angular velocity, so it makes it convenient to talk about the angular velocity instead. From there, we get to ideas like angular momentum and torque, which work the same way for angular motion as momentum and force do for linear motio... |
I know that the torque experience by a current carrying loop in a uniform magnetic field is given by Torque $= MB$ where $M$ is the magnetic moment of the loop. In my book, the derivation was provided only for a rectangular loop and was given that it can be extended to other loops as well.
But intuitively when I try to... |
An object is in free fall when the force acting on it is exclusively gravitational. But why then is the moon in free fall? Isn't there a centrifugal force acting on it?
|
An specialist in quantum information asserted that "entangled photons will never show an interference pattern", but that seems to contradict the response to another question I made here. He asserted that because which-path information is available to Alice (even if for a moment) the interference pattern cannot form bec... |
So, the diagram above shows two electrically charged particles, X and Y, being simultaneously fired horizontally with different speeds into an electric field at point P. The horizontal initial velocities are orthogonal to the external electric field. I want to know whether the masses and charges are the same or differ... |
Electromagnetic fields, masses, etc are absent. I can see that the converse of this statement is true (the frame becomes Galileian). The proof becomes trivial if gravitational field can be treated as a $3D$ vector i.e $g(x,y,z,t)=g_x i +g_yj+g_zk$, but I remember reading another PSE answer that says this is not always ... |
In the picture below, the three principal light rays are drawn refracting through the lens , forming an image on the other side. But which path does the light actually take? That is , if i place my eye where the image is said to be forming will I see light coming from the top ray, the middle ray or the bottom ray? It s... |
Electromagnetic waves are frequently described as "self-propagating", implying a mode of propagation distinct from that of electrostatic fields; but as I understand things, both have strength proportional to the inverse square of the distance from their source. Let me lay out what one ignorant of wave propagation and i... |
In the context of applying operators to find expectation values; is the 'complex conjugate' of a wave function, $\psi^*$, where $\psi$ has no complex numbers, just simply itself? For example, given the wave function:
$$
\psi(x)=\sqrt{\frac2L}\sin\biggl(\frac{2\pi}Lx\biggr)
$$
Is this set up to find the expectation valu... |
Consider a space aircraft. During its propulsion, I believe a lot of heat is transmitted to the aircraft by simple contact with the motor. But in space, there is no air to cool the aircraft. The only way to remain cool is by radiating infrared to the space. I believe that the corresponding equilibrium temperature is ve... |
In the general theory of relativity, the speed of light in vacuum is $c$. In the special theory of relativity, a postulate is made that the speed of light is the same (called $c$) in all inertial frames.
Consider the following statement:
"The speed of light is $c$ in all inertial frames but it can vary in accelerating... |
I'm trying to get a better understanding of "quantum psuedo telepathy." It seems as though all games that can be won with entanglement simply exploit coordination.
In any of these games, what stops me from pre-determining a random seed and just playing the game with that seed?
Is there really nothing special about thi... |
The problem reads:
An infinitely long thin wire carrying a uniform linear static charge density $\lambda$ is placed along the z-axis. The wire is set into motion along its length with a uniform velocity $\vec{v}$ = v $\hat{k}$. Calculate the poynting vector $\vec{S}$ = $\frac{1}{\mu_o}$ $(\vec{E} \times \vec{B)}$ at a ... |
We can distinguish semiconductors from metals by saying that metals still conduct at absolute zero whereas semiconductors don't.
Does this still apply to doped semiconductors which have an excess of electrons or holes? What happens to these charge carriers at absolute zero? Why can't they be freely moving the way elect... |
Whilst reading the quantum.country essay by Michael Nielsen and Andy Matuschak, they mention (a bit further down from here) that there is formulations of QM that can completely ignore global phase factors - which feels natural, as they are completely non-measurable in reality, and their only application (as far as I kn... |
How are the two different? I know that CC has negative pressure and opposes gravity. But what about VED? Is VED supposed to have positive pressure and cause gravity too?
|
It seems to me you can put a heater on without expelling cold to the other room like an air conditioner and freezer would. Is there a way to reduce heat locally by slowing down molecules for example?
Even if it cannot be done at a big scale, could laser trapping be used to achieve the freezing of an entire object?
Edit... |
I am studying the divergence of the current density and it is said that it is zero if the volume charge density is constant. Can anyone explain me why?
|
While going through the derivation of how to calculate the pressure of an ideal gas we consider only the translation of molecules. Why don't we take into account that the molecules may rotate and vibrate which may change the pressure of the gas under consideration?
Here is the link of the derivation
|
Sorry for asking this simple question, but really I couldn't find a good document discuss what I need exactly.
I am implementing a flight simulation, but my question is related to physics rather than aerodynamics so I find to ask the question to physics experts.
Suppose that I am having a cuboid (Simple form of the pla... |
The following Lagrangian density describes a charged scalar field. Determine the global U(1) symmetry. Make this global symmetry local, give the Lagrangian density and show that this is Gauge invariant. The Lagrangian density is given by: $$L = \partial_\mu \psi \partial^\mu \psi^* - \frac{1}{2}m^2|\psi|^2 - \frac{1}{... |
The addition of foreign particles reduces the surface tension between particles of the substance under observation.
This is something we accept and something that makes common sense.
But how do we explain the common observation that soap water has higher surface tension than pure water
, considering it's ability to for... |
I have implemented a method for simulating a point source located outside of a shew-box room in vacant space and I wish to compare the resulted impulse response (IR) with a more accurate one. Is there a free simulation program in which I can easily build such a scenario and calculate the IR with a very long, very accur... |
Let us suppose we have an harmonic oscillator hamiltonian, with a controlling term $xu(t)$:
\begin{equation} H(t)=\frac{1}{2}m\omega^2 x^2 - u(t)x \end{equation}
As stated in "A. G. Butkovskiy and Y. I. Samoilenko, Control of Quantum-Mechanical
Processes and Systems" an optimal $u(t)$ in order to maximize the probabili... |
Let's say I have an ideal open circuit (i.e. there's no resistance in the conductors) containing only a charged capacitor and then I close it. Now, the charge on one end of the capacitor will move to the other end until the voltage drop on the capacitor is zero. What confuses me is that if I try to apply Kirchoff's vo... |
As iron reacts with magnets producing a field dependent on magnet's pole orientation should an iron sphere when covered with little magnets which nord poles aim towards the center of the sphere become nothing less than a monopole with spawning south poles lines outwards?
|
I'm reading about gravitational waves and I'm wondering how we know we can always go to the transverse and traceless gauge? Going to the de Donder gauge is fine, I can follow that, but then showing that we can always go to traceless part and also have $\bar{h}_{0\mu}=0$ I don't follow (where I have defined $\bar{h}_{\m... |
Consider the First Law in Physics:
$$ dq = du + dw $$
Here dw refers to work done by System.
In Chemistry the First becomes:
$$ dq = du - dw$$
Here the work is the work done by surroundings .
In ideal cases - massless piston , work done by System is equal to the work done by surroundings.
Now I am aware that above laws... |
I saw this video on YT and what I can not figure out is why the coil used in the arrangement could not be replaced by a hollow magnetic torus?
|
Is the only difference due to leap seconds, etc. or other differences between UTC and updated forms of universal time, such as UT1? In other words, are all earth-centered inertial (ECI) coordinate frames constructed on purpose so they match at approximately midnight each day, and if so, how big of a difference could t... |
Suppose we have a mass that is being accelerated in empty space. Say by pulling on it by an accelerating rocket. This rocket is non-rigidly (say by a spring with spring constant $k$ and length $l$ when not stretched) connected to another rocket which gives the accelerating system behind it an acceleration.
The accelera... |
Recently my teacher taught me about Energy density(Energy per unit volume) and told us the formula for the same.
This was explained by taking "Energy" as Energy of a parallel plate Capacitor and dividing it by the volume contained within the capacitor.
And after this I was explained to integrate the Energy Density time... |
I'm trying to derive Eq. (10.17) & Eq. (10.18) from the textbook. Where does the term
-1/(4*pi) come from, and how do I cancel out the rest of the term (see my text, second picture).
|
Deriving the geodesic equation
$$ (\nabla_u u)^\mu = 0 $$
one uses the variation of proper time $\tau[C]$ along $C$
$$ \delta \int_C d\tau = \int_C d\tau \, g_{\mu\nu} \, \delta x^\mu \, (\nabla_u u)^\nu \qquad (1) $$
with arbitrary infinitesimal variation $\delta x$, 4-velocity $u = \dot{x}$ along $C$ and parallel tra... |
If we have the quantum fidelity function between two states as:
$F(\rho, \sigma)= (Tr \sqrt {\sqrt {\rho } \sigma \sqrt {\rho }})^2$
how we can calculate the gradient/derivative of the function with respect to only one of those two states (e.g. $\sigma$)?
|
What is the reason behind solubility of gas in water(closed vessel)? Actually gas tends to move freely, then why it restricts its motion by its own by getting dissolved?
Also, why whole gas doesn't get dissolved in water in a closed vessel of gas and water?
|
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