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According to Einstein's mass energy equivalence equation,
$$ E = mc^2$$
where $m$ is the rest mass and $c$ is speed of light.
According to Planck's equation,
$$ E=hv$$
If Planck's equation suggests that energy can only come in discrete packets, and if mass is equivalent to energy, then wouldn't this mean mass only come... |
In the Quantum Field Thoery of Many-Body Systems book by Xiao-Gang Wen, he introduced the Bogoliubov's transformation in the first equation of page 74 as following:
$$
\alpha_k = u_ka_k + v_k a_{-k}^\dagger
$$
with $|u_k^2|-|v_k^2|=1$. Then he said in the next page that
$$
a_k = u_k^* \alpha_k - v_k^* \alpha_{-k}^\dagg... |
I don't really know if the question is too stupid to be answered, so I apologize in advance, but I'm really confused about it.
I did an introductory course in General Relativity and studied hard for it, so I should be familar with these concepts, but turns out that I'm actually not.
Consider for example a field $\bolds... |
Because I could not understand the term "virtual displacement" properly I have too much questions with it. I will be helpful with your answer. My question:
Can we imagine a virtual displacement for a simple pendulum? Is it possible to have virtual displacement for the system?
If yes: then what will be its virtual displ... |
I was going through a text and it said that
The mean momentum $p$ of a nucleon in a nucleus of the mass number $A$ and atomic
number $Z$ depends on $A$ as $$
P\propto{A}^{-\frac{1}{3}}.
$$
All that I know is that the radius of the nucleus is proportional to mass number as $$
R \propto A^{\frac{1}{3}}.
$$ From here h... |
In what sense do sub atomic particles have a size? Or are they better understood as points?
If a quark has a size, and a radius - would you expect that if an event happened to the left of a quark, the left side of the quark would receive information before the right side?
Similarly, if you think of particles as waves o... |
It is said that the speed of light increases when moving from optically denser medium to rarer medium but
as light can be considered as a particle how does it get the energy to increase it velocity
|
Mathematically, in string theory, branes can be described using the notion of a category and the mathematical
category theory says that logic can change from one category to another. We can build categories fundamentally described by classical logic, other categories by quantum logic, other categories by intuitionistic... |
Consider the following figure:
Let us suppose we were at some point in gaseous phase. Can we go from gaseous to liquid phase by moving about critical point continuously?
Why isn’t any critical point in solid liquid coexistence curve? Can we move from liquid phase to solid phase continuously? If yes, how? And if not, w... |
For simple harmonic motion in a non-inertial frame is amplitude same on both sides? As in one direction pseudo force supports acceleration due to spring and in another direction it opposes acceleration due to spring. So how will it affect the amplitude of this motion?
|
When reading Sterile Neutrinos as Dark Matter it is stated (on page 5) that the formula for the Hubble expansion rate is
$$H= \frac{1.66 g_*^{1/2} T^2}{m_p}$$
where
$g_*=10.8$
$T$ represents the temperature of the universe
$m_p$ is Planck's mass.
I am trying to solve an equation How do I integrate and apply limits to... |
Maybe this is more of a reference request, but I'd also like an explanation of the example (if there is one). An answer with just a reference would suffice though.
Simply put, are there any known $(2+1)d$ QFT's with fermion matter in which a pure Chern-Simons field is the cause of a $0$ form symmetry spontaneously brea... |
I was watching a waterfall in the Austrian Alps. There were thousands of water droplets falling down, splattering on the stones below. I thought - how does nature find out so quickly where each droplet of water should go?
To find out what happens to a falling droplet of water, one can use the laws of motion and calcula... |
I was making coffee for myself, when I observed that when I poured coffee from the frying pan (having curved edges), the fluid went directly into the cup without falling; but when I transferred coffee from one cup to another at a particular inclination, the fluid ran down the edge of the cup in straight line rather tha... |
Let me define two complex-valued functions as follows:
$$
\psi_1(r_1,\theta_1)=r_1e^{i\theta_1}\\
\psi_2(r_2,\theta_2)=r_2e^{i\theta_2}
$$
By the Born rule I can calculate the probability density, a real-value function, as follows:
$$
\begin{align}
P(r_1,r_2,\theta_1,\theta_2)&=|\psi_1+\psi_2|^2\\
&=|r_1e^{i\theta_1}+r... |
I was knowing that the current is inversely proportional to resistance but recently i read that resistance has effect on voltage only and it doesn't have an effect on current because the current depends on the number of electric charges in motion but voltage is related to the energy of these charges. What is the explan... |
I've googled the heck out this (as a non-physicist) and found a ton of similar questions answered but did not find anything that made the light bulb go on. I don't think I'm a crank, so here it goes.
Overview
When one object exerts a force an another and they do not move, the net force is zero. I agree. But intuitively... |
I am trying to understand the solution to the infinite square well centered at zero in Principles of Quantum Mechanics by Shankar. Here is how it goes:
Inside the well (region II - Outside left is I and outside right is III) the solution is that of the free particle:
$$\psi_{II}(x)=Ae^{ikx}+Be^{-ikx}$$
$k$ has the obvi... |
When you have a sphere and a hoop on an incline, the sphere will always roll down faster because of the smaller moment of inertia. And this is the case no matter the angle of the incline. But what if the angle is $90^\circ$ (basically freefall). Shouldn't the sphere again get to the ground faster ((because the angle of... |
In this paper:
J. Wang, X. Wen and E. Witten, "A new ${\rm SU}(2)$ anomaly", J. Math. Phys. 60 (2019) 052301, arXiv:1810.00844,
it says the following in p.2,
It says for $3+1$ dimensional spacetime, the Weyl spinor with $SU(2)$ isospin $1/2$ , "Lorentz signature always carry a real structure; if a fermion field app... |
I'm trying to figure out how a humidity sensor using a Capacitor works, and every document I have managed to find seems to come to the conclusion that an increase in humidity causes the capacitance to increase Linearly.
However, I haven't been able to find a direct "formula" or dependence between humidity and dielectri... |
Consider a thin spherical conducting shell of radius $R$, which carries a total charge $Q$ on its surface.
Two point charges $Q$ and $2Q$ are at A and B respectively as shown in the figure ($C$ is the center of the shell).
If now the shell is earthed. How much total charge will flow into the earth ?
My attempt: Initia... |
To introduce the $pV$ work integral, my physics textbook gives me the classic setup of a vertical piston (which has face area $A$) with a gas of pressure $p$ and initial volume $V_i$ (please see the image for the exact setup). On the piston is lead shot which exerts a downward force. The force exerted by the gas is giv... |
I'm trying to understand the effect on a system when a voltage of a system is measured by connecting a voltmeter.
For example let's say we are trying to measure the voltage of a Li-ion battery. The junction is as follows:
Lead(Nickel alloy) | Current collector(Copper) | Anode active material(Lithium-intercalated graphi... |
Are there any physical processes of which we have a full understanding? For instance, we know that each orbit has a different energy, and electrons can move to a higher orbit by absorbing energy and drop to a lower orbit by emitting energy. However, do we understand everything related to atomic orbits? For example, wha... |
I'm looking for some help understanding quantum entanglement experiments and expected vs actual outcomes.
We have pairs of spin entangled particles separated by large distance (so $2$ locations). The spin of these particles is "indefinite" or unknown, Now I decide to start measuring at one location. I place my detector... |
If a slim conductor of some length $l$ and diameter $d\ll l$ is placed in a magnetic field $B$, and the field is changed by $\frac {dB}{dt}$, what (if any) is the voltage $V$ induced across the ends of the conductor?
In my case of interest, the slim conductor is a wire, fixed in space, that is victim of interference by... |
I've done some preliminary reading on how Tollmien-Schlichting waves play a part in these perturbations, but is there a formula that connects sound frequency with the transition stage?
|
Complex numbers are often used in Physics especially in Electrical Circuits to analyze them as they are easy to move around like phasors. They make the processes easy but it seems kind of amusing to use something which has no other real world analogous meaning to my knowledge being used to solve the most practical real... |
For a linear and non-dispersive medium $\vec{B} = \mu \vec{H}$.
So amperes circuital law in integral form (without Maxwell's correction term) can be written in two ways
$\oint_C \vec{B}\cdot\vec{dl} = \mu \int_S \vec{J}\cdot \hat{n}dS$
and
$\oint_C \vec{H}\cdot\vec{dl} = \int_S \vec{J}\cdot \hat{n}dS$
Both of them wor... |
As my textbook stated we use a convex lens of small focal length $f$ to keep an object at a distance such that the image is produced at a distance $D$ (our least distant clear vision point is around $25\ {\rm cm}$).
Then the magnification that comes assuming non-marginal rays is $1 + \frac{D}{f}$.
Why can't we keep red... |
In the double slit experiment (with electrons), physicists wanted to know which of the two slits the electron passed through. Of what use is knowing which slit the electron passed through?
|
I am interested in how the spatial and temporal spectral exponents – in other words the exponents of the power spectrum and eigenspectrum – of a high dimensional system at criticality are related. It is known that the dynamics of complex systems operating at criticality (I am working with neural data but this may also... |
The ideas of dark matter and dark energy are mind blowing.
Why is it said that dark matter overcomes dark energy in galaxies but it loses the battle in intergalactic space? In other words, why is dark energy dominant between galaxies but not inside galaxies?
|
Can we calculate the time when the Tower will lean to the extreme point that its center of mass will be out of its balance...?
|
Throughout this whole question, I will be referring solely to single element solids. According to band theory, ns and np bands are close enough in energy to overlap and create one band with 8N states available to fill. This band then splits into two 4N bands when the interatomic distance between atoms in the solid incr... |
Does it mean adding really small pressures on one side of the particle and subtracting from the other side to cancel out?
Also, what's with the delta sign and it's reverse? What's it called? (Sign on the lhs and rhs)
|
The slant block(M1) is placed on a horizontal surface, and there is an object(M2) on it.
There is no friction between objects。If a horizontal force(F1) is applied to the inclined block，
So what happens between objects。
How does horizontal force affect objects above。
Objects(M2) are subject to gravity and support,Is th... |
I am familiar with the common use for "channel" in terms of particle physics (like Mandelstam variables). What confuses me is how it's used in the following paper on QCD:
C. A. Dominguez, "Quark masses in QCD: a progress report", Mod. Phys. Lett. A 26 (2011) 691-710, arXiv:1103.5864.
To be specific, I quote several sen... |
Five identical capacitor plates, each of area A, are arranged such that the adjacent plates are at a distance d apart. The plates are connected to a battery of e.m.f. E volt as shown. The charges on plates 1 and 4 respectively are :
So, I started off this exercise problem by finding equivalent capacitance. Due to ch... |
Let say there is a sharp decrease in current, all the way to zero in a coil connected to a power supply, will the emf induced in another coil placed close to it in a bar form (see first picture) or spike form (as in the second picture).
The red colored ink is the answer, and the black one is my attempt of solution. I... |
I mean if the magnetic field is slightly increasing or decreasing at a place should'nt there be a gradient of iron filings instead of clear lines?
As to me clear lines mean that there is a comparatively strong magnetic area next to a weaker one hence the iron filings are more attracted to that particular area hence for... |
It's known that
In nuclear physics, secular equilibrium is a situation in which the quantity of a radioactive isotope remains constant because its production rate (e.g., due to decay of a parent isotope) is equal to its decay rate.
Secular equilibrium can occur in a radioactive decay chain only if the half-life of the... |
The way it is taught in school, you have a mass moving under the influence of an unchanging potential field. It can be proven that if the mass moves from point A to point B in the field, the increase in its kinetic energy can be calculated by simply subtracting the scalar valued potentials at the two points. So there i... |
I can understand why, if the speed of light is invariant, a photon clock would tick slower. I find this explanation very useful in terms of introducing the idea of time dilation (also because it allows for the Lorentz formula to be derived intuitively, only using Pythagora's Theorem).
But this approach has one importan... |
Background
Consider the familiar setting of statistical mechanics, an assembly of $N=4$ distinguishable gas particles. Let, the total energy be $4E_0$.
The possible ways energy of sharing energy between the particles gives us $5$ possible distributions $D(i)$:
$$\begin{vmatrix}
& 0 &E_0 & 2E_0 & 3E_0 & 4E_0 \\
D(1... |
If $\hat{H}$ is a Hamiltonian or any other operator in matrix form, what is the meaning of:
$$\langle 0 | \hat{H} | 0 \rangle$$
|
I was doing Kleppner-D.-Kolenkow-R.J. and I came across the following problem:-
A pendulum is tied vertically to a car at rest, the car suddenly accelerates at a rate A. Find the maximum angle of deflection $\phi$ through which the weight swings.
MY TRY: I saw the solution of this problem in the book which uses car's... |
It's well known and heavily documented that gravitational and inertial mass are identical.
This has been experimentally tested to many digits of precision.
But nothing I've seen ever describes how they could be different (e.g. linear or non-linear relationship) or what the universe would be like if they were significan... |
If I postulate the principle of relativity and the constancy of the speed of light for every inertial observer can I then prove all SR?
Or do I need some other postulate?
For example: do I need to also postulate the structure of the Lorentz transformations or the Lorentz transformations derive completely only from this... |
I wanted to ask if cast iron can be used as make-shift Electric and magnetic fields (EMF) shield.
For instance, can a frying-pan made of high-quality cast-iron and enamel be used as make-shift protection against laptop EMF?
I tried googling and found materials such as zinc, nickel, copper, steel. But none mentioned iro... |
I have been curious these days about how firefighting helicopters go about refilling their water reservoirs while hovering, and I was wondering,
If the helicopter hovers $5 m$ above the refill stations - the vertical hanging pipe is $5 m$ long. Is it more efficient to have a centrifugal pump at the bottom (at the water... |
Let's assume we have two BTS transmitters. One works with power of $10\ {\rm W}$ and the other with $200\ {\rm W}$. Both transmitters produce the same $2\ {\rm GHz}$ electromagnetic wave.
What's the difference between the two waves from a physical point of view? Just the number of photons? Why is the "wavelength range"... |
In an electromagnetic wave, is the maximum amplitude of the electric field the same as that of the magnetic field? I ask this question which may seem silly because on all the diagrams representing an electromagnetic wave these two amplitudes seem to be equal.
|
We know that for a body to be in equilibrium, the resultant force and resultant torque must be both zero. The question is: can we derive this from more fundamental principles mathematically, such as Newton's laws or Lagrangian formalism?
|
The Dirac equation for an electron in the presence of an electromagnetic 4-potential $A_\mu$, where $\hbar=c=1$, is given by
$$\gamma^\mu\big(i\partial_\mu-eA_\mu\big)\psi-m_e\psi=0.\tag{1}$$
I assume the Weyl basis so that
$$\psi=\begin{pmatrix}\psi_L\\\psi_R\end{pmatrix}\hbox{ and }\gamma_0=\begin{pmatrix}0&I\\I&0\en... |
I'm reading about gravitational waves at the moment (mainly using Maggiore's textbook). In it he gives the Pauli-Fierz action for a massive spin-2 field and the action contains the trace of the field. However, Maggiore argues that the irreps of the Lorentz group are either symmetric traceless tensors, or antisymmetric ... |
If a sphere slides down from rest on an inclined plane of hypotenuse $L$ and height $H$ : Work done by friction is converted into rolling kinetic energy and as well as heat energy.
If $f$ is the friction force then is work done by friction $fL = $Heat energy $+ $ rolling $KE$ ? Or does the formula $fL $ gives only the... |
I am searching for a possibility to see the shallow grounds of water without reflections on the surface.
I am sailing in an area where there are reefs and shallow coral patches which can be dangerous for the boat and its passengers.
Navigating with sight is important. My thought was to see the scenario from above could... |
I sort of understand why KE(com) is not the same as KE(total)... correct me if I'm wrong.. its like when a symmetric body is performing rotational motion even though the COM is not moving it still has (Rotational) kinetic energy. But does this translate to potential energy or can you calculate PE be considering the COM... |
Suppose I have a rod of uniform mass as follows. I'm confused how to pick the moment of inertia for this rod.
One possibility would be to use the formula corresponding to this picture :
$$I = \frac{1}{12} m \ell^2$$
Alternatively, I could use the moment of inertia corresponding to this picture :
$$I = \frac{1}{3} m \... |
If there is a gas in a container with pressure P, then it will exert a force on the walls of the container. By Newton's third law, there should be a reaction force where the container exerts an equal but opposite force on the gas. Does this force exists, and if so, how does it manifest? What does a force exerted on a g... |
Air has a density of about $\mathrm{1.3 kg/m^3}$.
From Carbon aerogels by Marcus A. Worsley and Theodore F. Baumann:
Though silica aerogels held the title of "world's lightest material" for a long time at $\sim \mathrm{ 1 mg/cm^3}$, recently, carbon-based aerogels have shattered that record with a density of less tha... |
This question is regarding the proof of the existence of locally inertial coordinates, outlined in Sean Carroll's Spacetime and Geometry book (Chapter 2, page 74). In particular, I believe that extra factors of $2$ or $\frac{1}{2}$ should be present in the Taylor expansions the proof uses - these are later flagged in r... |
There exist a few relativistic renderings, even videos of this kind of event from the perspective of the infalling object, yet I have never seen the same event from the perspective of a distant observer, with time/space dilation and possibly redshift and other effects modelled in.
Objects getting close to the event hor... |
According to this paper:
Claudia de Rham and Andrew J. Tolley, "DBI and the Galileon reunited", JCAP 1005 (2010) 015, arXiv:1003.5917.
around equation (1)-(2), the DBI action
$$S = \int d^4 x\Big(-\lambda\sqrt{1 + (\partial \pi)^2} + \lambda\Big)\tag{1}$$
is invariant under the non-linearly realized symmetry whose in... |
When using the ideal gas law and other equations, are we assuming that the gas has uniform pressure (i.e. the pressure does not vary inside the gas)?
|
This question has to do with analyzing how equipartition sets in for a system such as a coupled harmonic oscillator system.
Take, for example, a system as shown in the figure:
$\xi$ denoting the coupling strength; $\xi \ll 1$ indicates weak coupling" /> I now excite the system by giving a small displacement $ x_0$ to... |
When someone travels really fast, do things seem to slow down around him or
do things go faster around him?
|
For a body rolling with a constant velocity, there is no friction between the surface and lowermost point of the body, as there is no relative velocity between the body and the ground when it is rolling and no slipping. But if the body is accelerating with the help of another body or something, then the frictional forc... |
From David Morin's Classical Mechanics, problem 5.4
A massless string of length $2L$ connects two hockey pucks that lie on frictionless ice. A constant horizontal force F is applied to the midpoint of the string, perpendicular to it (see Fig. 5.20). By calculating the work done in the transverse direction, find how mu... |
I am trying to calculate the Von Neumann Entropy of a quantum state.
Given a state $ | \psi \rangle$, I am calculating the Von Neumann entropy by doing the following:
$$ S = -\mathrm{tr}(\rho \ln(\rho)) = -\mathrm{tr}(|\psi \rangle \langle \psi | (\ln (|\psi \rangle \langle \psi | ))$$
If our original state $| \psi \ra... |
If we were to start with the delayed choice quantum eraser setup in the attached image, what would the interference pattern look like for the photons at D0 if D3 and D4 were eliminated (and the two beam splitters that feed them) and the beam splitter configuration between D1 and D2 was altered so that 75% of the photon... |
At this exercise, the equation given in the textbook solution is:
$$I\ddot\theta = l_2u-k_1\theta l_1^2-k_2(l_2\theta-y)l_2\qquad (1)$$
$$m_2\ddot y=k_2(l_2\theta-y)\qquad (2)$$
Now, I can't figure out the following terms:
$-k_2(l_2\theta-y)l_2$ in equation (1). Why the displacement $y$ is subtracted from $l_2\theta$... |
I am trying to make sense of the underlined notes above. I don't understand how did the term $$\Large e^{-2i\frac{E_k t}{\hbar}}$$ got cancelled out? I understand the wave k function times its complex conjugates normalized to $1$, but I am puzzled with the coefficient terms.
Many thanks!
|
If I throw a stone in the air,how does earth know that it(stone) needs to be pulled. My point is are the rules of physics contained inside every single particle? Or is there a central body checking the conditions every single frame and then doing the respective actions?(here frame means periodic update of the universe ... |
In the Wikipedia site for Lagrangian (field theory) the Lagrangian density for Newtonian gravity is given by
$${\cal L}(\mathbf{x},t) = \frac{1}{2}\rho(\mathbf{x},t)\mathbf{v}^2 -\rho(\mathbf{x},t) \Phi(\mathbf{x},t) – \frac{1}{8\pi G}(\nabla\Phi(\mathbf{x},t))^2$$
I understand how variation of this Lagrangian leads t... |
A bullet of mass $25\,\rm{g}$ is fired horizontally into a ballistic pendulum of mass $5.0\,\rm{kg}$ and gets embedded in. If the centre of the pendulum rises by a distance of $10\, \rm{cm}$, find the speed of the bullet.
In the above types of questions, why we don't include both the initial and final velocities of ... |
Let’s put a lot of material points at coordinates (0,0).
Let’s give them completely random velocities.
Let’s evolve this system for some time t0.
Let’s look at the system from the point of view or randomly chosen material point and call this point E.
From its perspective every other point is moving away from E.
The rec... |
Bernoulli's principle states that, in a steady, incompressible, inviscid flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of the fluid's kinetic energy, gravitational potential energy, and internal energy (i.e. pressur... |
If I have a system of differential equations, say $x' = f(x,p)$ and a set of data $(t_n,x_n)$, where $p$ is the set of constant parameters. I can then use a fitting method like least squared to obtain $p^{best fit}$ with some uncertainty $\delta p$. When using this $p^{best fit}$, it will result in some uncertainty $\d... |
This is my first question in stack Exchange,I'm making the overall calculus por a piston dossifier of viscous fluid like Honey and Carob Syrup, and I am currently struggling with the minor losses of concentric reducers in my system,
**The picture from below is a concept of the system **
So in the system a plunger goes... |
Say we have $n$ engines sitting on a rigid body. Each engine has position $R_i$ and points in a certain direction and generates a force in that direction, $F_i$. The magnitude of that force ($k_i$) follows this constraint: $0 \leq k_i \leq m_i$. In other words, the engine can only output so much force.
I want to be abl... |
I have found contradictory information about this. Does the Higgs field give mass only to the $W^+$, $W^-$, and $Z^0$ bosons or does it give mass to other particles as well?
|
I've always liked lattice QFT because it's mathematically unambiguous and non-perturbative, but it does have two drawbacks: (1) the lattice is artificial, and (2) some features are messy. One of those messy features is chiral symmetry. As an example, the lattice model of a free Dirac fermion in even-dimensional spaceti... |
When reading about black holes, I have also read about things relating to black holes like holographic principles, parallel universes, black hole connecting multiple universes, etc. But black holes are just very dense stars which bend space-time like ordinary stars. (It just bends more because it's much denser). But st... |
Consider a wall and a ball that is traveling towards the wall with uniform velocity. Assuming no friction of any kind in this situation. When ball collides with the ball, the ball gets squished as its kinetic energy is changed to elastic potential energy and bounces back with Potential energy changing back to kinetic e... |
What is the exact constraint for two bodies remain in contact? Consider the case of a rod constrained to move downward on an inclined wedge. It is known that the velocity of the wedge and the velocity of the rod in the common normal direction should be the same because they must not lose contact.
Differentiating this w... |
During storms, I have often watched ocean waves breaking at the shore as if they were in slow motion. I've wondered if the slow curling of the waves during these times was somehow due to their increased power, when compared to waves breaking faster under calmer conditions. However, it has occurred to me that remarkably... |
Some forces are perpendicular to the displacement of a body placed in a "vehicle", if the vehicle at rest. But, the motion of "vehicle" causes the body to move in some direction not perpendicular to the force. Now, the net displacement no longer remains perpendicular to the forces. And they start to do work on the body... |
In this question when I solve for time I get $t=-1$ & $t=5$. What does it actually mean at $t=-1$?
|
The inflation slow-roll parameters are:
$\epsilon = \frac{M_{pl}^2}{2}(\frac{V'}{V})^2$
$\eta=M_{pl}^2 \frac{V''}{V}$
What are the dimensions of $\epsilon$ and $\eta$? What about $V$ and its derivatives? $M_{pl}$ clearly has dimensions of mass.
The slow-roll conditions are usually given as $\epsilon \ll 1$ and $\eta \l... |
Long time ago, I found a question in the book Introduction to Classical Mechanics-David Morin.
The question was
Sliding sideways on a plane:
A block is placed on a plane inclined at an angle $\theta$. The coefficient of friction between the block and the plane is $\mu= \tan \theta$. The block is given a kick so that i... |
TL; DR: According to a book by Tomonaga in a chapter introducing second quantization, the formula
$$e^{\pm i \Theta/\hbar} \,\psi(N) = \psi(N\pm 1)$$
is supposed to prove that the second quantization procedure using commutation relations is suitable for bosons. I am able to follow Tomonaga's mathematics up to this form... |
From Griffiths, Faraday's law is given by:
$$
\oint_C \mathbf{E}_{induced} \cdot d\mathbf{l} = - \iint_S \frac{\partial \mathbf{B}}{\partial t} \cdot d\mathbf{a} = - \frac{d \Phi}{dt}
$$
On page 323, it states that if we are using this to compute the induced electric field, we are making a quasistatic assumption by ass... |
To the question regarding the relation between the energy of a photon (E = hf) and the energy of the associated electromagnetic wave, I read somewhere that the energy of an electromagnetic wave is Nhf, N representing the number of photons per second that pass through a unit area. How could the electromagnetic wave asso... |
I am trying to figure out what is the entropy expression as a function of the external field in a 2D Ising model with nearest neighbour interaction.
My Hamiltonian is the following:
$\mathcal{H}=-\Lambda\sum_i c_i -\varepsilon\sum_{<i,j>}c_i c_j$
where $\Lambda$ is given by some function of the external field $h$ and $... |
I am computing the diffraction pattern of some specific grating. I end up with the following integral
$$I = \int dx\, J_m(x)e^{-ax^2}e^{-ikx}$$
which is the Fourier transform of the Bessel function of the first kind $J_m$, times a gaussian. I searched the literature and the tables of integrals involving Bessel function... |
Background
My question concerns Beenakker's paper on "Specular Andreev Reflection in Graphene": cond-mat/0604594 (arxiv)/Phys.Rev.Lett. 97, 067007 (The same topic is also discussed in Rev. Mod. Phys. 80, 1337)
In this paper the conductance is calculated for a N-S interface using the Blonder-Tinkham-Klapwijk formalism. ... |
I would like to ask about gravitational mass. I know inertial mass is changing by motion (speed) according to $m=\frac{m_o}{(1-v^2/c^2)^{1/2}}$ And also that is inertial mass which sits in $E=mc^2$. If the statements above is correct, now how about gravitational mass? Does it change with motion (speed)? And what mass s... |
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