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Let us take a laptop which is plugged into a charger where the socket has improper grounding. (I do not know much more regarding this, might be current leakage.)
Now, when the charger is turned on and you drag your finger along the casing of the laptop, there is an unmistakable feeling your finger moving over a bumpy s... |
From Wikipedia,
"The local energy conservation in quantum field theory is ensured by the quantum Noether's theorem for the energy-momentum tensor operator. Thus energy is conserved by the normal unitary evolution of a quantum system."
I know that it is the case in GR that conservation of energy and other conservation... |
Can anyone provide exact mathematical reasoning as to why the following fundamental unbounded symmetric operators are essentially self-adjoint? I.e. on, their natural domains, they admit a unique selfadjoint extension.
I know that the position and momentum operators $\hat{X}$ and $\hat{P}$ are self-adjoint on their d... |
I don't know if this should be asked here or in a math stack exchange, but I'll try here first.
Consider the classical 1d Ising model with periodic boundary condition:
\begin{equation}
H_2 (\vec{\sigma}) = \sum_{i=1}^n \sigma_i \sigma_{i+1}
\end{equation}
where $\sigma_i=\pm1$, and we refer to the collective $(\sigma_1... |
Generally, text books cover the recoil of a target after absorption of a photon. What happens when a target, it might be an atom, recoil after emission of a photon? The scientific literature shows a mathematical treatment, however not in case the recoil velocity is relativistic. Therefore, I am approaching this problem... |
I am trying to simplify gyroscopic precession for PPL Helicopter students and in the process confused myself. Many texts define it as processing a force 90 degrees when the force is applied 'parallel to the axis of rotation' while others say 'perpendicular to the axis of rotation'. I even read text where they brought i... |
My book says:
Let a current $I$ be flowing through a conductor of resistance $R$ for a time $t$, when a source of potential difference $V$ is connected across its ends.
Then, it proceeds to prove that:
Electrical energy $W$ supplied by the source is$$W = VIt = I^2Rt$$
Then, a few pages later, it is also given (with... |
Consider a density operator $\hat{\rho}$ for a mixed state defined by
$$\hat{\rho} = \sum_k p_k |\psi_k\rangle \langle\psi_k|$$
Here $p_k$ is the probability of finding the $k$th system of the ensemble in the normalised state $|\psi_k \rangle$.
I wish to show for the mixed state that $\hat{\rho}^2 \neq \hat{\rho}$. Ple... |
Four charges each equal to Q are placed at the four corners of a
square and a charge q is placed at the centre of the square. If the
system is in equilibrium, the value of q is:
I found the potential energy of this system as:
$$U = \frac{-4 \sqrt{2}kQq}{a} + \frac{4+2 \sqrt{2}kQ^2}{a}$$
And I'm visualizing a U-Q grap... |
In a star gravity creates the pressure, and fusion reactions create the temperature for fusion.
In a thermonuclear bomb the fissile shell around the core exploding inwards create the temperature and pressure for fusion.
In a Dense-Plasma-Focus device, the "pinch" creates the extremely dense and hot ball of plasma withi... |
I am writing this as a mathematician trying to understand fermionic Gaussian states.
Up to global phase, a quantum state can be faithfully represented in terms of a quasi-probability distribution on its phase space by its Wigner function.
In particular, if this quantum state is a (bosonic) Gaussian state, then this res... |
To my best knowledge the intensity of light determines the rate of electron emission and the frequency of light determines whether electrons will be ejected and their maximum kinetic energy.
If frequency is increased but intensity remains the same:
electrons will get more kinetic energy (larger speed)
the rate of emis... |
I’m an engineering student. So far, I’ve learned about 3 types of pressure:
Static fluid pressure ($P=\frac{F}{A}$). This wouldn't exist without gravity. I’ve solved problems related to the force exerted on inclined surface by fluids. This concept is similar to stress in solid mechanics.
Static pressure of flowing flu... |
In electromagnetism, the electric displacement field D represents the distribution of electric charges in a given medium resulting from the presence of an electric field E. Its relation to permittivity in the very simple case of linear, homogeneous, isotropic materials with "instantaneous" response to changes in electr... |
I want to know why the back-and-forth vibration of a material produces a spherical wavefront, for the produced sound wave, and not a plane wavefront.
|
The telegraphers' equations are commonly written as
$$\frac{{\partial v(z,t)}}{{\partial z}} + R\space i(z,t) + L\frac{{\partial i(z,t)}}{{\partial t}} = 0$$
$$\frac{{\partial i(z,t)}}{{\partial z}} + G\space v(z,t) + C\frac{{\partial v(z,t)}}{{\partial t}} = 0$$
for which a solution may be found in frequency domain fr... |
I am conducting computational simulation tests and have observed that when simulating systems like molybdenum disulfide ($\rm MoS_2$), the interaction between layers (S-S interaction) is quite strong, preventing the system from 'sliding' in comparison to others, such as graphene, for instance. To substantiate this hypo... |
lets say a fish tank leaks along a vertical edge seam. What is the equation for the flow rate as the volume and discharge area changes?
|
I know that Helmholtz tells us that any vector field can be expressed as a superposition af an irrotational part and a solinoidal part. So for the electric field we get
$$
\begin{equation}
\vec{E} = \vec{E}_i + \vec{E}_s. \tag{1}
\end{equation}
$$
Now the argument to get towards
$$
\begin{equation}
\vec{E} = -\vec{... |
So please correct me if I am wrong but:
First 2 proton’s (each with an electron) fuse together,
The mass stays the same so no energy is produced?
Then 1 of the protons turns into a neutron with a Neutrino and a positron.
The positron and the electron collide and produce energy equivalent to the mass of 2 electrons (E=M... |
I was looking through the book "Astronomy - Principles and Practice 4th ed. - A. Roy, D. Clarke" and I got stuck at the following lines:
The month is the next period of any significance to our watcher. During this time, the ideas about the heavens and their movements change. It will be noted that after a few nights th... |
If the chemical potential of a fermionic system is $0$ at temperature $T=0$, will it be zero at any arbitrary finite temperature?
|
Can anyone explain to me why, when the spin-orbit interaction is a relativistic effect, the Coulomb potential is then used in calculating the hydrogen energy levels, rather than the retarded potential? Surely if the electron is assumed to be moving at a relativistic velocity, the correction to the Coulomb potential wil... |
I see "critical system" being used all the time. For example:
Excellent candidates for this approach
are systems exhibiting phase transitions. At the critical
point of a phase transition, the eigenstates of the system are extremely sensitive to any changes of the system
parameters [29–32]. If the final state of such a... |
Current situation: a bullet is fired towards a block that is connected to a string which is connect to a ceiling. The bullet is embedded to the block and the object(block+bullet) swings up to a certain height.
Consider this scenario: if there is friction when the bullet is embedding into the block, energy will be conve... |
My 12th grade physics book on electrostatics says:
Potential difference between two points in electric field can be defined as work done in displacing a unit positive charge from one point to another against the electric forces.
By this logic, the potential difference between two points in an electric field should al... |
Suppose you have a car sitting stationary. Then it gets rear ended by a truck going at $x$ speed.
Then you have a tricycle with the same size wheels and same weight. It also gets hit by a truck also going at $x$ speed.
Assume the roads on which the car and the tricycle have the same amount of friction. Also assume the ... |
I've read that Newton determined the average density of Earth is twice the density of the surface rocks, but I can't find his computation anywhere. I presume he used the differential calculus in some way. This is the correct result.
The density of granite is 2.765 g/cc, so the density of Earth should be about 5,530 k... |
Started reading the book "How Einstein found his field equations" by Janssen and Renn and I am already blocked on chapter 1. What do the authors means after the "split" below?:
"What Einstein made relative [in GR] is not motion but gravity. Two observers, one moving on a geodesic, the other moving on a non-geodesic, ... |
Consider an ideal gas in a cubical container as our system (only the gas is the system, not the walls of the container). If I understand correctly, if the gas expands at constant pressure $P_{int}$ greater than the ambient pressure $P_{ext}$ (after heating the gas to a certain temperature, the walls of the container, w... |
Consider two cells of e.m.f. $ε_1$ and $ε_2$ with internal resistances $r_1$ and $r_2$ respectively set up parallel to each other in a circuit as shown in the figure:
Let the equivalent e.m.f. be $ε_{eq}$
How can it be proven that $ε_1 < ε_{eq} < ε_2$ if it's given that $ε_1 < ε_2$?
|
In problem 2.1 part c of Introduction to Quantum Mechanics, 3rd ed. by Griffiths and Schroeter, they ask the reader to prove that if the potential is an even function of $x$, then if $\psi(x)$ satisfies the time-independent Schrödinger equation, then so does $\psi(-x)$.
Now the solution just requires one to prove that... |
I am currently taking analytical mechanics,
My professor directed us in the lecture to Hand and Finch, problem 6.9, to prove ourselves (as he didn't have time) that the equation $$[Q,P]_{Q,P} = [Q(q,p),P(q,p)]_{q,p} = 1\tag{6.39}$$
is both necessary and sufficient condition for the transformation between $q, p$, and $Q... |
I was reading BH Bransden's chapter on wave packets and he derives the group velocity expression taking into account that: $$ \psi (x,t)=\int e^{i[p_{x}x-E(p_{x})t]/ \hbar} \phi (p_{x}) dp_{x} $$
where $\phi (p_{x}) $ is very "sharply peaked" at $p_{x}=p_{0} $.
It is clear that if we make this "sharply peaked" assumpti... |
I'm studying the thermal comportement of a "mass stove". I would like to do a materials selection. My first constraint is to have a temeperature of my "mass" between a lower and an upper born. I used this relation : $$Q_{fire} = ρ*c_p*dT$$
My second constraint is to stay above my upper born a certain time at minimum. I... |
I am currently trying to go through some literature on the classification of symmetry protected topological phases. Primarily, I am interested in the classical of topological phases using mathematical tools: group cohomology, cobordism, higher category theory etc.
One shortcoming in my background is that I am unable to... |
I am trying to replicate the results found for Gliese 710's closest approach of ~0.05 parsecs in 1.3 million years approximately. I thought that by plotting the sun at (0,0) and using the stars ra,dec, and distance i could plot its position in cartesian. This was simple enough using the following:
x = dist_pc * np.cos(... |
Consider the following Hamiltonian, with two species of fermions ($c$ and $f$) and only inter-species local interactions:
$$ H = \sum_k \epsilon_k c_k^\dagger c_k + \sum_q \varepsilon_q f_q^\dagger f_q + \sum_i V c_i^\dagger c_i f_i^\dagger f_i.$$
I could define a mean-field parameter $\langle b \rangle = \langle{c_i^\... |
I was solving the following problem on harmonic oscillation and I don't understand a specific part in the proof. I will emphasize (italic) the part which I don't understand.
Problem:
The following system is considered: Consider a rigid, massless bar that connects a body of mass $m$ (lower) and another body of mass $m'$... |
So I'm trying to find the wave function in momentum representation for the state $\hat{T}|\psi⟩$, where $\hat{T}$ is the time-reversal operator.
First, we know that the time reversal operator acts on momentum as follows:
$$ \hat{T}|\hat{p}⟩ = |-\hat{p}⟩ $$
and that the wave function in momentum space can be written as:... |
In the standard model Lagrangian, the electric charges of the particles are the coefficients of the interaction terms (e.g. $(-2/3e)u'Au$ for the up quark shows it's charge is $(2/3)e $)
How can we see what the baryon numbers and lepton numbers for each particle are just by looking at the Lagrangian terms?
|
I have several questions regarding EMW reflection. If it will be helpful, I am thinking about the reflection of powerful EMW and problems like heating associated with it.
Does EMW reflect from dielectric materials?
If so, does it heat up or stay cool due to the absence of current? And if there is no current, where does... |
While I am deriving the relativistic fluid equation for the radiation component I am getting an extra term like $\vec{v} \cdot \vec{\nabla}P$ where $\vec{v}$ is the velocity and $P$ is the pressure.
Is this term is equal to $0$? How can I prove that is the case?
|
The energy flux in a conductor paints the picture that the "collisions" of the electrons with atoms (Drude Model) are not the reason for an resistance warming up in the presence of an electric current, but rather through properties of the surface charge distribution. Although of course any magnetic field (in this case... |
I have to compute the translational correlation function of a 2 dimensional set of particles. The function is given in literature like following:
$$
G_k(r) = \sum_{l = 1}^6\frac{1}{N}\sum_{<j,k>}^{N_r} e^{-i q_l ( r_k-r_j)}
$$
Where q are the 6 reciprocal lattice vectors derived from the first order Bragg peaks in the ... |
It seems like lifting objects requires more effort compared to dropping them, although the law of conservation of energy still applies. As discussed Physics Stack Exchange answer, energy transfers from my muscles to the object and then back to my muscles.
(I suppose equal conditions for both case (such as speed, time, ... |
Imagine the following (moving) charge distribution in a one-dimensional space
$$f(x) = \begin{cases}
1 & |x - vt| \leq 1 \\
0 & else
\end{cases}$$
Given the ends of this distribution two to Amperes & Faradays law there should be an infinitely strong electric field.
How would an expirement (moving some... |
Some background, Im making a electric assisted bicycle trailer( 1 axel, 2 wheel with hubmotors) that is going to be pulled by a bicycle, the motors are torque controlled(very accurate and precise control from the motor drivers. I can give torque instructions and will receive that torque instant). There is a force senso... |
I think this sort of problem is known and relatively simple when on a single angle of incline, but I'm trying to understand a problem with two points of contact of a uniform vehicle where each contact point is on a different incline, ie. the front point is in contact with an incline at theta1 and the back respectively ... |
Beta decay is generally displayed as below with a fairly significant intensity of electrons emitted with KE ~ 0. In this case, all the energy of the decay is given to the neutrino and the momentum is conserved between the neutron and the recoiling nucleus. However, for free neutron decay, I am under the impression th... |
Hello guys I have homework that has tasked me with connecting the effect of the scattering parameter to the energy transfer in a 2d elastic collision of two arbitrary spheres with one of them standing still and I feel like I'm really struggling in connecting the two without feeling like it's circle logic like. what I h... |
It has been hypothesized that in the very far future, most or all matter will have decayed into radiation.
A planet like Earth is composed of matter, forming a gravity well based upon the total energy content $M$. If, over a long period, the atoms all decay into photons, all the photons will escape the gravity well to... |
It is well known that the energy levels
$$
E_n = \hbar \omega\left(n+\frac{1}{2}\right)
$$
of the quantum harmonic oscillator verify the eigenvalue problem
$$
\hat{H}|\psi_n\rangle = E_n |\psi_n \rangle
$$
where
$$
\hat{H} = \frac{\hat{p}^2}{2m} +\frac{1}{2}m\omega^2 \hat{x}^2.
$$
Now let us assume that the harmoni... |
Let's say there's a supermarket selling a hundred different products. Before it opens for the day, the staff arrange all the products into their appropriate shelves. This should be a low entropy state, since the products are highly ordered.
After the supermarket opens, a shopper with a trolley goes in. They select some... |
According to my textbook and various sources on internet I found that susceptibility of paramagnetic substance is related to temperature by the following formula: $$χ=Cμ_0/T$$
Susceptibility of ferromagnetic substance beyond Curie's temperature is related to temperature by the following formula: $$χ=C/(T-T_c)$$
Why the... |
I was solving a test this morning and came across this question. Now by intuition, I know that there should be only two images formed. Rays shall converge through the upper section of the lens to form an image at Principal Focus 1; rays shall converge through the lower section to form an image at Principal Focus 2. Sin... |
https://abc7news.com/118-freeway-crash-caught-on-video-los-angeles/13027476/
The incident happened on Thursday, March 23, in Chatsworth, Los Angeles. In which a vehicle went flying into the air after being hit by a loose tire from a pickup truck nearby.
Even I see it, don't understand how the car went flying.
What was ... |
I'm currently reading Kardar's Statistical physics of Fields. In the book, the $\mathbb{Z}_2$ lattice gauge theory is constructed as the dual of the 3d Ising model.
(Note: the Hamiltonian is $H = \sum_{\text{all plaquette } P} K \sigma_P^1 \sigma_P^2 \sigma_P^3 \sigma_P^4$).
And Elitzur's theorem states that there is n... |
Laser light is known to produce "coherent state light," which consists of a superposition of different photon numbers. However, wouldn't the entanglement between the atoms and the light suggest that photons become distinguishable, preventing the probability amplitudes from coherently adding to produce coherent state li... |
When refraction takes place at the interface of two media, wavefronts can be extended to intersect as below:
At point of intersection, light requires no time to travel between the wavefronts. However, between other point on the wavefront, time is rquired by the light to travel.
This clearly contradicts Huygens' princi... |
I know the tau lepton has been predicted before it was discovered – unlike the muon. But how does our theory (SM/electroweak theory) predict the existence of a third lepton generation?
|
I was looking through the book "Astronomy - Principles and Practice 4th ed. - A. Roy, D. Clarke" and I got stuck at the following bold lines:
The month is the next period of any significance to our watcher. During this time, the ideas about the heavens and their movements change. It will be noted that after a few nigh... |
I am not much clear regarding the defintion of "gravitational potential":
Is the work done for bringing the unit mass from infinity to that point by, gravitaional force or external force? (As you can see in the image, one source say external force and the other source says gravitational force)
And for the negative sig... |
I am trying to understand how to calculate the bending moment for a cantilever with a uniformly distributed load so that I can build an equation of moments, as shown in this example:
I tried calculating the moment but didn't arrive at their expression. I tried the following:
$$M = -\int_0^x wl*dl + \int_0^{L-x} (L-x-l... |
I have a request. Please clarify these doubts for me:
In the loops in quantum field theory there is a momentum $k$ which is integrated over. In a lecture, Professor Hong Liu says that this free $k$ running in these loops is integrated over all real values and thus this means that the momentum fluctuates over all these ... |
Weinberg's QFT vol 1 has excellent discussion on symmetries and projective representations. Because physical states are represented by rays in the Hilbert space, symmetries are realized as projective representations
\begin{align}
U(g_1) U(g_2) = e^{\phi(g_1,g_2)} U(g_1g_2)
\end{align}
where $g$'s are group elements an... |
It is well established that if two photons of the same polarization, identical wavelength, phase, and spatial distribution of wavefunction enter a non-polarizing beam splitter (N-PBS), they exhibit the Hong-Ou-Mandel (HOM) effect. Essentially, they show bunching behavior. But what exactly happens for the same setup if ... |
Here I am posting a question of Jee Adv. 2023 based on refraction.
A monochromatic light wave is incident normally on a glass slab of
thickness , as shown in the figure. The refractive index of the slab
increases linearly from 1 to 2 over the height ℎ. Which of the
following statement(s) is(are) true about the light w... |
This is a conceptual question I can't quite wrap my head around.
Take two blackbodies with temperatures $T_{hot} > T_{cold}$. Both should have a spectral intensity described by Planck's law
$$I(\lambda, T) = \frac{2 \pi h c^2}{\lambda^5} \frac{1}{\exp{(hc/\lambda k_B T)} - 1}$$
That seems to imply that the spectral int... |
This question is specific to the experimental quantum optics community. I am attempting to perform a Mach-Zehnder interference experiment using single photons as a source. However, I am encountering difficulties. While I do observe the visibility pattern typical of single-photon interference, the visibility is quite lo... |
lets say that we have a cube made of say 1kg, and using some means, managed to impart enough angular momentum to make it rotate at the speed of light or at least 99% of light speed. ignoring the fact that it would take infinite energy to do so, what would happen?
you can take some theoretical liberties when it comes to... |
I am taking an course on quantum mechanics, and we have just encountered the quantum teleportation protocol that allows for the transfer of one qubit from Alice to Bob. I think I have a way for Eve to break the security of this protocol. For completeness, the protocol is as follows.
$\textbf{Protocol:}$
Alice and Bob, ... |
I don't know why the taylor expansion for the time dilation and lorentz contraction look like this. Here, the velocity $\mathbf v$ of $\overline{\mathit O}$ relative to $\mathit O$ is nearly that of light, $\vert \mathbf v \vert = 1 - \epsilon$, $0 \lt \epsilon \ll 1$.
(a) $\Delta t \approx \Delta \overline{t}/\sqrt{2\... |
There is an old question posted (Regularization) which did not get an answer, about the validation of analytic continuation as regularization. It did get some discussion in the comments, referring to Terence Tao's blog T.Tao, but questions seem to remain:
Why is analytical continuation allowed to regulate a diverging ... |
I want to calculate the net phase at a point on the screen in Fresnel diffraction. Attached below is a rough diagram if needed.
For this I considered hypothetical $n+1 $ small slits acting as sources within the original slit namely $ S_0 , S_1 … S_n$ equally spaced at a distance $x$. The thought was to calculate the ne... |
(Boyer-Lindquist coordinates and $ c = G =1 $ taken)
As I know, line element in Kerr metric $ d s^2 = - \left( 1 - \frac{2Mr}{\rho^2} \right) d t^2 - \frac{4 M a r \sin^2 \theta}{\rho^2} d \phi d t + \frac{\rho^2}{\Delta} d r^2 + \rho^2 d \theta^2 + \left( r^2 + a^2 + \frac{2 M r a^2 \sin^2 \theta}{\rho^2} \right) \sin... |
I am new to fluctuation statistical mechanics, In all examples that I encountered, the Langevin equation always has the fluctuation force accompanied by a friction force.
$$\frac{d^2x}{dt^2}+\gamma \frac{dx}{dt}+w_o^2 x=f(t)$$
From Fokker-Plank formula, I can see that if the system has no dissipation or fraction, then ... |
I am dealing with a system that has some secondary constraints. I am trying to use Dirac-Bergmann procedure by following chapter 10 of Ashok Das, Lectures on Quantum Field Theory ( 2021, Second Edition ). Let me denote my extended hamiltonian as
$$ H_{Extended} = H_{canonical} + \lambda_i \phi^i_p + \lambda_i \phi^i_s ... |
The potential of a $2^n$ pole can be found by,
$$
\varphi_n =\frac{p^{(n)}}{4\pi\epsilon_0 n!}\frac{\partial^{'n}}{\partial l_n \partial l_{n-1} ... \partial l_1} \bigg(\frac{1}{r} \bigg)
$$
where
$$
p^{(n)} = n ! q \Delta l_n \Delta l_{n-1} ... \Delta l_1
$$
is the multipole moment. $\Delta l_n$ is the distance betwee... |
The title more or less covers it. I thought of this while ago at a talk, and I couldn't get the idea out of my head. Going further, I wonder if there is some sort of solution for the distribution of the surface charge. I think if we restrict ourselves exclusively to hyperspheres, there might be an actual tractable answ... |
I am reading Introductory Nuclear Physics by Wong. In Appendix B-2, he shows that the Coulomb scattering amplitude is given by
$$
f^c(\theta)
=
-\frac{\gamma}{2k\sin^2(\theta/2)}
e^{i[\gamma\ln(\sin^2\theta/2) + 2\sigma_0]}
$$
where
$$
k^2 = \frac{2\mu E}{\hbar^2},
\qquad
\gamma = \frac{Z_1 Z_2 \alpha\mu c}{\hbar k},
\... |
When I hear people talk about qubit operations, they usually make a distinction between local and multi-qubit (global) operations. I understand what they mean intuitively (the local operations act on each qubit individually, but the global operations act on all qubits at once), but I want to understand what this means ... |
(This question is about non-tempered glass.)
I broke my favorite glass (tumbler) today, dropping it in my (ceramic) sink while trying to refill it. :(
I'm kind of a klutz - that's far from the first time I've dropped that glass in that sink. However, there was nothing different this time from all the other times. It's ... |
I was recently solving a problem from Jaan Kalda's handouts;
Parallel to and at a distance $h$ above the surface of an infinite planar superconductor is an
infinitely long straight wire with current $I$ running though it. Determine the force acting on a unit length
of this wire.
In this problem, I have an intuitive fee... |
For a perfectly elastic body, Bulk modulus always remains constant and is defined as,
$$B=-V_i \frac{\Delta P}{\Delta V} \tag{1}$$
Which means,
$$B \left(\frac{V_f -V_i}{V_i}\right)= -(P_f-P_i)$$
But, the definition of bulk modulus in a lot of places is given as,
$$B=-V\frac{dP}{dV}\tag{2}$$
In particular, this definit... |
I tried to find an elegant way to solve (without approximating for low densities)
$$\dot{R}^2=\frac{8 \pi G}{3 c^2} \rho R^2-k c^2+\frac{c^2 \Lambda}{3} R^2$$
for $k=\pm 1$ and $\Lambda \neq 0$ (one time considering $\Lambda>0$ and another time considering $\Lambda<0$) and without using calculus software. I wasn't able... |
Consider scattering towards a hard sphere with radius a and potential (Assume ka=1):
$$ V(r) =\begin{cases}
\infty , &r<a\\
0 , &r>a \\
\end{cases} $$
So first I determined the phase shifts for the first two partial waves $l= 0,1$ by applying boundary condition at $r=a$ and got:
$$ \tan \delta_l = \frac... |
I know that when we are dealing with a charge inside a, initially neutral, spherical conductor, the outside induced charge will rearrange uniformly.
But, let's say now we have two conductive planes, both connected by a wire and initially neutral, with a non-conducting charged plane between it. My question is: this phen... |
Thank you in advance for any answer to my question.
I'm having trouble understanding the behaviour of the mode functions of a massless Klein-Gordon field in Rindler coordinates. We are in 3+1 dimensions. For reference, take the review of the Unruh effect by Crispino, Higuchi and Matsas (2009); I will use the same notat... |
In some texts (e.g. Taylor's Classical Mechanics), the generalized force is defined to be (I'll simplify to one particle in one dimension for ease of notation): $Q \equiv \frac{\partial{L}}{\partial{q}}$.
While other texts (e.g. Goldstein's Classical Mechanics) define the generalized force to be: $Q \equiv F\frac{\part... |
Galileo's principle of relativity states that the laws of mechanics are invariant in every inertial frame of reference.
This is well illustrated by Galileo’s ship. What is meant here by "laws of mechanics"? Are these Newton's laws of motion, conservation laws, Lagrange/Hamilton equations, or something else?
|
Consider an electro-magnetic field represented in phasor notation $E_0e^{-jwt}$ incident upon a photodetector/photodiode, what is the expression of the generated photo-current $I(t)$? Here $E_0e^{-jwt}$ is an abstract way usually assumed for an optical signal in the Scattering-matrix method (or transfer-matrix method).... |
When an electron collides with a positron, both are destroyed and pure energy in the form of photons is released. It seems then that electrons are composed of photons, if photons were released on collision with the antimatter.
The process works in the other direction as well - gamma rays can collide to form positrons a... |
Consider a standing sound wave formed in the air in conditions close to standard pressure and temperature in the antinode region. On the molecular level, it will involve multiple collisions of air particles moving in the opposite direction. This includes head-on collision of collinear $\rm N_2$ and $\rm CO_2$ molecules... |
I'm trying to understand the meaning of Lighthill equation. Based on my text book (sound and source of sound, Dowling and Williams 1983), it is derived from combining mass conservation and momentum conservation equations.
$$\frac{\partial \rho}{\partial t}+\frac{\partial}{\partial x_i}\left(\rho v_i \right) = 0$$
$$\fr... |
Does anyone know the DOI of the article below or where I can download it?
P. Rhodes and G. Rowlands, “Demagnetising energies of uniformly
magnetized rectangular blocks,” Proc. Leeds Phil. Lit. Soc., vol. 6, pp.
191–210, Dec. 1954.
|
I understand that atom-bound electrons can absorb photons (explanation for why they are typically atom-bound). However, what is the particular mechanism for this occurring? I am familiar with the idea that there is an energy-state lifetime, but would like to know exactly how the electron is able to store, bind, or capt... |
This phase diagram of water shows how the phase of water is determined by the pressure and temperature.
I find it easy enough to understand; as the pressure increases, the boiling point of water also increases and thus water can stay liquid even if the temperature is higher than $100 °C$.
Additionally, the freezing po... |
I have been struggling with this one all day.
A 20kg block is pulled along a level plane with a force of 100N, at an upward angle of 30 degrees above the horizontal. At d = 15m, the velocity of the block is 8 m/s. At d = 25m, determine the velocity of the block if the coefficient of friction, uk, is 0.25.
The horizon... |
There are similar questions answered already but the answers disagree. I understand that simultaneity/time is local in GR and that in a given region of space, an event horizon and singularity can form in finite proper time for a local observer. For a distant observer, will the event horizon form in a finite amount of t... |
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