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When deriving the Lienard-Wiechert Potentials, there is one step that you need to perform:
$$
\nabla_{\mathbf r}|\mathbf r - \mathbf r_s(t_r)|
$$
Where $t_r$ is:
$$
t_r = t - \frac{|\mathbf r - \mathbf r_s(t_r)|}{c}
$$
$\mathbf r$, is the position where you are calculating the field and $\mathbf r_s$ is the position of... |
How do I calculated the second Reflection (2) of light in glass (which equations and tools)
|
The solution of the differential equation (DGL)
$$
(-\epsilon_0\nabla^2 + l^{-2} )G(\vec{r},\vec{r}') = \delta(\vec{r},\vec{r}')
$$
is given by a screened Coulomb potential
$$
G(\vec{r},\vec{r}') = \frac{1}{4\pi\epsilon_0}\frac{e^{-\vert\vec{r}-\vec{r}'\vert/l}}{\vert\vec{r}-\vec{r}'},
$$
with $l$ being some screenin... |
I want to determine the time a photon needs in order to cover a distance, say $l_0$, where $l_0$ is the length of a spaceship (reference system S'). So, the photon is going from one end of the spaceship to another. But, what I am after is the time elapsed between the two events in the system of reference of an observer... |
I have read that a large number of partial waves, around 200, are required in a situation such as ${}^{16}$O incident on ${}^{152}$Sm at c.m. 65 MeV in Coulomb excitation
Anybody familiar with scattering knows incoming partial waves are in units of angular momentum $L$, so $L \,= \,0, \, 1,\, 2$, etc are the incoming p... |
Context: I am embarking on my journey into physics as a beginner. Four years ago, I completed my Baccalaureate (high school diploma) and subsequently pursued software engineering independently. It's only now, four years later, that I am beginning to appreciate the beauty of physics and science in general. I've had to r... |
I am struggling to understand a general method to calculate the independent components of the Riemann Curvature Tensor (RCT).
Firstly, as far as I am aware the number of independent components of the RCT for a $d$-dimensional manifold is given by (1) which is equal to 1 for $d=2$.
$$\frac{d^2(d^2-1)}{12}\tag1$$
The que... |
I have the Mukhanov-Sasaki equation in terms of $Q(t)$
\begin{align*}
Q''(t)+3HQ'(t)+k^2Q/a^2+\left(3\phi'(t)^2-\phi'(t)^4/2H^2+2\phi'(t)V_\phi/H+V_{\phi\phi}\right)Q=0,\ u=aQ
\end{align*}
and also the initial condition from Bunch-Davies
\begin{align*}
\lim_{k>>aH}u_k(\tau)=\frac{e^{-ik\tau}}{\sqrt{2k}}
\end{align*}
Ho... |
How angle of incidence affect the lines of sodium when we are observing refracted rays from prism ? Or is it the deviation of rays that makes the lines broader.
Let me put it in a better way , when doing the experiment of measuring angle of deviation with a spectrometer , I observed the refracted rays from prism, now ... |
Good afternoon, I am attempting to calculate the ratio of temperature and luminosity between two stars, one entirely made of iron and the other of hydrogen, with the same volume.
To do so, I have employed
$$
m = \frac{1}{2X+0.75Y+0.5Z} m_H
$$
to obtain the average molecular weight (X=fraction of H, Y=fraction of He, Z=... |
After studying action-angle variables and Eulers two-fixed-center problem in a course on mechanics and symplectic geometry, I understand that a two-fixed-center system is Liouville integrable and therefore (as long as the orbits are bounded) there exists a transformation to action-angle variables.
What I'm wondering is... |
In the book Field Theories of Condensed Matter Physics by Fradkin
In Page 311, when discussing the effects of boundary conditions on $Z_2$ lattice gauge theory, in the weak coupling phase, Fradkin says,
for a system with
an open boundary the axial gauge condition (such as $σ^1_z = 1$) completely and
unambiguously fixe... |
in Introduction to Electrodynamics by David J. Griffiths I have latched upon this definition of current density vector $\mathbf{J}$ (Chapter 5, section 5.1.3, p. 220 in 4th edition) and I would appreciate your help in getting a feel for this:
$$\mathbf{J}=\frac{d\mathbf{I}}{da_{\perp}}$$
Where $da_{\perp}$ is an infini... |
In electromagnetism, the circulation of the $\vec{E}$ field is zero,
\begin{equation}
\oint_C \vec{E}\cdot d\vec{\ell}=0.
\end{equation}
With Stokes law, this implies that
\begin{equation}
\int_S \nabla\times \vec{E}\cdot d\vec{A}=0.
\end{equation}
The usual argument: As this must be true for any surface $S$, the secon... |
While reading Introduction to Electrodynamics by David J. Griffiths, I have encountered some troubles in understanding the energy in the dielectric system. Without the dielectric, we considered the work required to assemble the spatial configuration of charges (firstly we bring the first charge from infinity to its fi... |
I'm trying to find sufficient additional conditions to derive Coulomb equation for the electric field generated by a steady point charge in free space from Maxwell equations in said conditions.
I know that a way to do this is assuming that the solution of Maxwell equations must have spherical symmetry due to the dispos... |
I am reading The Quantum Theory of light by Rodney Loudon.
In Chapter 7 the author defines a phase operator $\hat{\phi}$ using the destruction $\hat{a}$ and creation $\hat{a}^{\dagger}$ operators of the quantum-harmonic oscillator as follows.
$\hat{a} = (\hat{n}+1)^{\frac{1}{2}}exp(i\hat{\phi})$ and $\hat{a}^{\dagger} ... |
In my optics textbook, the derivation of the expression for the linear momentum of a plane wave shocks me as rather sloppy, but I don't know if I should be so shocked. It goes as follows:
Let a plane EM wave travel (in the vacuum) in the direction of the unit vector $\vec{s}$. Then, since the wave has an energy $E$ ass... |
I am struggling with this question and cannot find any resources to help me. Even the tutors at my school don't know how to help me and my professor just tells me to reference the slides, but I have been staring at the question for days and I have no idea how to answer it. I think I normalized it okay, I got e to come ... |
Which type of potentials lead to Kepler's second law "same area in same time"?
$$dA=\frac{1}{2} \vec{r} \times \vec{dr}.$$
$$\frac{dA}{dt}=c=\vec{r} \times \frac{\vec{dr}}{dt}=\vec{r} \times \dot{\vec{r}}. $$
Differentiating both sides we can get a statement on the force field
$\dot{\vec{r}} \times \ddot{\vec{r}}=0, ... |
Let's consider for example water. There is the classical phase diagram shown below which depicts the three states liquid, solid, and gaseous. My question is, how were the exact positions of the equilibrium lines determined? In case those are theoretical results, how would one determine them experimentally? I could obse... |
In Quantum Mechanics, for coherent states $|z\rangle$ it can be prooved that if $|0\rangle$ is the vacuum state for an harmonic oscillator, therefore:
\begin{equation}
|z\rangle=e^{za^{\dagger}-z^*a}|0\rangle\equiv \hat{D}(z)|0\rangle
\end{equation}
with displacement operator $\hat{D}(z)$ that is unitary: $\hat{D}^{\da... |
Suppose we were standing in the vacuum with a photoelectric effect experiment. If we had a source of EM radiation emitting photons with a high enough frequency, we would begin to observe said effect and therefore register some current. Now let's say we are in the same scenario as before, but moving at a high enough spe... |
Struggling to understand where I should measure lens thickness and distance between lenses from.
I've attached an example multiple lens setup.
For determining individual lenses thickness is it simply the distance between the two outermost points of the lens?
For determining distances between lenses, I understand that i... |
This question has been bugging me for quite some time, I have seen some explanations which are mathematical and don't make sense to me, most of them talk about Galilean relativity, but I am looking for a nice simple explanation which can help me understand why $F$ is invariant since both, Mass $M$ and Acceleration $A$ ... |
In his book, Non-Equilibrium Thermodynamics and Statistical Mechanics, Attard takes an approach to deduce a relationship between the probability of state (Boltzmann's statement of the 2nd Law) and the probability of transition (Clausius' statement). He considers two situations, the change of state within "a large enoug... |
As I understood it,
the reason I cannot stick my hand through a metal block is due to the repelling force between electrons in my hand and in the block. QED depicts two electrons repelling with a photon exchange, but it's not clear to me what determines which electron emits the photon and which one absorbs it. Does it ... |
I don’t understand the following concept and I wonder whether any of you could explain it to me.
Let’s consider a wheel rolling without slipping on a horizontal plane. We only consider the moment when it’s already rolling. Suppose it moves to the right so the only force (except the gravitational and reaction of the gro... |
I'm not sure I understand how to compute the gyromagnetic ratios.
Here's what figured out:
if we consider an orbiting charged point-like massive particle we can $\textit{classically}$ compute the dipole angular momentum:
$\mu=iS=\frac{q}{2m}L=\gamma L$
where $\gamma$ is the gyromagnetic ratio (ratio between dipole ang... |
According to Wikipedia, greybody factors are corrections to the black hole Hawking radiation spectrum. They say that at the horizon the emission is that of a perfect black body, but the gravitational potential well makes so that the spectrum at infinity does not correspond to a black body anymore. Greybody factors give... |
I've been studying capillary action, and I've drawn some conclusions about the behavior which surprised me, and I want to know if I'm understanding it correctly.
According to Jurin's law, the height of liquid in a capillary tube is inversely proportional to the radius, so assuming all other variables are constant, heig... |
In the microcanonical ensemble, we have the standard Boltzmann expression for entropy:
\begin{equation}\label{1}
S = k_B\ln \Omega
\end{equation}
where $\Omega$ is the number of elements of the microcanonical ensemble. It is then stated that this expression is equivalent to the Gibbs expression for entropy
$$S = -k_B\s... |
I understand that the high wind speed can accelerate said objects to immense velocities but I do not understand why do not fragile objects simply get destroyed upon impact?
|
Can I rewrite the continuity equation like this ? :
$$
\iiint\limits_{V}\dfrac{\partial\rho}{\partial t}\mathrm dV +\iiint\limits_{V}\rho\boldsymbol{\nabla\cdot}\mathbf v\,\mathrm dV + \iiint\limits_{V}\mathbf v\boldsymbol{\cdot\nabla}\rho\,\mathrm dV=0
\tag{01}\label{01}
$$
|
This might sound like a random question, but it came to me while I was trying to conceptualize the size of the universe and started thinking of entire galaxies resembling grands of sand floating around in the middle of the Pacific ocean. This actually did help me to truly "feel" the vastness of it. But then I started... |
In my University physics class [first year engineering student] I learned that
"for a capacitor in a vacuum, capacitance $C$ depends only on the shapes, dimensions, and separations of the conductors that make up the capacitors".
Does this mean that the vacuum makes material properties null.
This statement, which, wit... |
My friend came to me with a simple question: What is the charge distribution on a conductive solid sphere? Of course, I answered: 'Since the solid sphere is conductive, the electric potential would be the same everywhere inside the solid sphere, hence there would be no charge inside, only on the surface of the solid sp... |
Wikipedia says that microwave ovens can be around 50-64% efficient at converting electricity into microwaves. Where does the energy lost at this stage go? And how much of the energy that is successfully turned into radiation ends up turning into heat in the food? What happens to the radiation that isn't absorbed by the... |
I'm in undergraduate stat mech/thermo. In the context of the Maxwell-Boltzmann distribution, the mean kinetic energy of a gas particle is $\langle KE \rangle = \frac{1}{2}m \langle v^2 \rangle$.
I do not see why we use $\langle v^2 \rangle$, and not $\langle v \rangle ^2$. I understand that they are different terms mat... |
After linearization of the nonlinear equations, I want to find the covariance matrix $v$ through the numerical solution of time dependent Lyapunov equation, $$dv/dt=a*v + v*a'+ d,$$ where $a$ is my system matrix ($a'$ is transpose) and $d$ is diffusion matrix (stochastic noise). The numerical solution of the mean equat... |
I am currently studying electrostatics and I've come across confusing definitions of electric flux.
One definition is the number of field lines crossing a surface. However, I have a hard time making sense of this definition, as field lines are only a conceptual visualisation and do not actually exist. Hence, you can't ... |
Just like there are ways to solve for the force between two straight parallel wires, what is the way we could find the force between non-parallel wires?
|
I was looking at some old slow motion videos showing a phenomenon where a bubble is popped by firing a sphere (or pea) through it.
One obvious thing that happens is that the pea does not pop the bubble immediately, it goes through the first side and then only bursts the bubble when going out the other side.
Is there so... |
I have never thought so deeply about addition and subtraction. But today I noticed something. When adding or subtracting numbers, we actually apply the rules we use for vectors (for example, the vectors we use in physics). only it were one size, wouldn't all vectors form a set of real numbers? Or in another way, wouldn... |
Purdue university in its article on Bohr's Model explains:
At first glance, the Bohr model looks like a two-dimensional model of the atom because it restricts the motion of the electron to a circular orbit in a two-dimensional plane. In reality the Bohr model is a one-dimensional model, because a circle can be defined... |
I am reading Maxwell-Boltzmann distribution for describing the velocities of ideal gas molecules. I went through the PSE question Derivation of the Maxwell-Boltzmann speed distribution and the Wikipedia article and several other resources for some clarification. The following is my understanding of the concept, derivat... |
Good morning. I was reading Tong's Quantum Field Theory course and got stuck on a somewhat stupid step. Essentially, considering the Lagrangian density
$$
L = - F_{\mu \nu}F^{\mu \nu} + i \bar{\psi} \gamma^\mu (\partial_\mu +i A_\mu) \psi
$$
in 1+1 dimension. This lagrangian is invariant under vectorial transformations... |
I wanted to know if it is possible to perform a double slit experiment with electrons travelling at 0.99c as the wavelength is very short.
|
Consider the Wigner-Eckart theorem given by
$$\langle \alpha' j m'|A^q|\alpha j m\rangle = \frac{\langle \alpha' j m'|\mathbf{J}\cdot\mathbf{A}|\alpha j m\rangle}{j(j+1)}\langle j m'| J^q|j, m\rangle$$
where $A^q$ is a tensor operator. Can something be said about the completeness relation for the states $|\alpha j m\ra... |
I was solving this question,
I arrived at the correct answer which is 'A' the reason 'C' and 'D' are incorrect is cuz the fringes would eventually converge as if we look at this question from another point of view it's similar to a light source striking a plano-convex lens (But the lens is cut out from a cylinder).
As... |
In the context of the Lindblad equation in the Heisenberg picture, the adjoint of the Lindblad generator, denoted as $\mathcal{L}^\dagger$, is known to be non-contractive in different cases. I would like to gain a deeper understanding of the conditions under which we can assert that $\mathcal{L}^\dagger$ forms a contra... |
The trajectory of an observer with a uniform proper acceleration $a$ (Rindler) in an inertial frame $(t,z)$ can be described by the hyperbola
\begin{equation}
\left(z+\frac{\gamma_{0}}{a}\right)^{2} - \left(t+\frac{\gamma_{0}\beta_{0}}{a}\right)^{2} = \frac{1}{a^2}\,,
\end{equation}
where $\beta_{0}$ is the initial... |
I am currently studying longitudinal vibrations in an elastic beam. However, I am struggling a bit because it is the first time I have done continuum mechanics. More specifically, when isolating an infinitesimal portion of the beam, who is applying the force on each face? Is it the infinitesimal elements next to it $[x... |
When you consider the positive terminal of battery, wire and capacitor plate, they form a single conductor, which is polarised by the field of the other capacitor plate, but it is not polarised as much as it would if the wire to the battery were longer or stretched to infinity. Surely the maximum charge held on the cap... |
There are uniqueness theorems that classify Black holes according to its mass, angular momentum and charge. One of the theorem is Carter-Robinson theorem which has many assumptions and then it says axis-symmetric and stationary black holes are kerr black holes which depends only on two parameters.
One of the assumption... |
I understand how to show in general, that under the diffeomorphism $x^\mu\to x^\mu+\epsilon^\mu (x)$, the metric tensor changes as $$g'_{\mu\nu}(x')=g_{\mu\nu}(x)-\partial_\mu\epsilon_\nu(x)-\partial_\nu\epsilon_\mu(x),\tag{1}$$ and the differential $dx^\mu$ changes as
$$dx'^\mu=\frac{\partial x^\mu}{\partial x^{\gamma... |
Assume a spin s= 1/2 is subjected to an external magnetic field $B=Be_z$. The Hamiltonian is then given by
$$ \hat{H} = -\frac{eB}{mc} \hat{S}_z = w\hat{S_z} $$
and that at t= 0, the spin of the particle is in the eigenstate of the $S_x$ operator with the eigenvalue $ \hbar/2 $, e.g.
$$ \hat{S}_x|\psi (t= 0)⟩= \frac{\h... |
Consider some toy N-body simulation: we start with a bunch of particles, discretize time, and simulate their interactions at each timestep. What numerical features should the simulation include to recover the equilibrium energy distribution of these particles with time?
|
S. Weinberg in his book "The quantum theory of fields" page 82 says: the elements $T,\bar{T}$, etc, of the symmetry group may be represented on the physical Hilbert space by unitary operators $U(T),U(\bar{T})$, etc. (by Wigner's theorem) which satisfy the composition rule $$U(T)U(\bar{T})=\exp \big( i\phi (T,\bar{T})\b... |
The radius of the earth is higher at the equator than at the pole. Would it mean then, that if I put a giant ball at the equator, it would roll up towards the pole? Why, why not?
|
I understand that when choosing a system for the problem that interests me I need to consider all the things that effect what I want to calculate and try to pick the thing that fits my interests the most, the answer I get will depend on my choice, for example the velocity of an object, if I am considering the velocity ... |
The problem is as follows:
A ball moving in a straight line is experiencing acceleration $a(t)=kt$ until it arrives at a certain length $l$ when some time $t_f$ has passed. The initial speed and position are both $0$
In order to solve this equation I tried using the alternative form $\int v dv = \int a dx$
In which I f... |
I am doing an experiment on electromagnetism, basically I am just testing the pulling force of an electromagnet using a newton meter with a magnetic hook and seeing how the pulling force changes as i decrease the amount of coils. Part of the experiment is comparing my experimental data to the expected results, the prob... |
I understand that momentum can be conserved along a certain axis while not along another. If there are forces that are affecting our system in the axis we are interested in that means the momentum along that axis is not conserved since the derivative of momentum is the force. That means if the net force is $0$ then the... |
The ground state (GS) bleach (B) is usually described by "less absorption due to depletion of electrons in the ground state". See here.
But the bleaching should also occur when there are many excited states, right? In a two level system there is no difference in saying that, but let's assume the following:
A sample wit... |
I am interested in determining whether or not it is possible to tune, by polling and/or nanomaterial loading, PVDF such that it would respond to stimulus from ionizing radiation such as Gamma rays.
This mechanical movement/vibration (or response) would be imparted to the crystalline structure of the polymer by converti... |
Suppose A is a unitary operator, a is the annhilation operator in usual sense and we know the value of the quantity, $A^{\dagger}aA$.
Then how would I calculate the value of the quantity,
$AaA^{\dagger}$?
|
I keep reading that it is supposed to account for the particle-medium interactions, but why do we need another potential besides the Coulomb one that includes the interaction between every particle in the system?
|
I have been studying heat transfer and came across the concept of the critical radius of insulation for cylindrical objects. According to the material I have, the critical radius of insulation is defined by the equation:
$$ r_{\text{critical}} = \frac{k}{h}$$
where $ k $ is the thermal conductivity of the insulating ma... |
I have been trying to calculate the determinant of the Kerr metric (described by equation 11.71, A First Course in General Relativity: 3rd Edition, B. Schutz):
$$\begin{align}ds^2 &=-\frac{(\Delta-a^2\sin^2\theta)}{\rho^2}dt^2-2a\frac{2Mr\sin^2\theta}{\rho^2}dtd\phi\\&+\frac{(r^2+a^2)^2-a^2\Delta\sin^2\theta}{\rho^2}\s... |
In the Wikipedia Quantum Point Contact (QPC) page the conductance is described as a function if the gate voltage, and has discrete jumps of the size of the conductance quantum $G_0 = 2 e^2/h$. In this Nature paper there a setup with a quantum point contact but the gate voltage instead controls the transmission $D$ of t... |
I just came across a paragraph in a set of physics notes where they implicitly claim that imposing a cut-off $k<\Lambda$ to the modes in Fourier space is equivalent to smoothing the field in real space at a scale $R=1/\Lambda$.
Can anyone give me any tips to prove this or just to understand it better? I keep hearing in... |
Upon researching the double-slit experiment, it seems to me that electrons are somehow cloaked in wavelike behavior (not at all like my previous idea that electrons were waves and somehow were also particles). To elaborate, the hypothetical scenario that electrons behave as waves and only waves bound observed electron ... |
Well, it is fiction: in Isaac Asimov's stories there are "nuclear amplifiers" that magically (fiction without even an attempt of explanation) produce a beam of W-bosons, thus amplifying the (fictional) fusion reactions in spaceships making them explode.
In a part of these stories, those amplifiers are also used to fast... |
What are the disadvantages of using a single mode Fabry-Perot laser diodes in interferometry, as opposed to distributed feedback laser diodes? I'm specifically interested in potential problems that FB laser diodes could cause when used in Michelson or Mach-Zehnder interferometers, due to a wider spectrum of FB lasers a... |
A derivation of the Klein-Gordon equation starts with the following lagrangian for a scalar field ϕ:
$$
L=\frac{1}{2}g^{ab}(∇_a\phi)(∇_b\phi)-V(\phi)
$$
If we plug this lagrangian in the Euler-Lagrange equations:
$$
\frac{∂L}{∂\phi} - ∇_a \left[ \frac{∂L}{∂(∇_a\phi)} \right]=0
$$
we obtain:
$$
\frac{∂L}{∂\phi} = -\frac... |
I'm trying to solve an exercise from my astrophysics and cosmology class, the request is the following, starting from the RW metric expression:
$$ \begin{equation*}
ds^2=c^2 dt^2 - a^2 \left ( \frac{dr^2}{1-kr^2} + r^2 (d{\theta} ^2 + \sin^2{\theta}\, d\phi^2) \right )
\end{equation*} $$
I have to find his expression i... |
Exercise 1.9 of the book Covariant LQG by Rovelli and Vidotto reads:
If we raise the index of the Pauli matrices with $\epsilon$ we obtain the 2-index spinors $(\sigma_i)^{AB} = (\sigma_i)^A_C\epsilon^{CB}$. Show that these are invariant tensors in the representation $\frac12\otimes\frac12\otimes1$.
In what sense are t... |
It is well known that under a conformal transformation, we have
$$\tilde{g}_{\mu \nu}=\Omega^2 g_{\mu \nu}, \; ; \tilde{w}_{\mu}=w_{\mu}-\frac{1}{\alpha} \partial_{\mu} \log(\Omega^2),$$
where $\omega_{\mu}$ is the Weyl vector, describing the non-metricity $Q_{\rho \nu \alpha}=-2 g_{\rho \nu} w_{\alpha}$. Let us consid... |
Let $\mathcal{D}'(\mathbb{R}^n)$ denote the dual of $C^\infty_C(\mathbb{R}^n)$, that is distributions on the set of infinitely differentiable functions with compact support. If $d\mu$ is a probability measure on $\mathcal{D}'(\mathbb{R}^n)$, then the $n$-point Schwinger function $S_n$ is the density of the $n$th moment... |
I was given this question for high schoolers - which I'm a bit embarrassed I can't answer.
Fig. 1 shows the equilibrium positions of 14 equally spaced air
molecules, labelled 1 to 14, along a line AB. The separation between
two adjacent equilibrium positions is
0.020 m.
When a point source of sound located on the left... |
This is the character table for the group $C_{3}$
The last column represents the binary basis corresponding to different irrep, But I did not understand from where we are getting this basis ($x^2+y^2, yz$, etc.). Could you please explain this? Is there a rigorous way of getting this?
Reference: Group Theory for Physic... |
In 2d CFT we know that the Casimir energy of the vacuum is proportional to the conformal central charge $c$.
$$
F_L=f_0 L-\frac{\pi c}{6 L} \tag{1}
$$
where $F$ is the free energy and L is the circumference of the 2d cylinder. However is we search the Wikipedia we find the Casimir energy is due to the quantum fluctuati... |
I think if curl of a vector field $\vec{v}$ corresponds to an applied rotation, it's cross product with a velocity vector field $\vec{w}$ (say) should give something analogous to the resulting torque. Am I close?
|
The way I've seen the motion of a ball thrown vertically:
All balls are thrown with an initial speed. In my understanding, it's not possible that something goes either upward or downward with nonzero velocity.
When thrown upward: the initial velocity a ball is thrown with is the maximum velocity of the motion and the... |
If every mass has an equal force of gravity — on, say, a circle — then wouldn’t gravity act towards every point equally and not towards the circle? Do we just say that gravity acts at the centre of mass to make calculations simpler? Also, is this true for every object… even those that are unequal and not symmetrical? O... |
Fermi (Quantum Theory of Radiation 1932), using the electromagnetic energy expression $W_e$, a new variable $v_s$ is derived in equation: $$v_s=\frac{\partial W_e}{\partial \dot{u}_s}$$ which is canonically conjugate to $u_s$ (generalized position variable).
I'm not sure how he did that. What I understand is that, from... |
Is the radius equal to the length/radians.
Since the circumference is 2 pi times r and radians of an entire circle is 2 pi r should be equal to lentgh/radians
I needed this proof to understand why we use radians/s and not degrees/second when calculating velocity using angular velocity
This way the units cancel out and ... |
I am instinctively skeptical of the existence of "dark matter" and "dark energy". Together, they strike me as being analogous to luminiferous aether -- something that was invented to explain a gap in our understanding that was actually due to our physical models being incomplete.
As far as I know, there is no widely-ac... |
Since the definition of sound speed, ($c_{s}$), in each ion s$th$ species ($is$) expressed that:
\begin{align*}
c_{s,is} = \sqrt{\frac{k(T_{e}+T_{is})}{m_{is}}}.
\end{align*}
How can we determine sound speed for multi-component plasma when the multi-component plasmas containing with $\text{e}^{-},\, \text{p}^{+}$, and ... |
The low-energy effective action of the bosonic string in the critical dimension $D=26$ is given by:
$$S=\frac{1}{2\kappa_0^2}\int d^{26}x\sqrt{-G} \left[ \phi^2\left( R-\frac{1}{12}H_{\mu\nu\lambda}H^{\mu\nu\lambda} \right) + 4\partial_\mu\phi \partial^\mu \phi\right].$$
which involves the dilaton field $\phi$, the met... |
The P-function of a state $\rho$ (focusing on the single-mode case) can be written as, using a notation analogous to the one in Gerry&Knight' book,
$$P_\rho(\alpha) = \int \frac{d^2\eta}{\pi^2} \chi_N(\eta) e^{\alpha\bar\eta-\bar\alpha\eta},
\quad \chi_N(\eta)\equiv \operatorname{tr}[\rho\exp(\eta a^\dagger) \exp(-\bar... |
So I was reading the lecture notes by Asboth on topological insulators . In the first chapter the SSH model is discussed :
$H_{SSH} = \sum_{i = 1}^N v|i,A\rangle \langle i,B | + h.c. + \sum_{i = 1}^{N-1} w|i,B\rangle \langle i+1,A | + h.c. $
In the discussion, it is said that the Hamiltonian of the boundary has two edg... |
If we consider a practial situation, where air resistance exists, why does a ball/object take more time to come down than to go up?
This seems contradicting to me at the first glance, but I am pretty sure this might be due to the direction of air resistance acting.
Any help is appreciated.
|
Non-contact forces like gravitational forces exist between two objects in any medium because of the establishment of a field/wave.
Since at an atomic level, 'physical' contact won't really be possible for any kind of force (contact or non-contact) , so is a 'field' established here as well? (albeit extremely small)
Als... |
Significant figures are used to ensure that the value is precise, and fall in within error in the positive and negative direction.
327 degrees true can also be written as N33degreesW. As such, would this direction be 2 or 3 significant figures? It is understood that their total is 360 degrees, where addition and subtra... |
I understand that if neutrino flavour is just a superposition of mass eigenstates, the probabilities of detecting a particular flavour of neutrino will vary as they propagate since the time evolution factors of the mass eigenstates advance differently. The problem I'm having is understanding why the flavour and mass ei... |
I was reading this wikepedia page, about the dipole radiation, and I was wondering how to derive the $\mathbf E$ and $\mathbf B$ fields in this situation.
I've started using the retarded potentials:
$$
\phi(\mathbf r, t) = \left ( \frac{q}{4 \pi \varepsilon_0} \frac{1}{|\mathbf r - \mathbf r_s|(1-\mathbf{\hat n}\cdot\b... |
In non-linear cosmological perturbation theory, one can compute loop corrections to the linear matter power spectrum which are necessary to accurately describe the statistics of matter at quasi-linear scales. In the Standard Perturbation Theory (SPT) approach, these loop corrections are generally UV divergent. The term... |
I have a task to arrange MZI using very weak source with photons coming one at a time. On top the wavelength is 810 nm. How to 'see' the interference pattern to 100% in one channel and 0% in other. I have a CCD and suppose to let it integrate over a big interval of time. I heard about plates which can multiply the num... |
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