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An air coaxial transmission line has a solid inner conductor of radius $a$ and an outer conductor of inner radius $b$ and outer radius $c$.Find the $\vec B$ as a functions of radial distance $r$
We only consider the range of $b<r<c$,because i can't understand the equation which is written by the book
$Bl=\mu_0I_{in},... |
In my assignments the density operator is given as follows:
$$\rho = \sum_{\alpha = 1}^{6} w_\alpha |\alpha\rangle\langle\alpha|\quad \text{where}\quad w = \left(\dfrac{1}{10},\dfrac{1}{10},\dfrac{1}{10},\dfrac{1}{10},\dfrac{1}{10},\dfrac{1}{2}\right)$$
Calculating this thing seems trivial, but expanding the formula, I... |
I've been recently reading about the derivation of the Bleaney-Bowers equation from Van Vleck paramagnetism and I am looking forward to derive it but using a statistical mechanics formalism instead.
The Bleaney-Bowers equation for the magnetic susceptibility is:
$$\chi = \frac{2ng_S\mu_B^2}{k_BT(3+e^{\Delta/k_BT})}$$
N... |
In Fermi's book "Thermodynamics", in page 20, Fermi shows the first law of thermodynamics:
$dU + pdV = dQ$ (equation 21 in the book).
He then goes on and shows how, if we were to take $T$ and $p$ as independent variables, we'd have:
$\left[ \left( \frac{\partial U}{\partial T} \right)_p + p \left( \frac{\partial V}{\pa... |
I am working on a project which requires solving TOV equation. The equation is as below:
$$
\frac{dP}{dr} = -\frac{G m \rho}{r^2}\left[
1+\frac{P}{\rho c^2}
\right]
\left[ 1+ \frac{4\pi r^3 P}{mc^2}\right]\left[
1-\frac{2Gm}{rc^2}\right]^{-1}
$$
I need to use $c=1$ but then I should I change the gravitational constant?... |
Given the electrostatic field $\mathbf E$, its integral over a closed surface $\mathcal A$ is the total charge enclosed by it: $$\epsilon_0\oint_{\mathcal A} \mathbf E \cdot d \mathbf A = Q_{\mathcal A} \tag{1}\label{1}.$$ Now let there be given a a dipole field $\mathbf P$, so that $\mathbf D =\epsilon_0(\mathbf E+\ma... |
It is known that the Lindblad equation is a master equation.
Does there exist a general approach to a detailed balance condition/solution for this equation?
Please either kindly provide the solution or a reference in scientific literature.
|
In a condition that there is a closed tank with water in it, and also there’s some air on that water. Tank is closed.
Somehow(let’s say through a very thin hole) if I vacuum the air on the water from tank suddenly, what would happen to the water?
I think the water would get sucked, vacuumed because there was air on it,... |
I've been reading through this paper, and there is one small part that I was hoping someone can help me understand better. If you care to, you can read the paper for more context, but broadly speaking one has the following setup:
(i) One has some spacetime manifold (in this case a Schwartzschild black hole) with metric... |
I have a doubt in one of the problems, I came across in a book.
Though I searched answers for it, I was not able to develop a satisfactory understanding.
The question asks us to draw a free body diagram of each block and find the acceleration of each block.
Most of the answers take the system to have a acceleration of... |
In Einstein's paper, he deduced that the diffusion equation is satisfied for the number of particles per unit volume ($f(x, t)$), i.e
$$\frac{\partial f}{\partial t}=D\cdot \frac{\partial ^2 f}{\partial x^2}$$
The solution of this equation for $N$ particles starting at the origin is
$$f(x, t)=\frac{N}{\sqrt{4\pi Dt}}\c... |
In Sec. 8.7 of this Applied Conformal Field Theory, Ginsparg discusses the space of $1+1$ dimensional CFTs with central charge $c=1$, and the summary is in figure 14. Essentially there are two continuous families of such CFTs, one along the horizontal axis and the other along the vertical axis, together with 3 other th... |
I don't know if math stack exchange is more suitable for this question, but I'll try here first.
It is often stated in quantum mechanics textbooks (e.g. the first volume of Cohen-Tannoudji, Diu, Laloë, page 135) that
“If two observables $A$ and $B$ commute, it is possible to construct an orthonormal basis of the Hilbe... |
I am thinking about one question. If the Hamiltonian matrix is based on the non-orthogonal basis, how to compute the charge conductance with the non-equilibrium green function (NEGF) method.
Suppose the Hamiltonian of the system is denoted by $H$ and the overlap matrix is denoted by $S$. They are written below.
$$\left... |
Following Setup:
There is a Pendulum swinging around a vertical axis, with angles $\varphi$ for rotation, and $\theta$ for the incline compared to the horizontal axis. The mass is $m$ and the length is $\ell =const.$
(maybe required pre-knowledge):
The lagrangian is
$$
L=\frac{1}{2}m(\ell^2\dot{\theta}^2+\ell^2\sin^2{... |
I do not completely understand the concept of chemical potential $\mu$:
It is usually defined by
$$\delta Q = T dS = dU + pdV + \mu dn$$
By adding, lets say 1 mole of mass to a gas of 10 moles ($\delta n = 1 mole$), I will have 11 moles afterwards.
But what does it mean in that context to "add" some amount of a compone... |
I solved this question and I got the values of charges on capacitors in figure B. But my question is charge on capacitors is getting redistributed,but how is it possible when potential difference between the capacitor is zero since they are at equal potential. So there is no chance of charge flowing in the circuit.ple... |
I'm trying to read An Introduction to the Mathematical Structure of Quantum Mechanics by Strocchi, which (as I understand) takes measurements first and states second, and argues that if we allow observables to be formally added then they form a Jordan algebra, which usually can be embedded into a $C^*$-algebra. Then he... |
We say that Brownian motion is caused by the random collisions of particles. But let's consider an ionized gas; in that case, there's a nonzero net charge on the atom. Doesn't this mean the electrostatic force determines the paths the gas ions take, and hence their motion is predictable rather than random? Even with m... |
The Joule Coefficient for a van der Waals gas can be shown to be
\begin{equation}
\left(\frac{\partial T}{\partial V}\right)_U=-\frac{a}{C_VV^2}
\end{equation}
where $U$ is the internal energy of the gas, $V$ is the volume, $T$ is the temperature, $a$ is a constant (a parameter in the vdw equation of state) and $C_V$ i... |
Is it possible to determine the adiabatic gas coefficient of an ideal gas when measuring the pressure of the gas in an isothermal process?
|
Consider the energy-momentum tensor in quantum field theory for a massless scalar field $\phi$;
$$T_{\alpha \beta} = \phi_{, \alpha} \phi_{, \beta} - \frac{1}{2} \eta_{\alpha \beta} \eta^{\lambda \delta} \phi_{, \lambda} \phi_{, \delta}.$$
For introductory purposes, further simplifcation usually reduces this to $1 + 1$... |
Let us take a nuclear reaction as follows: $$\rm _7^{16}N +{}_2^4He \rightarrow {}_8^{19}O+{}_1^1H$$
Now the question is that we have to find the minimum kinetic energy of the Helium atom for the nuclear reaction to occur. Given are the masses of the atoms/nuclei.
Now I can easily calculate the $Q$ value of the reactio... |
One often finds in quantum mechanics textbooks (for physicists) a "proof" that self-adjoint and commuting operators $A,B$ have a common eigenbasis. However, in the standard proof of Bloch's theorem (see e.g. Ballentine Chapter 5.3) one uses that commuting normal operators have a joint eigenbasis. How does one show this... |
Let us take the capillary dipped in water and we let the water climb normally till its maximum height. Now we break the capillary (assume clean cleavage so there aren't any rough surfaces produced) at some point so that there is some water present above the point.
Question is what will happen to the waterline shape at ... |
In the system of 4 distinguishable particles. How is it possible that the more massive particle went into the first excited states while the rest of the particles remained in their ground states?DO the particle with more mass have higher energy which causes its transition from one state to another? As it is written in ... |
This might seem a dumb question but it is at the heart of mechanics.
We learn that in our universe the total energy of a closed physical system is conserved, never destroyed, never created, only transformed in different types of energy as time goes by.
Then we learn that potential energy is the kind of energy reservoir... |
In Section 15 of Landau and Lifshitz Classical Mechanics, they discuss the path of a particle under a central field. They show that the path is a conic with a focus at the origin. When the energy of the system is 0, the say the path is a parabola. Here they say, "This case occurs if the particle starts from rest at inf... |
I have to add two measures with their respectiuve absolute uncertainties, given by the instruments I have used to measure them. The measures are:
x = 0.486 +- 0.001 m
y = 0.01230 +- 0.00001 m
They have been measured with two different instruments with different sensibility. I need to find the final lenght.
As far as I ... |
I have arrived at the equations of motion for a double pendulum, with gravity $g$, masses $m_i$, link lengths $l_i$, angles $\theta_i$, and applied torques $\tau_i$.
Please see the diagram and derivation at Diego Assencio's blog.
I end up with a vector equation in matrix $2\times 2$ matrix $A$ and $2 \times 1$ vector $... |
I am reading the nice discussion on this MO thread on the idea behind Quantization mathematically. This answer is quite nice, and for my question, I take some quotes from it:
"quantum mathematics" is when you try to take geometric facts, written algebraically, and interpret them in a noncommutative algebra.
.
.
.
Th... |
Work is done when an applied force displaces the point of application in the same direction as the force. I don't understand this definition. The point of application is defined as the point at which the force is applied to a body. So doesn't this point remain unchanged if the force is applied to the same point. Could ... |
While deriving the electric field profile of a diode, 1D Gauss's Law is typically used:
$$\frac{dE}{dx}= \frac{\rho}{\varepsilon_0}.$$
However, the diode is at least 2-dimentional and, in real world, even 3-dimentional.
So how can we use a 1D equation to model this, when it should be at least 2D?
Also, the equations of... |
The vacuum wavefunctional of a quantum field theory is often generally expressed in terms of a path integral as
\begin{equation}
\langle\Phi(\vec{x})|\Omega\rangle = \int_{\varphi(\tau=0, \vec{x}) = \Phi(\vec{x})} \mathcal{D}\varphi\, e^{-S_E[\varphi]}
\end{equation}
where $|\Omega\rangle$ is the vacuum state, $S_E[\va... |
While calculating the time period of a simple pendulum, i.e $$T=2\pi\sqrt{\frac{L}{g}}$$
Why do we consider the effective length, $L$?
It is the distance from the point of suspension to the centre of the bob. Why don't we just use only the length of rod? What importantce does the extra length (radius of the bob) give i... |
This question is inspired by the recent "double-slit experiment in time" experiment that was popularized. See here and here. I have not looked into the original paper in detail, so my question may not be strictly related.
In any case, let me explain my understanding of the role of Fourier transforms in the Fraunhofer s... |
I am told that the probability of measuring $\lambda$ is $$p_\lambda = Tr(\hat{P}_\lambda\hat{\rho}) = Tr(\hat{P}_\lambda\hat{\rho}\hat{P}_\lambda)$$ where $\hat{P}_\lambda = \sum_{n:\lambda_n = \lambda}|n\rangle\langle n|$ is the projection operator for eigenstates $n$ with an eigenvalue $\lambda$.
I have no idea how ... |
I understand that at resonance, a spring-mass-damper system will only require input energy from a forcing that matches the energy dissipated per cycle by the damper.
Let's say that you have a system with a natural frequency $f_o$, are forcing it at some frequency that is roughly twice that frequency, and I let the syst... |
I was interested in electromagnetic induction in loops, since ground loops and such tend to be a problem in electronic system engineering. To me, it seems like induction in loops may tend to cancel out. For example, if the plane of a simple wire loop (that is just a ring of wire and nothing else) is perpendicular to an... |
Does there exist a mathematical rigorous theory of the Feynman-Path-Integral in Quantum Mechanics or Quantum Field Theory?
|
I am currently starting to work on LED but I am confused how can I calculate the external quantum efficiency for my LED? like I know the basic idea, I want to know what experimental setup should I used for my LED and how? In my Lab we have Raman spectrometer with CCD detector.
|
So, say we define a clock as measuring an electronic oscillation on a quartz atom, eg, a normal clock.
The fine structure constant is a relation between the electron mass and C. If C goes up, electron mass goes up for a fixed alpha.
It's technically not based on the electron mass, but if the mass to charge ratio is fix... |
I'm reading Khan Academy which says in this picture:
That P1 > P2 since P1's positive work is greater than P2's negative work. However, I thought forces do work, not pressures. Since F = P * A, I only understand why P1 * A1 > P2 * A2. You can even see in the picture that A1 is greater than A2. How come we can confiden... |
The most general scalar field defined at all points of a Minkowski spacetime can be modelled as;
$$\phi({\bf{x}}, t) = \Sigma_{{\bf{k}}} \left(a^{\dagger}_{{\bf{k}}}u_{{\bf{k}}} + a_{{\bf{k}}}u^{*}_{{\bf{k}}}\right)$$
where $$u_{{\bf{k}}} = \dfrac{1}{\sqrt{2 \omega (2 \pi)^3\vphantom{\tfrac{1}{2}}}} e^{i{\bf{k}\vphanto... |
This is for an isochoric system held at a temperature $T$ by its surroundings, and that heat $dQ$ is added to the system by its surroundings.
According to chapter 16.5 in Concepts in Thermal Physics by Blundell and Blundell, for a system held at a constant temperature and volume, the inequality
$$
dw \geq dF
$$
show... |
I am trying to understand parts of this webpage on the quantum hall effect, and I am stuck on the part where they talk about Corbino geometry. So we have a conductive 2D annulus and a changing magnetic flux confined to the middle of the annulus.
We will also try to do the experiment in reverse i.e. apply an electric f... |
I am having some trouble understanding parity violation in the weak interaction. Specifically, I have been reading about the 1956 Wu Experiment. From what I understand, it is the anisotropic distribution of electrons that implies parity violation. Why, however, is this necessarily true. By placing the atom in a magneti... |
Electric potential is the amount of Work required to move a unit positive charge from infinity to a region of an electric field. Why do we need a positive charge for that? Can't we use negative charge?
|
I have a complex area of a pipe system where I'm not totally sure all that's going to be going on in terms of turbulence and compressible flow, though I would still like to verify that nothing in the area is going to be under too much pressure.
My thinking is that I can just calculate the stagnation pressure upstream a... |
For the hydrogen atom, a simple separation of variables give the energy eigenvalue of the Schrodinger operator for one electron in a spherical potential. It is well known that there are no such explicit solutions for the helium atom. However, is there a rigorous mathematical proof that the helium atom's Hamiltonian ope... |
Many people have said that the noise that affects laser light is proportional to the square root of the illumination. But I can't find the formula. Can anyone help?
Maybe it has something to do with this: photon (radiation) noise caused by fluctuations in the number of photons emitted by the source and absorbed by the ... |
I have a problem in getting the transformation of the intensity of light.
1>> Using the transformation of the energy-momentum tensor $T^{ik}$, we can obtain
We have used the fact that $T^{00}=W$ is the energy density of the electromagnetic field. And the intensity of light is
$$\mathbf{S}=\mathbf{n}cW$$
So we can get ... |
The natural units of Planck and Stoney differ by the inverse of the finestructure constant.
For example, the Stoney-mass is:
$$m_s=\sqrt{\frac{k_e e^2}{G}}= 1.85921×10^{-9} kg,$$
where $k_e$ is Coulomb's constant, $G$ the gravitational constant, and $c$ the speed of light.
In contrast, the Planck mass is given by:
$$m... |
Is the statement "if an operator commutes with every generator of the Lie group, it is a Casimir operator" true? (I'm interested in the case of quadratic Casimir invariants, but any answers about higher-order ones would also be appreciated.) I understand its converse holds (for example, this post is helpful) at least f... |
I'm learning about semiconductors and I'm trying to find out the dependence the Hall coefficient has on temperature.
So far, the Hall coefficient for a semiconductor, in terms of the mobilities and the densities of the charge charriers (electrons and holes), is given by:
$$R_H = \frac{1}{e} \frac{p_v\mu_h^2-n_c\mu_e^2}... |
The exercise is to calculate the surface current density of Pb at $T = 4.2K$. The critical temperature $T_c$ and the critical field at zero temperature is given: $T_c = 7.2K$ and $H_c(0) = 803Oe$. I use $H_c(T) = H_c(0) [1-(T/T_c)^2]$ to calculate $H_c(4.2K)$.
For the surface current density I use $j_{surf} = \frac{\ma... |
In the answer to question 5.1 of "Problems and Solutions in Introductory Mechanics" by David Morin, he says that:
A normal force does work if you push on a book with your hand
I'm unable to imagine what he means by this. If we are talking about pushing the book sideways, the normal force is perpendicular to the motio... |
I have seen articles online discussing the roundness of electrons. This goes a bit against my understanding of electrons as elementary point like particles. How can a point have a shape? What does roundness mean in this context?
|
When the size of the observable universe was small as a proton what was the physical content of it?
Was there a limit of particles in such a tiny volume with enormous high density and energy?
Can we find more than one proton inside such a volume, can we assume that because an electron, a quark, or a photon are point pa... |
Suppose $f(i,t)$ indicates state $i$ at time $t$. Are there examples of exactly solvable models where $f$ is described by differential equations similar to one below?
$$\frac{\partial}{\partial t} f(i,t) = -2 f(i,t)d(i) + u(i) \int_0^\infty \mathrm {d} i\, v(i) f(i,t).$$
It feels like solving this needs a continuous ve... |
Question: What is the magnetic field at a point a distance $x$ from the center of the axis of a circular loop of radius $R$ carrying current $I$?
I was given the answer $\frac{\mu_0}2 \frac{IR^2}{(x^2+r^2)^{3/2}}.$ I am trying to figure out how to use Biot-Savart Law to derive this.
$$dB = \frac{\mu_0}{4\pi} \frac{I ... |
I don't understand rectilinear sinusoidal motion well, for exemple if I have the time of achieve the end of the trajectory how I can find the period T to calculate Omega? I really need a text book to study it.
|
Hello so I am having an issue with a question I am trying to solve.
So far I have learnt that the work done by a force $F$ is equal to $F$ multiplied by $x$ where $x$ is the displacement in the direction of the force. Also, I think that it should not matter in the case of having 2 forces acting on an object if you fin... |
Can someone point me to resources where this process is described using the Schrödinger equation? It's not obvious to me how that could be done, as you'd need to define the proper potential.
|
In Semiconductor Physics, the bottom of conduction band $E_C$ is treated as the electrostatic potential. This energy level is typically used to express the carrier concentration in terms of the electrostatic potential and then is used in combination with Poisson's equation to obtain the potential distribution throughou... |
I wished to understand a particular case of Euler's equation applied in the following cylindrical body:
where $I_{1,2,3}$ are the moments of inertia. By symmetry, $I_1=I_2=I_T$.
Here I consider that no external forces are applied to the cylinder. Stating the equations by their components, we have that:
$$I_1\dot{\omeg... |
In Statistical mechanics, when we are to find the most probable configuration for the assembly using Lagrange undetermined multiplier method, why it is convenient to maximize $\log(W)$ instead of $W$, where $W$ is the weight of the configuration.
$$dW + adN + bdE = 0$$
$$ d logW + \alpha dN + \beta dE = 0$$
|
I am creating a model which aims to predict a Land Surface Temperature related variable (from satellite thermal infrared measurements) which uses a vegetation related variable (created using satellite near infrared, red and blue light measurements).
I have had a comment that this is a circular exercise as they both use... |
If I have a quantum system with energy levels that exhibit random matrix statistics (so basically level repulsion).
I would like to study the thermodynamics of such systems, maybe see a macroscopic effect due to level repulsion, how should proceed?
I have the density-density correlator (that highlight the energy level ... |
If we accept that eigenvalues of operators show correspond with possible values measurements by that operator can take, then it makes sense to define the position operator $X$ on a "deterministic"/eigenvector ket "state" $|x_0 \rangle$ to be $x_0$. This is exactly what the Wikipedia page says https://en.wikipedia.org/w... |
In order to prove the $2$ to $1$ homomorphism $SL(2,\mathbb{C}) \rightarrow SO^{+}(1,3)$ I was given the following trace identity for $2 \times 2$ complex matrices $M_{1},M_{2}$:
$$\text{tr}(M_{1}M_{2}) = \frac{1}{2}\text{tr}(M_{1}\overline{\sigma}^{\mu})\text{tr}(\sigma_{\mu}M_{2})$$
I want to prove this identity.
whe... |
On page 522 of Peskin and Schroeder, we try to calculate the self-energy of gauge boson. Figure 16.7 gives the following diagrams:
However, Peskin and Schroeder says there are three additional tadpole diagrams that automatically vanish by Furry's theorem. What are those three additional diagrams?
Edit: are these what ... |
Based on this question, and paying attending to shell theorem, what would happen to gravity if there were multiple hollow shells within each other?
Would the effective mass and gravity of each shell combine into one gravity field at the surface of the outer sphere with complete zero g throughout the entire inside the ... |
In the Born-Oppenheimer approximation, the effective potential energy, is the potential energy that an electron gains when considering all the inter-particle interactions in a molecule? Said in another way, which particles do experience this effective potential?
Is it correct to say that the effective potential is the ... |
There has been a bit of discussion about this already, however, my question arises more from the mathematical requirements to allow for Fraunhofer diffraction proposed by Born and Wolf's optics book.
First: variable definitions: Given $r'$ is the distance of the source from the aperture and $s'$ is the distance of resu... |
Given a slow-roll potential $V (\phi)$, how do the cosmological parameters (see e.g. the Dodelson book on Cosmology, section 8.7) relate to this potential? I'm a bit confused how parameters such as primordial tilt and tensor modes relate to this potential.
Also, is this all just measured from looking at the CMB?
|
Suppose I have 2 Grassmann scalars $\theta$ and $\bar{\theta}$ and form the bosonic quantity $X = \bar{\theta}\theta$. Is there a purely bosonic representation of the delta function $\delta(X - \overline{\theta}\theta)$, which can be used in integrals to replace
$$f(\bar{\theta}\theta) = \int dX \;\delta(X - \bar\theta... |
In a problem, I have the expression of acceleration and velocity in Cartesian coordinates , and it ask me to calculate the tangential and normal acceleration, so we don't know how I can do that, can any one help me?
|
Perhaps another way to put it is, what exactly does it mean to quantize the EM field and why is it necessary? What mathematical properties does the quantized version of the field have that the classical version doesn't and vice versa?
For context, I was reading a thread about where specifically classical E&M fails and... |
If a centrifuge without a ballast is centered on the origin of an $x$-$y$ coordinate plane, and starts at the $x$-axis rotating with increasing velocity counter-clockwise around the origin, how can the centripetal force of this accelerating centrifuge be calculated in the $x$-direction, and in the $y$-direction separa... |
For the wedge product of two, 3D real vectors in a vector space with basis vectors $u1$, $u2$ and $u3$ [just for a simple example], I understand that there is a natural basis for the Wedge product space given by $u_1 \wedge u_2$, $u_1 \wedge u_3$, $u_2 \wedge u_3$.
How about the more simple case of the wedge product of... |
I just read this answer to "What exactly is a Photon?" which has me a bit confused. It seems to be arguing that "photon" is just a catch-all term for any sort of interaction with the EM field and the implication is that it's not even a particularly useful concept, in contrast to the fundamental particles of other fiel... |
I viewed many relevant threads but didn't quite find the answer. I don't really know what I'm talking about so I'm mostly looking for a lead on how I should be thinking about this
From my understanding a Kerr black hole with a high rate of rotation can have a very close innermost stable circular orbit. For my question ... |
If relativity is symmetrical (triplets moving away and returning to the center) then what happens to the Doppler effect as seen by the moving triplets?
A B C
A should see C moving (Doppler) away/to faster than B
C should see A moving (Doppler) away/to faster than B
B should see A and C moving (Doppler) away/to at the s... |
I am trying to understand subject effect in the framework of general relativity. Wikipedia says as follows:
imagine that a north–south-oriented ice skater, in orbit over the equator of a rotating
black hole and rotationally at rest with respect to the stars
Than, frame dragging is described as:
Also, an inner region... |
Working with Lagrangian we often encounter derivatives of particles fields, for example let's consider the first term of the LO chiral Lagrangian
$$ \mathcal{L}_{B\phi}^{LO}=\text{Tr}[\overline{B}(i\gamma^\mu \nabla_{\mu} - M_B)B]$$
where $B$ is the baryons matrix, and $\nabla_\mu = \partial_{\mu}B + [\Gamma_{\mu}, B]$... |
In the famous paper about semiclassical Bloch theory https://arxiv.org/abs/cond-mat/9511014, the Lagrangian
\begin{eqnarray}
L (\mathbf{k},\dot{\mathbf{k}}) = -e \delta \mathbf{A}(r,t)\cdot\dot{\mathbf{r}} -\hbar \mathbf{k}\cdot\dot{\mathbf{r}} + \hbar \dot{\mathbf{k}} \cdot \mathcal{A}(\mathbf{k}) - E(\mathbf{k}), \t... |
Why is hydrogen considered the most efficient fuel? I mean I know it is very light and can be accelerated very fast, but can’t you use a denser fuel but throw it at a slower speed bunch, and it’ll still achieve the same force as it’s heavier?
Also, why do people say that a rocket engine with hydrogen fuel also generall... |
Suppose a horizontal rod (ignore gravity) of mass $m$ and length $L$ is rotating about one of its ends with constant angular velocity $ω$. Then, the tension must decrease as we move away from the axis. Same goes for the centripetal force. Then on an element $dx$ at $x$ distance from the axis the forces must be $T$ and ... |
If I released a giant cloud of Oxygen into space, would you be able to hear sound inside of it before it dissipated?
From my understanding, the reason there is no sound in space is because there are no atoms for the sounds waves to interact with. So if you theoretically put atoms in space would they carry the sound?
|
I heard that $\phi^4$ theory in $4-$dimensions is NOT asymptotically free.
But in lower dimensions like $2$ and $3$, it is said to be asymptotically free.
However, what confuses me is that in $3-$dimensions, $\phi^4$ theory is said to be asymptotically free "only" on a speicific trajectory in the renormalization group.... |
I'm trying to understand inner Bremsstrahlung. I know this applies to beta minus decay, but have a hard time understanding how it works. In the beta decay, electron is emitted from nucleus. I believe it's quite energetic/fast, but where does the electron go?
does it completely go out of the emitted atom?
or does it st... |
I was going through the proof that Maxwell's equations are not invariant under Galilean Transformations. If we consider two inertial frames (S and S' moving with velocity $\vec u$ with respect to the first) then the forces on a charge must be the same, which allows us to say that
$$\frac{\vec F}{q} = \vec E + \vec v\ti... |
Suppose we have a simple $LC$ circuit as shown below.
I want to determine the following:
The charge function on capacitor plates at any given moment
The current at any given moment
For this, let us write the KVL in counterclockwise direction:
$$ \varphi_A - \varphi_B + \varphi_B - \varphi_A = 0$$
Now suppose the vo... |
I translate into English what is written in Italian in the adopted text.
Two forces are parallel if they have parallel lines of action; two parallel forces are concordant if they have the same direction. The resultant of two parallel and concordant forces $\vec{F_1}$ and $\vec{F_2}$, applied at points $A$ and $B$ res... |
In the situation above, we have a power line which uses an alternating current. This alternating current causes a change in magnetic flux through the loop below the power line, which induces a current according to Lenz's law/Faraday's law, which eventually goes to the farmer's equipment. This is classed as power theft... |
Why are there two different $J = \frac{1}{2}$ baryons with quark content $uds$ (the $\Lambda_{0}$ and $\Sigma_{0}$) but only one $J = \frac{3}{2}$ baryon (the $Σ_{*,0}$) with the same quark content?
I think it might be something to do with the symmetric and antisymmetric spin wavefunctions. I think that a fully symmetr... |
Method 1:
(i) Expand the density operator in the Fock basis as
$\rho=\sum_{m,n}{\rho_{mn}|m\rangle\langle n|}$.
(ii) Purity = $tr{\rho^2}=\sum_{m,n,f,g, \lambda}{\rho_{mn}\rho_{fg}\langle \lambda|m\rangle\langle n|f\rangle\langle g|\lambda\rangle}$
(iii) Three out of five sums vanish due to the inner products
(iv) Ther... |
Although neutron stars are mostly made of neutronium, the pressure at the surface is not very high which allows regular atomic matters to exist. Emission spectrum can reveal the chemical composition of distant stars. However, neutron stars are surrounded with extremely strong magnetic field which is enough to distort t... |
I have trouble deriving a supposedly "well-known" equation used in condensed matter physics:
$$n^2=\mu_r\varepsilon_r+\frac{i\mu_r\sigma}{\varepsilon_r\omega}$$
I'm sure that $n$ and $\sigma$ are complex, and this equition is obtained by solving
$$\mu_0\mu_r\sigma\frac{\partial}{\partial t}E+\mu_0\mu_r\varepsilon_0\var... |
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