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I am looking for an analytical expression for $$\langle r\rangle = \int dr r^2 R_{n'l'} r R_{nl}$$ where $R_{nl}$ are the radial wave functions, defined as
$$R_{nl}(r)=N_{{nl}}\,r^{{l}}\,e^{{-{\frac {1}{2}}\gamma r^{2}}}\;L_{{{\frac {1}{2}}(n-l)}}^{{(l+{\frac {1}{2}})}}(\gamma r^{2}).$$
The function ${\displaystyle ... |
I'm working on phase transitions in the early universe. Generally, a particle physics model in form of a Lagrangian is taken, the one-loop corrections in the potential for zero and finite temperature are added and then one searces for the existence of different phases with individual vacua in the model for different pa... |
In the mathematical sense, I understand what is the solution for a wave equation of such form:
$$\frac{\partial^2 u}{\partial t^2}=c^2\left(
\frac{\partial^2 u}{\partial x_1^2} +
\frac{\partial^2 u}{\partial x_2^2} +
\cdots +
\frac{\partial^2 u}{\partial x_n^2}
\right)$$
But I have a hard time digesting its physical me... |
If you ask the question: "how many atoms per cubic meter in space", you can get a consensus of around $5$ atoms per cubic cm or about $5\times 10^6\space \text{atoms}\space m^{-3}$. If we assume these are hydrogen atoms, that works out to a density of $$5\times 10^6\space \text{atoms}\space m^{-3}\times 1.67\times 10^{... |
I'm studying atomic orbitals and the shape is usually represented with real form spherical harmonics, taken as an appropriate linear combination of the complex ones. If, however, the physical quantity is the probability density, which is the square of the absolute value and thus always real, why don't we just use this ... |
Let us consider a classical dynamical system whose obserbvables $A$ evolve according to the following equation of motion
\begin{align}
\dot A &= -\{H,A\}+f(q)
\end{align}
$f(q)$ is a non-Hamiltonian perturbation to an otherwise Hamiltonian system and
\begin{equation}
\ H = \frac{p^2}{2m}+V(q)
\end{equation}
I would lik... |
I don't understand this statement:
"The homoclinic orbit is characterized by $E = mgl$. When $E < mgl$, the pendulum is tracing other orbits."
If energy is conserved, then $E_0 = E$ ($E$ is shorthand for $E(t)$, the energy at time $t$, and $E_0$ is the energy at time 0).
Therefore, if the homoclinic orbit is satisfie... |
It's a well known fact that classical mechanics isn't a deterministic theory if you only include the positions and masses of various particles as part of the initial conditions. You also need to include the velocities/momenta of the various particles, which are formulated in terms of time-derivatives. This is somewhat ... |
I was studying about spectrum emissions but I have a question.
For example if I have $2$ electrons from different atoms with different distances from the nucleus, then I hit them with fire causing the excitation of both electrons, after this each electron generate a series of spectral lines. What factors depend on w... |
What are applications of nanomechanics beyond its use in atomic force microscopy? The question is specifically about the existing applications rather than the potential/future ones (which are quite a few).
|
Please consider the below image which is from Rana and Joag, Classical Mechanics. They build on a proof, which I reiterate below and through it they show that angular velocity of any point B in the rigid body is the same about a point $B_0$ and then state that the angular velocity of B is same about any other point too... |
Is there any difference between signature $(1,1)$ and $(2,0)$ in 2D CFT?
The only thing I could thought of was that the previous one had Lorentz symmetry and the later one was Euclidean (rotation), but were they both 2D CFT? How do they differ? (such as two-point functions etc.)
Does study one of such structure the sam... |
In an electron velocity selector, we use a positively charged plate (with a slit) to accelerate the electrons which then go through the slit and into an area with an electric and magnetic field. If that charged plate accelerates the electrons before they reach the slit, wouldn't it slow the electrons down once they hav... |
Topologically speaking, our universe is either open (topologically $E^3$) or closed (topologically $S^3$). Then with time we'd have another factor of $E^1$ and a metric connection would determine the curvature. If curvature was non-positive, then it's easy to see that the universe would be open. On the other hand, the ... |
Speaking just about space, we say that the universe is either open (topologically $E^3$) or closed (topologically $S^3$). But since a metric connection defines curvature on spacetime and not just space, does this mean a closed universe (having positive curvature) is also a closed spacetime (topologically $S^4$)? In oth... |
Let's consider a system of two nucleons (protons and neutrons). $\hat T$ is the total isospin operator and $\hat T_3$ it's projection on the axis. The eigenstate are:
singlet state: $|0,0\rangle$
triplet states
$|1,1\rangle$, $|1,0\rangle$, $|1,-1\rangle$
Since $[\hat H, \hat T]=0$ the states I wrote above can be stati... |
Refering to the paper "Replica Wormholes and the Entropy of Hawking Radiation" by Almheiri et al. in arXiv:1991.12333. The authors consider Jackiw-Teitelboim gravity theory describing a nearly AdS2 spacetime coupled to CFT matter, where the dilaton background in Eq. (3.5) of the paper (before considering conical singul... |
I'm struggling with understanding how one can generally use the a known line current density $\vec{K}$ of a single loop of current in order to calculate the magnetic field of an object with a surface, like a cylinder. In other words, if I know $\vec{K} = \alpha \hat{\varphi}$ on some cylinder, meaning it is like a sole... |
I know one can get the Fermi theory of weak interactions as a low energy effective theory of the electroweak interaction by writing down Feynman amplitudes for weak decay processes, noting that $\tfrac{1}{p^2-M_W^2}\approx-\tfrac{1}{M_W^2}$ for small momenta $p^2\ll M_W^2$, and then identifying the new effective coupli... |
In my book about quantum mechanics it state that the time derivative of an arbitrary observable is:
$$\frac{d}{dt}\langle A \rangle = \frac{1}{i\hbar} \langle [A,H] \rangle + \bigg{\langle }\frac{dA}{dt} \bigg{\rangle} $$
with $H$ being the Hamiltonian. They derived this equation by using the product rule of differenti... |
The title says it all really.
Does this mean that the crystal is moving?
From my notes, I read that
The effect of an external force on an electron in the crystal is to
change the crystal momentum $\hbar k$. In the absence of a force, the crystal momentum must be constant
and thus conserved.
In a full band the net cr... |
I'm not a physicist, but I have been reading several sources of how electric fields and magnetic fields are connected.
One question in particular (How do moving charges produce magnetic fields?) caught my attention
and have two well written answers:
The accepted answer of this question concludes:
We can conclude that ... |
What is the difference between $T^{\mu}{}_{\nu}$ and $T_{\nu}{}^{\mu}$ where $T$ is a tensor?
|
There is a newly discovered Proxima Centauri c, to complement the already-known 'b'....
Why no planet 'a'?
|
Question: On April 15 an airplane takes off at 4:40 P.M. from Belém, Brazil bound for Villamil, Ecuador (in the Galapagos). The plane lands at 8:40 P.M. Villamil local time. The sun sets at 6:15 P.M. in Belém (local time), and 7:06 P.M. in Villamil (local time). At what time during the flight do the airplane passengers... |
In a quantum optics lab, imagine that we are given with a collection of experimental tools to set-up an experiment on an optical table. This collection could consist of devices like photon detectors, phase shifters, beam splitters etc. In this collection, how can we distinguish between measuring devices and 'sources of... |
(My question is different than this one and the similar one about the free particle, so hold back on casting a close vote, please).
So, I was reading on Wikipedia, and ran into this statement in the Dirac-von Neumann axioms: The space $\mathbb{H}$ is a fixed complex Hilbert space of countable infinite dimension.
This i... |
I meant it is a new quantity. Why is it defined to be $\vec{r}\times \vec{F}$ ? Why not any other definition of the torque?
|
I have doubt in the last equality. My argument is that since $g_{ik}$ $g^{ik}$ is a scalar but it can be dependent on $x_i$ so its partial derivative w.r.t $x_i$ shouldn't be zero.
It is a scalar but they are not inverse of each other. Because for inverse $g_{ik} g^{ak}$ should be there i.e. both indices shouldn't mat... |
Can someone recommend a good book on vectors for High school and pre University students. Nothing too complex but enough for first year physic students and helps cover the basics and helps you in applying them. I have tried checking similiar post but they were mostly about string theory and special relativity which is ... |
I'm trying to make sense of QFT (I am a mathematician). I have absorbed "from the ether" the following physical interpretation of Feynman diagrams in the Hamiltonian picture, which I really like, but which I have not seen written anywhere explicitly and I suspect it might be wrong. Is it correct, or fixable?
Here's the... |
In the book Introduction to Quantum Mechanics by Griffiths, the mathematical form of the uncertainty principle is stated as $$\sigma_x \sigma_p \ge \frac{\hbar}{2}.$$ However, another book on QM, that by Bransden and Joachain, states the principle as $$\Delta x \Delta p \gtrsim \hbar.$$ What I am confused about them is... |
What I know
Angular momentum is conserved at the point where there is no external torque on the system
When solving questions based on pure rolling (fairly simple concept), if for example, we have a ball that is slipping and not rolling on a rough surface, we are asked to find the velocity when pure rolling starts. Out... |
Is the EDM of a fundamental (or almost) particle (e.g. electron, neutron) T-odd? On wikipedia it says that it is not (check the diagram). But I found some papers (e.g. this review and the references within) which claims that the EDM is T-odd (check the second page). I am confused now. Of course I trust that paper (more... |
I have an electromagnetic field system for a cavity with a current source, whose Lagrangian has the form
$$ L=\int_V dV (w_{e}+w_{h} +i(E\cdot J)/\omega)+ \oint_A dA (E\times H)\cdot \hat{n}, $$
where $w_e$, $w_h$ are the electric/magnetic energy densities, $E,H$ are the fields, $J$ is a current density, $\omega$ is t... |
What happens to a free electron in vacuum? Does it accelerate? Does it keep absorbing energy from vacuum fluctuations? Or does it lose all its energy and ceases to be an electron? Please avoid technical terms, as I am relatively new to this field. Thank you!!
|
Say there is a liquid which behaves like an incompressible fluid and is flowing steadily through a pipe which is moving from a cross section of area $A_1$ to the cross section of area $A_2$, where $A_2$ is less than $A_1$. As per the continuity equation, $v_2>v_1$ and so the liquid seems to be accelerating. What force ... |
If I have a sphere of charge Q and I ground it then the charges would flow from the sphere to the earth because Earth's potential is zero. But the potential difference between the two ends of the connecting wire would be distance dependent(?).
As in the figure the potential at $A$ would be potential due to the sphere ... |
This is taken from arXiv:1910.14051, pg 32:
Decomposing this $SO(d+ 1, 1)$ representation into $SO(1, 1)× SO(d)$
representations as in (A.4), we find
$$\square \underset{\operatorname{SO}(1,1) \times
\operatorname{SO}(d)}{\longrightarrow}(\bullet)_{-1}
\oplus(\square)_{0} \oplus(\bullet)_{1}\tag{A.7}$$
where • denot... |
In the NS, a well known expression of the convective term is
$$\bf v \times (\nabla\times \bf v) = \bf v\cdot \nabla v - \frac{1}{2}\nabla v^2 $$
In order to derive it I use the commute rule of the vectors cross products:
$$\bf a\times (b\times c) = (a\cdot c)b - (a\cdot b)c$$
hence I got
$$\bf v \times (\nabla\times ... |
The Lie derivative is the change in the components of a tensor under an infinitesimal diffeomorphism. It seems that this definition does not depend on the metric:
$$ \mathcal{L}_X T^{\mu_1...\mu_p}_{\nu_1...\nu_q}= X^\lambda \partial_\lambda T^{\mu_1...\mu_p}_{\nu_1...\nu_q} - X^{\mu_1}\partial_\lambda T^{\lambda \mu_2... |
The problem is quite simple but there might be something I'm not getting right or I must have missed some concept. Suppose we have a train moving in $y (ĵ)$ with $ v = v(-ĵ)$. The reference event is when João and Maria see each other $t = 0$ in Maria reference frame. When they do so, Maria presses the button which acti... |
In quantum mechanics, I read that, square of the angular momentum operator (or Casimir operator) $\hat{L}^2$ commutes with angular momentum in $x$, $y$, and $z$ directions.
Now my question is, since $\hat{L}^2$ commutes with $\hat{L}_x$, $\hat{L}_y$ and $\hat{L}_z$, then it must be rotationally invariant. But when we w... |
The active material in a helium-neon laser is Neon. Thus the laser frequency matches energy levels in the Neon atom. This also means the Neon atoms will absorb this frequency well. I imaging that this effective absorption may lead to a noticeable trace when the laser is shone through a tube filled with Neon.
Did anyon... |
It's been a few days now trying to realize how is it possible that calculating the magnetic field exerted by a cylinder of finite length $h$ and radius $R$ very far away in two different ways - one as a superposition of magnetic dipoles and the other by Biot-Savart's law gets me two completely different answers. Should... |
I often read that the Dirac equation is covariant under Lorentz transformations and that this property makes it the right equation and in some sense beautiful.
The thing is, the equation
$$
\left(i\gamma^\mu\partial_\mu-\frac{mc}{\hbar}\right)\psi(x)=0
$$
is not covariant at all unless one assumes that the spinor trans... |
Currently struggling with a momentum problem. I have searched other online answers to similar questions, and the solutions contradict the book answer.
Problem:
A jet airplane travelling $200\ m/s$ takes air into its engines at a rate of $50\ kg/s$. This air is mixed with $2\ kg$ of fuel (per second), burned, and ejecte... |
I've been working as an EE intern for the past 5 months and have been trying to wrap my head around a couple concepts.
Is the principle of self-inductance due to a circuit's inherent property of being a loop of wire? Or is it that loops are simply the most efficient shape with which to sum of a bunch of magnetic field ... |
Let $F(t)= \cos (\omega_d t) $ be the driving force of a harmonic oscillator of mass $m$ which is damped with a damping constant $b$ such that $F= -bv $ is the damping force and the spring exerts a force $F=-kx$
A 2nd D.E. is obtained of the form: $$\ddot{x}+2\beta \dot{x}+\omega_0^2 x = \frac{F}{m}\cos(\omega_dt)$$ wh... |
I am trying to perform the following one-loop computation
$$
\int \frac{d^Dq}{(2\pi)^D} \frac{(k+q)^2 q^2}{((k+q)^2+m^2)(q^2+m^2)}
$$
where $k$ is fixed and everything is on the Euclidean setting, so there is no need to perform any Wick rotation.
I can not find the solution anywhere and I am not realizing how to do it ... |
The Lagrangian density of electromagnetism is
$$
\mathcal{L}_{EM}=\frac{1}{4\mu_0}F^{ab}F_{ab}
$$
This represents one of two fundamental Lorentz invariants of electromagnetism. The second one is:
$$
\frac{1}{2}\epsilon_{abcd}F^{ab}F^{cd}
$$
Since $\mathcal{L}_{EM}$ contains only 1 out of 2 fundamental Lorentz invariant... |
In quantum thermodynamics, allowed operations (free transformations in the sense of resource theories) are usually defined via unitaries $U$ that leave the Gibbs state $e^{-\beta H}/Z$ ($Z=\text{Tr}\, e^{-\beta H}$) on system S and bath B invariant:
$U [e^{-\beta H_S}/Z_S \otimes e^{-\beta H_B}/Z_B] U^\dagger= e^{-\bet... |
For a non-ideal gas,
When the gas is compressed, the potential energy of its molecules decreases. Doesn’t it?
Internal energy is the sum of kinetic and potential energies of the molecules.
Considering that, I don’t see why the internal energy increases. Is it because the increase in kinetic energy exceeds the decrease ... |
Note: If a better title can be made, pls do so.
Consider a parallel circuit with each branch of equal resistance. If you increase the resistance of the further branch, how long would it take to detect that from the intersection (since (the majority of the) current takes the path of least resistance)?
|
I am reading this article on extrinsic curvature embedding diagrams in general relativity: it seems that these are used to visualize curved space. On page 2, it is stated that in the case of the constant Schwarzschild time hypersurface in a Schwarzschild spacetime, the extrinsic curvature embedding is a flat surface. ... |
When an object such as a feather is dropped from a height, the initial velocity is said to be $0$. I would assume that the final velocity would also be $0$ as when the feather reaches the ground, it stops moving. However, the final velocity is not $0$. Could anyone please answer why?
|
If $E=hf$ and the frequency of electromagnetic waves is continuous (i.e. you can have frequencies of $1.5\ Hz$ or $0.3\ Hz$ for example) then surely energy isn’t discrete or quantized into because one could simply have any multiple whatsoever of a place constant and so any value for energy. As an extension of this ther... |
The susceptibility $\chi$ can be defined as
$$ \chi = \frac{\partial \langle M \rangle}{\partial H}, \tag{1}$$
where $\langle M \rangle$ is defined as the average magnetization and thus can be written as
$$\langle M \rangle = \frac{1}{Z} \sum M \exp\left(-\beta\left(\sum_{\langle i,j \rangle} J_{ij}\sigma_i \sigma_j + ... |
The real world doesn't care about our choice of coordinate to describe nature.
Maxwell equations in vectorial form are written with respect to an Inertial frame of reference as:
\begin{align}
\vec\nabla\cdot\vec{E} &= 4\pi\rho \label{Diff I}\\
\vec\nabla\times\vec{B} &= \dfrac{4\pi}{c} \vec{j}+\dfrac{1}{c}\dfrac{\par... |
Since the important things in the QFT Lagrangian are vectors and matrices, I wanted to do a "matrix dimensional analysis" of each term.
The electromagnetic Lagrangian (ignoring all constants and signs) is :
$\bar{\psi}\gamma^{\mu}\partial_{\mu}\psi + \bar{\psi}\gamma^{\mu}\partial^{\mu}A_{\mu}\psi + \bar{\psi}\psi + F_... |
I would like to calculate the effective stiffness of a structure which can be represented as follows:
(Image source: Link to paper with image.)
The yellow part is flexible and the blue is a rigid-body-like part. In this paper a derivation for this structure under the assumption that the yellow strut can be modeled as ... |
In my thermodynamics schoolbook, it is asked to apply the Clausius inequality to a Carnot cycle. According to the book the answer is to evaluate $\oint\frac{\delta Q}{T}$ over the cycle which should yield
$$ \oint\frac{\delta Q}{T} = \frac{Q_H}{T_H}+\frac{Q_C}{T_C}=0 $$
$Q_H$ is the heat transferred from the hot reser... |
A hemispherical shell of mass $m$ and radius $R$ is hinged at point $O$ and placed on a horizontal surface $M N$ as shown in the figure. A ball of mass $m$ moving with velocity $u$ inclined at an angle $\theta=\tan ^{-1}\left(\frac{1}{2}\right)$ strikes the shell at point $A$ (as shown in the figure) and stops. What i... |
If a conducting rod moves within a magnetic field, the electrons within it will move for a short amount of time to create a potential difference. When the current is created within this rod, the rod starts moving. In this case, why isn't the magnetic field moving the electrons inside of the rod, but the whole rod inste... |
For the hermite polyniomials the Rodrigues formula states:
$$
H_n(\xi) = (-1)^{n}e^{\xi^2}\left(\frac{d}{d\xi} \right)^n e^{-\xi^2}
$$
If we differentiate this expression we should obtain:
$$
\frac{dH_n}{d\xi} = 2nH_{n-1}
$$
However, I am a bit confused why the result is $2nH_{n-1}$, this was my reasoning:
$$
\frac{dH_... |
I am trying to derive: $T=\frac{2\pi}{\omega}$ for S.H.M.
I want to use the following method.
A particle is at position $x=x_1$ on the x-axis.
It starts with zero velocity. $x_1$ is therefore the amplitude of the motion.
Given: The particle experiences an acceleration $a=-\omega^2x$
I want to use calculus to show that ... |
I am recently studying solid mechanics and I met a problem regarding Nabla operator. I am trying to prove the following relation:
$$\nabla \otimes\textbf{u}=\frac{\partial\textbf{u}}{\partial x_{i}} \otimes \mathbf{e}_{i} \tag{1}$$
where $\nabla$ is the Nabla operator and $(\bullet)$ represents a smooth vector or tenso... |
In de Sitter-Schwarzschild spacetime things close to the black hole are falling towards it whereas in greater distance they are receding. So there should be a certain (unstable) $r$-coordinate, where things are stationary. The de Sitter-Schwarzschild metric yields 2 solutions:
$f(r)=1-2M/r$
$f(r)=1-\Lambda*r^2$
From th... |
I believe we have all been told that current flows from high potential to low potential by convention but in reality current is flow of electrons which flow from low to high. Now as in reality current flows from low to high then potential should increase across a resistor or any other electrical device which means that... |
I have seen this shape in many different phenomena in physics, for example- when two neutral atoms are brought together, then potential between them as a function of separation takes this type of shape, also in kepplers law I have seen this type of potential. Today I was studying QM, and I saw this shape of potential... |
the RMS (root mean square) value of $f(x)$ is defined as:
$$f(x)_{rms}=\sqrt{\frac{\int^b_a (f(x))^2dx}{b-a}}$$
Why do we do this very specific thing of taking the square, the mean, and then the square root of the function? For an AC circuit, why does this tell us the power consumption and not something like the expres... |
I was reading this question (Why does Light get caught by Gravity, when both are travelling at the Speed of Light?) and it brought me to the following:
Can photons create gravitational waves?
My rationale here is:
(1) although photos have no mass, they do have momentum (and I've always been a bit confused by this - how... |
In statistical field theory, one usually considers the so-called Landau Hamiltonian:
$$\beta H = \int d^{d}x\bigg{[}\frac{t}{2}m^{2}(x) + \alpha m^{4}(x)+\frac{\beta}{2}(\nabla m)^{2}+\cdots+ \vec{h}\cdot \vec{m}(x)\bigg{]}$$
This Hamiltonian seems to be general enough to study Landau's theory on phase transitions. The... |
In thermodynamics, we usually find the work done by/on an ideal gas by considering a cylinder with a moveable piston as one of its flat ends. We consider the work done by moving the piston end a small amount, and find the well known result that
$dW = P dV$ (up to sign convention and inexact differential notation).
In... |
In an ideal Bose gas there is a symmetry breaking phase transition, namely Bose-Einstein condensation. In a weakly interacting Bose gas or in helium-4 there is a longitudinal phonon because of the symmetry breaking, which leads to a linear dispersion relation for small energies and momenta.
I would expect to have somet... |
I met a problem in Nonlinear Solid Mechanics: A Continuum Approach for Engineering by Gerhard A. Holzapfel. This is the problem and the solution given bu the author.
My question is WHY $W_{ij}=\partial u_{j} / \partial x_{i}$. In my knowledge, $W=\frac12(A-A^T)$ and $W_{ij}=\frac12(A_{ij}-A^T_{ij})$, where $A=grad\... |
Can time-dependent Schrodinger equation be written in integral form using Green functions?
And if so, has it been applied in solving a particular problem?
|
I know centripetal acceleration changes the velocity direction but if we observe any instant in time the velocity does not need to be changed.
|
I have a substrate with some chemical bonded to it. I want to selectively etch the chemical in certain spots, hence I am using a mask with through-hole on top of the substrate, then exposing it to air plasma. I noticed that the when I expose the substrate to plasma, without adding the mask, it takes around 1 minute to ... |
Coulomb's Law states that the repelling force felt by two charges is proportional to the magnitude of their charges and inversely proportional to the square of the distance between them.
Defining voltage as the potential energy per unit charge, you get that the voltage is proportional to the charge and inversely propor... |
Presumably this should be a tiny cross-section (or not?), but presumably it should be at least qualitatively similar to the 511 keV line that clearly distinguishes electron-positron annihilation, although by the upper mass bounds on the different types of neutrinos, such line should be presumably be somewhere in the mi... |
How would I go about verifying that the energy a body possesses, is directly proportional to its mass to the first degree, without using the definition of work?
How could I show this fact without the prior knowledge that work is the sum of the product of the force and the distance travelled over a distance?
|
If we think of projectile motion as a general curvilinear motion, the magnitude of tangential acceleration is given by $g sinθ$, and magnitude of normal acceleration is given by $g cosθ$, where $θ$ is the angle made by the velocity vector at that point with $x$-axis. θ does not remain constant as velocity vector change... |
A proof about the exponentiated commutation relations is mentioned In this book page 285:
The exponentiated momentum operators satisfy:
$(e^{itP_j}\psi)(\textbf{x})=\psi(\textbf{x}+t\hbar \textbf{e}_j)$.
It is then evident that $e^{isP_j}$ commutes with $e^{itP_k} $.
I know that the same operators of different indic... |
I am going through the Peskin and Schroeder QFT book. While proving the Gell-Mann and Low theorem in chapter 4 of their book, the authors started with the equation
\begin{equation}
e^{-iHT}|0\rangle = e^{-iE_{0}T}| \Omega\rangle \langle \Omega | 0 \rangle + \sum_{n\ne0}e^{-iE_{n}T}| n\rangle \langle n | 0 \rangle.\tag{... |
I am teaching myself Electrodynamics through Griffiths' text, but am having trouble understanding how much work it takes to move a test charge $Q$ from a point $\mathbf{a}$ to a point $\mathbf{b}$ in the presence of a stationary configuration of source charges.
So suppose that we have a stationary configuration of sour... |
My school textbook says that we don't need to use unit vectors (i ,j,k) to represent the direction of vectors in 1D motion as + and - sign indicate direction. But that is creating a lot of confusion like this:
Suppose a question for one dimensional motion is like this: a body is thrown vertically upwards with a speed o... |
Doppler effects are calculated based on the velocity of the sound source. Suppose the side of a swerving car (which is moving) grinds a guardrail (which is "not" moving). Will the screech sound higher-pitched to pedestrians ahead of the car than to those behind it?
|
I had this exercise on a test the other day and I still don't know how to solve it. Being given the image below, I have to say what's the type for each spectra, absorption or emission. I didn't find any answers about the differences in representations on the internet so I've come here to ask for help.
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I heard that a magnetic field only creates a force on a moving charge, not a stationary one. However, what if the solenoid containing the magnetic field was moving through a stationary charge. Would that create a similar force? Thanks!
|
I have been recently looking into something called Quark Fusion. The whole thing is a theoretical concept of colliding heavier and lighter Quarks to produce energy.
There is one thing to it tho. It is impossible to let those Quarks live long enough for actual storage and collision. But im now questioning if there would... |
How may I calculate Earth's angular speed at specific point (The green dot for example)?
Note: I know that angular speed $= \dfrac{2\pi}{T}$ But how may I found $T$ in this case?
I found too that $R_{\text{new}}=R_{\text{old}}\sin (43)$ where $R_{old}$ stands for radius of Earth
|
I can understand that an idempotent operator can be represented as a projection operator, such as $|x\rangle\langle x|$. But some authors seem to use projection operators, instead of vectors, to represent states (presumably only mixed states?).
I would like to have an intuitive grip on this because it just looks to me ... |
For some reason this question disappeared, so I am re-asking it.
I would think yes, because, if a rope tied to a swinging rock breaks, the rock flies off in the direction that is perpendicular to the direction of the last instant of the acceleration. The acceleration which existed at the last instant determined the dir... |
Take an example of a space ship moving at speed comparable with speed of light (like 60% of c) now if spaceship launched from earth to near star does time dilation affects the time taken by space ship to travel from earth to star? I mean does time taken is different for observer on earth and observer on spaceship or it... |
I am now reading a book "Superconductivity, Superfluids, and Condensates" by Jame F. Annett. I am stuck at the part of writing dispersion relation of the quasiparticle in superfluid here. The author does not seem to give any explanation about this. He somehow mentioned the Fermi's golden rule previously, but I could no... |
Can a constant force cause variable acceleration?
I think that the answer is no.
How can a force cause variable acceleration?
|
Consider a wheel on a frictionless horizontal surface. If we apply a horizontal force (parallel to the surface and above the level of the center of mass), what happens to the wheel? Does it roll or slide forward or rotate only or does any other phenomenon happen? Please guide me. Also draw a free body diagram.
Note: Th... |
According to mathematics, everything has its opponent. Suppose something is $x$. Let $x = 5$, then $x^2 = 25$, and again if $x^2 = 25$, then x may be positive or negative. In the same way, let $x = time$, then is there something like $antitime$?
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In the electron-hole recombination process, the electron passes from the conduction band to the valence band, in this process the other leaves a gap in the conduction band and fills the gap in the valence band. And this is called electron-hole pair annihilation? Or is everything destroyed?
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