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Say there's a positron and an electron which are occupying quantum states and are entangled.
There's two observers, Alice and Bob.
Assume Alice measured spin of positron along $z-$axis and obtained $+z$ spin.
Now entangled electron will have $-z$ spin, if Bob tried to measure it.
Now my question is that,
what if, Alic... |
I visited some other QA threads about this topic, and I don't understand why people think it's mysterious that the bucket knows about its rotation.
If a non-rotating bucket is all there is in the universe, then, initially, all the parts of the bucket are at rest wrt to each other.
But if we want to rotate that bucket w... |
I am an absolute beginner, with little to no knowledge on the subject but I have somehow developed a strong interest in theories like String theory and M-theory, by reading about them on other forums. So can you recommend me any farily accessible books or other materials that could help me understand these theories i... |
I will make a few observations (if any of these is incorrect please let me know) and then ask my question :-
i) For a Quantum Mechanical Harmonic Oscillator (QMHO) we have, at least, two kinds of representations : WaveFunction representation (in Hilbert Space, $\mathcal{H}$) and Occupation Number representation (in Foc... |
Consider events A and B with coordinates $(t_A, x_A, y_A,z_A)$ and $(t_B, x_B, y_B,z_B)$ respectively.
I am trying to prove that the quantity
$$\Delta r^2 =\Delta x^2+\Delta y^2 +\Delta z^2$$
where $\Delta x = x_A-x_B$ etc.
is invariant under Galilean transformation.
The Galilean transformation I used was $$t'=t,$$ $$... |
Imagine a uniform spherical ball of mass $m$ and radius $r$ rolling without slipping in a spherical bowl of radius $R$ with $r<<R$.
There are two special cases of small amplitude oscillations: a ball that rolls directly back and forth at the bottom of a bowl, as well as a ball that rolls in a circle around the bottom ... |
In a books Concepts of Physics by HC Verma,It is written that one a conductor only one surface cannot be charged.Both the surfaces have to be charged in order for the net electric field inside the conductor to be zero.I had a doubt regarding this.Suppose a conductor has a positive charge only on one side.Then the posit... |
I am looking into different cameras or sensors that i could use to measure the following em ranges that are useful to agriculture. I'm hoping to construct an open source device(s) to measure the following within a small and reproducible device(s):
Cellulose Absorption Index: 2000-2200nm
Plant Water Index: 902-970nm
Dis... |
Is there any reason one would choose a sine wave instead of a rectangular wave for example? What are the differences between them? Why would one prefer one waveform over the other in certain circumstances? I'm trying to understand why sometimes one form is used and another time a different one.
|
There was a question asking the electrostatic force between two charges if a a copper plate of thickness d/2 is kept between them. The effective force was 0. How?
|
I've learned that moving charges produce magnetic fields which in turn affect other charges in motion. After seeing explanations that point to special relativity, I am kind of confused. Can ALL magnetic fields be accounted as some kind of electric field from a particular reference frame?
And if there is relative motio... |
Just shown as the above picture, if the right part removed, would electromagnetic waves still be produced near the inductor and what the changing electromanetic field are in this situation? I used to watch some video to explain EM waves by the similar circuit, in witch he says the EM waves could not detached from the ... |
Usually when one reads about the recombination in the standard model ($\Lambda$-$ CDM$) its written that the recombination occurs at a temperature $T\approx 3000 K$. Since, at this temperature the free electrons of the plasma become bound with the ionized hydrogen.
Let's call the Hubble parameter of the standard model... |
We get a super conductor by cooling down a metal to a certain temperature, and this has 0 resistance but in the quantum model as the temperature of the metal is reduced, there are no electrons above the fermi level or more specifically no conduction electrons and hence no current, so how does this justify super conduct... |
This is how I understand Coulomb's Law's derivation, please let me know if it's correct.
Charles Augustin de Coulomb and some other scientists 'experimentally' deduced that there are three factors that affect the electrostatic force between two stationary charged particles with equal distribution of electric charge, th... |
Famously, the collapse of the wave function is considered one of the biggest puzzles of quantum mechanics and motivates people to take ideas like the many-worlds interpretation seriously.
Something I always found puzzling is that there seems to be a quite similar phenomenon in classical physics. In a purely classical ... |
If we have a beam of spin-1 particles and let them pass through a Stern-Gerlach apparatus (oriented along z-axis, we get three output beams. Suppose we now take only the $+\hbar$ beam and pass it thorugh a Stern-Gerlach apparatus oriented along x-axis, we again get three states and we expect them to have equal probabil... |
As we know that gravity of earth influences Moon gravity and vice-versa. Suppose, Moon escapes to infinite distance where there is no other object to affect it, will we weight higher there? If yes how mass increases as per $g= GM/r^2$.
|
The beginning of this paper (pg.no. 1) on generalised Schmidt decomposition of three qubit states mentions the following:
The Schmidt decomposition allows one to write any pure state of a bipartitie system as a linear combination of biorthogonal product states or, equivalently, of a non-superfluous set of product stat... |
this is the first time that I study fields quantization and in particular I'm starting with the free em field. Previously I've just studied the non relativistic, Schrodinger equation for a non zero mass particle (in the Schrodinger picture), so I'm trying to use the same ideas to understand this topic. If you feel like... |
I'm studying QFT on Weinberg's book. And I have a question about its notation for Lorentz transformation property of the free fields (Chap.5).
In Sec. 5.1 of Vol. 1, annihilation fields $\psi_{\ell}^{+}(x)$ and creation fields $\psi_{\ell}^{-}(x)$ are given (as (5.1.4), (5.1.5)) so that they satisfy the transformation ... |
I’m trying to model “bending tree branch like motion” and it seems, that it can be described with some kind of «upward facing torsional pendulum” I guess.
The construction is facing upward and start moving if something hits or bends it, then it tries to return to its original position.
The system looks something like ... |
PKE have high importance on fuel consummation and Eco-driving.
I have a data frame with 3 columns, Time (each second), Speed(KM/H) in each second, and RPM ,from this data frame I want to calculate positive kinetic energy.
Time Engine RPM [RPM] Vehicle Speed Sensor [km/h] Air Flow Rate from Mass Flow Sensor [g... |
Every atom contains charges and charges emit EM wave when they are accelerated. So if an atom is accelerated, the charges inside will also accelerate. Which means that the charges inside will also emit EM wave.
But I don't think I'm right. Because then everything in earth is accelerating around the sun. And so we shou... |
I have been given in our QM course, the task to show the differences between the number representation for fermions and bosons. I have had no problem with the mathematical aspects, but I have problems interpreting one of the results, and the books I have don't show a physical explanation for it.
For bosons the eigenval... |
Couldn't Google credible answer.
What is accepted constant in applied physics to estimate radio wave speed in earth atmosphere near water surface?
Taking on account humidity inside few meters off water surface.
Disregarding ionisation clouds and all other high altitude effects
|
I am trying to show that "Non-vanishing vacuum expectation value of some field" and "Non-unique vacuum state" are two equivalent definitions for symmetry breaking in a simple case. Below is what I am doing:
Now suppose we have a Lagrangian $\mathcal{L}(\phi^{i},\partial_{\mu}\phi^{i})$, $i=1,2,...N$, which is invariant... |
I'm struggling to make sense of the following problem: Consider a sphere which undergoes a series of sequential rotations of the same angle $x$ about multiple axes identified by unit vectors $\{\boldsymbol{v}_j\}$. Then a vector $\boldsymbol{a}(0)$ representing a point on the sphere will move to
$$
\boldsymbol{a}(x) =... |
Let's consider a PDF $\rho(x)$, with normalization 1. Let's perturb it in the following way:
$$
\rho(x+\varepsilon F(x) ),
$$
with $\varepsilon$ small. I impose that the perturbed PDF is again a PDF with normalization one.
I think that the following formula, which describes the linear variation of the PDF, holds:
$$
\... |
Consider the Langevin equation in the overdamped regime,
$$
0 = -\gamma \dot{\mathbf{x}} -\nabla U(\mathbf{x}) +\boldsymbol{\eta}(t) \,
$$
where $\boldsymbol{\eta}$ is the usual white-noise term, $U$ a potential for the force and $\gamma$ the damping coefficient (or a "damping matrix"). Note: thanks to the good refer... |
Consider this spinning disk, in a 3D coordinate system. It is translated above the origin of the coordinate system and spinning around the axis given by this translation vector.
Every source I can find on the internet claims that angular velocity is the same for very particle of this rigid body, but at the same time ... |
For the Kerr metric, with line element
$$
ds^2 = -\frac{\Delta-a^2\sin^2\theta}{\rho^2}dt^2 - \frac{4Mar\sin^2\theta}{\rho^2}dtd\phi +\frac{(r^2+a^2)^2-a^2\Delta\sin^2\theta}{\rho^2}\sin^2\theta d\phi^2 +\frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2
$$
in the Boyer-Linquist coordinates
$$
\Delta = r^2 - 2Mr +a^2\\
\rho^2 =... |
When doing a calculation involving a force of $F=1000$ N on a mass of $m=100$ kg we use the formula $a=\frac{F}{m}$
$$a=\frac{F}{m}=\frac{1000\ N}{100\ kg}=10\ N\ kg^{-1}$$
Is there any reason why I should convert this to $m\ s^{-2}$ or is it perfectly reasonable to leave it in this form?
|
One has $\cos{\theta_W}=m_W/m_Z$, and $\sin^2{\theta_W}=1-(m_W/m_Z)^2$
Is the sign of the Weinberg angle defined or an important quantity?
If yes, are there constraints?
|
In the chapter about transmission lines, there was the following question:
Given a frequency of 1GHz and a relative permittivity of 2.25, what is the wavelength of the sinusoidal wave?
In an unofficial solution they do the following:
$$c = \frac{1}{\sqrt{\mu\epsilon}} = \frac{1}{\sqrt{\mu_0\epsilon_0 \cdot \epsilon_r}}... |
Following the Lagrangian:
$$\tag{1} \mathcal{L} = \mathcal{L}_{initial}-M^2 \varphi^* \varphi - g\varphi^*\varphi -g\phi^3$$
where $\phi$ is a particle associated with a real scalar field, and $\varphi$ is a particle associated to a complex scalar field.
I know that I have two interaction vertices: one with 3 $\phi$ p... |
How to find the maximum work that can be extracted by two objects which have variable temperatures $T_1$ and $T_2$ with $T_1 > T_2$?
I've thought that the maximum work obtainable is the one produced by a reversible machine, but since the temperatures are not constant I can't use the efficiency of a Carnot heat engine.... |
Given the special unitary group, we can define
$$ M = -iX =
\begin{bmatrix}
b_{11} & -ia_{12}+b_{12} & ... & -a_{1n} + b_{1n} \\
ia_{12}+b_{12} & b_{22} & ... & ... \\
... & ... & ... & ... \\
ia_{1n}+b_{1n} & ... & ... & b_nn = -\sum_{k=1}^{n-1} b_{kk}
\end{bmatrix}$$
where all elements $a,b$ are Real.
How would one... |
I'm quite familiar with rotation in quantum/classical mechanics. I know rotation for an operator $O$ or state $|\psi \rangle$ acts like:
$$O \rightarrow R O R^{-1} \\ |\psi \rangle \rightarrow R |\psi \rangle $$
However, I don't understand how to apply this to the second quantized operator for example $c_{i \sigma} c_{... |
We can get coherent state from the formula
$$|\alpha\rangle =D(\alpha)|0\rangle = \exp (\alpha a^\dagger-\alpha a)|0\rangle = \exp\left(-\frac{|\alpha |^2}{2} \right) \exp(\alpha a^\dagger) \exp(\alpha a)|0\rangle$$,
Also can get by expanding in terms of Fock state
$$|\alpha\rangle = \exp\left(-\frac{|\alpha |^2}{2}\r... |
Suppose I am at rest at a great distance $r_0$ from a black hole with a mass $M$ without rotation or charge.
During my free fall in vacuum from $\tau=0$ and $r=r_0$, I will pass the event horizon in finite proper time and the increment of my proper time in Schwarzschild coordinates is $$\text{d}\tau=(2M/r-2M/r_0)^{-1/2... |
My prof said that if you have a relative permittivity which is real, the reflection coefficient is 0 (which means a lossless line). Why is this?
|
Usually you study a GR system with an electromagnetic field using the standard action
\begin{equation}
S=\int{(R-\frac{1}{4}F^2)\sqrt{-g} d^4 x}
\end{equation}
(where $F_{\mu\nu}=A_{\mu,\nu}-A_{\nu,\mu}$)which you then use to derive e.o.m. and the like. The coupling between gravity and the electromagnetic field arises ... |
We construct identical particle state by symmetrizing or antisymmetrizing the tensor product of single partice states. When considering spin, a two fermions state should be $$|\psi\rangle=\frac{1}{\sqrt{2}}(|\psi_1\rangle_{\sigma_1}\otimes|\psi_2\rangle_{\sigma_2}-|\psi_2\rangle_{\sigma_2}\otimes|\psi_1\rangle_{\sigma_... |
The first is from a textbook, the second is from Wikipedia.
Intuitively, I think the textbook one is correct.
|
The Bloch states $\{|\Psi_{n,\vec{k}}\rangle\}$ form a basis and fulfill the completeness relation
$$
\mathbb{1}=\sum_{n\vec{k}}|\Psi_{n\vec{k}}\rangle\langle\Psi_{n\vec{k}}|.
$$
Using the completeness relation we can write an operator $\hat{A}$ in terms of the Bloch state basis
$$
\hat{A}=\mathbb{1}\hat{A}\mathbb{1}=... |
$$ T = 2\pi \sqrt{\frac{l}{g}}$$
$$U_{c}(T) =?$$
That's the only thing my teacher left me with. I don't understand how am I supposed to solve this without any measurements.
|
I am having difficulty in understanding problem number 14 in Goldstein's Classical Mechanics, 3rd edition, chapter 7 on special relativity. Here is the problem ---
A rocket of length $l_0$ in its rest system is moving with constant
speed along the $z$ axis of an inertial system. An observer at the
origin of this s... |
The inflationary hypothesis as I understand it is a correction to GR to account for the observed flatness of the universe in a model in which the universe is expanding.
How are the constants behind this inflationary hypothesis derived?
I am looking to establish whether this model predicts or is derived from an estimate... |
My textbook says:
We take
the most general transformation relating the coordinates of a given event in the two systems to be of the form:
$$x' = Ax +Bt$$
$$y' = y$$
$$z' = z $$
$$ t' = Cx + Dt $$
I understand why the $y'$ and $z'$ have to be the same as $y$ and $z$ and that the equations have to be linear for havin... |
In free vortices (such as water draining in a sink) the molecules away from the center axis will be irrotational. Why is this the case in terms of how the forces on the individual molecules differ from a rotational vortex case?
|
Since weight is storage for energy, the light vehicle will have a slight advantage on the flat ground due to low stress applied on wheels meaning less friction pulling the vehicle back. When though, the ground has any amount of decline, the heavier vehicle will literally get pulled by gravity since its got its energy s... |
so I'm trying to solve the one dimensional particle in a box problem known from quantum physics in a classical context. So according to Wikipedia (see picture on the right) we would get a particle that is just moving from one potential-wall to the other.
Usually, when solving such a problem, I just solve the differenti... |
When calculating the amplitude of a scattering process for the scalar Yukawa theory involving two scalar ($\phi$) and two complex scalar particles ($\varphi$ and $\bar{\varphi}$) I have noticed the integrating function is ignored. The rules I follow for the mathematical representation of the different type of lines in... |
I work for a large plant bakery and we have recently coated the inside steel walls of our very large oven with a reflective coating. I have taken temperature readings inside the insulation void and there is a noticeable decrease.
What I am trying to do is quantify the theoretical energy savings in LPG usage from this.
... |
I seem to remember that higher orders (m) of interference for a thin-film (or multilayer) are increasingly weaker in intensity. That is, the first order interference will always produce a peak of the greatest intensity. However, now that I try to find why this is, I can't find an answer, or even any source specifically... |
The capacitance of a parallel plate capacitor is given by C=Aε/d.
For concentric spherical capacitor the value of capacitance is given by 4πεba/(b-a) (where b is the radius of the outer sphere and a is the radius of the inner sphere and the distance between the plates b-a).
Now a very interesting thing to note:
The geo... |
A Circular ring of radius r made of a non conducting is placed with its axis parallel to a uniform electric field.
The ring is rotated about a diameter through 180 degrees.
Does the Flux increase, decrease or doesn't change?
My opinion:
A Circular ring is quantity that is not associated with any area itself( It enclos... |
I have read this question:
Explanation about black color, and hence color
where John Rennie says:
For example suppose you're looking at red light. Only the "red" cones will generate a signal and your brain interprets this as red.
https://pages.jh.edu/~rschlei1/Photographic/violet/violet.html
Red light more strongly ... |
I will measure an object that is either in a mixed state of $\vert A\rangle$ and $ \vert B \rangle$ or a superposition $\vert A\rangle + \vert B\rangle$, and I am trying to find out which. I have set up the experiment so that:
If the object is in state $\vert A\rangle$ or $\vert B\rangle$, then either detector $1$ or... |
$$ Z = 23,8937 * 10^{-5} [u] $$
$$ u(Z) = 3,721 * 10^{-7} [u] $$
I have to write this uncertainty in complete form.
Would this be correct?
$$ 0.0002389 \pm 0.0003721 $$
|
If there are two electrons coupled by interaction having hamiltonian H=A*S1*S2 where S1 and S2 are spin angular momentum operators of two electrons, we know we have four possible eigenstates for the combined system. The diagram here shows the possible situations. I have following questions:
1)- Two of the four states a... |
I know about the existence of certain windows for which it is more suitable to launch a probe for the exploration of a cellestial body in our Solar System (see the Wikipedia Launch window). I wondered about a different problem.
In the past, if I refer well there was in the literature projects to build certain structure... |
The time-independent Shrödinger equation (TISE) is
$$\dfrac{-\hbar^2}{2m} \nabla^2 \psi + V \psi = E \psi,$$
where $m$ is the mass of the particle.
I just had a thought: If $m$ is the particle's mass, then the TISE is invalid for photons, since they're massless! But I know that the Shrödinger equation is used to model... |
The following is an improved version of my previous post Falling electric dipole contradicts equivalence principle?
Consider the following system comprising a particle on the left with charge $+q$ that is a large distance $d$ away from two oppositely charged particles on the right, with charges $+q$,$-q$, held apart by... |
I have a question about the link between volts and amperes.
I understand the math theory behind it.
V = W /A
so if i double V i got
2V = 2 (W / A) = 2W / A
So if i raise the voltage i raise the power and not the flow.
Electricity is always explained using the water metaphor, V being the pressure, and A being the flow o... |
I don't understand why if we apply a potential to a metal it can attract electrons. An example of this is an electron gun, the anode is at a positive potential and its function is to attract the electrons to leave the gun.
This means that if we apply a positive potential to a metal it behaves like a positive charge? T... |
Consider a box with rigid walls containing an elasic medium, subject possibly to some body forces or tractions.
The volume is an additive quantity, in the sense that the total volume change of the system may be written as the sum of volume changes of subsystems. Therefore, if I define the strain tensor $\epsilon_{ij}$,... |
So I'm reading Landau's mechanics books and there was a question for the angular distribution of the resulting particles in the lab system (p.44 Q2 Chpt 4). It says when $v_0>V$, it is given by
$$\frac{1}{2}\sin\theta\,d\theta\left(2\frac{V}{v_0}\cos\theta+\frac{1+\frac{V^2}{v_0^2}\cos2\theta}{\sqrt{1-\frac{V^2}{v_0^2... |
I'm reading Shankar's quantum mechanics textbook and I am on the part about ladder operators. The portion where he explains the function of the annihilation operator goes as follows:
$$\hat{H}a|\epsilon\rangle = (a\hat{H} - [a, \hat{H}])|\epsilon\rangle = (a\hat{H} - a)|\epsilon\rangle = (\epsilon-1)a|\epsilon\rangle$$... |
For $\phi^4$ theory, when $d>4$, the theory becomes nonrenormalizable, but when $d>4$, we can use mean field theory to calculate the exact critical exponents. The intuition behind mean field theory is that when d is large, there are more neighbors, so the mean field approximation gets better.
Another example is gravi... |
I'm not getting why is the capacitance a constant, and how you can deduce it from the potential and charge.
The potential of the sphere is (in the radial magnitude)
$V(r) = \dfrac{kQ}{r} $ if $r > R$ and $V(r) = \dfrac{kQ}{R} $ if $r \leq R$
From this the claim is that if you evaluate at $r = R$ you would get the seco... |
Fuzzy dark matter (FDM) has a typical mass of $10^{-22}$ eV. With such a low mass, why is it typically assumed to be cold? That is, what keeps the FDM non-relativistic. With such a low mass, wouldn't almost any energy input cause a FDM particle to have a momentum significantly larger than its mass? Or is it assumed tha... |
How does static electricity create waves in an electric field in-between my hair and the balloon that I rubbed on my hair? So why is my hair attracted to the balloon when I pull it away and there is space in-between them?
I've read this answer which says that the source of electric field is the charge distribution in ... |
I'm studying electromagnetism and I have found that vacuum permittivity is equal to:
\begin{equation}
8.854 × 10^{-12} C m^{-1} V^{-1}
\end{equation}
and the relative permittivity of plastic is almost $2.39$
(this is an approximate value that I've found in an experiment)
and I want to know:
1- why the value of va... |
I'm just starting out studying the Cosmological Perturbation Theory and most of the things do NOT make sense to me. For example, how these two equations came to be. Please, also mention some starting points I should keep in mind to understand this subject better.
|
I am currently only a high school student wanting to pursue physics at the tertiary level of education.
Are there any books people can recommend on ultra-cold atoms? I would like to discover more about them, but the ones I have viewed so far require lots of mathematics, and I only want some introductory knowledge.
|
I am running a 2D fluids simulation with a stochastic forcing $f$ in a doubly-periodic box, i.e. solving
$$ \frac{\partial \nabla^2 \psi}{\partial t} = J(\psi,\nabla^2 \psi) +f,$$
where $J$ is a Poisson bracket.
The forcing I've chosen is of the form
$$f= \sum_{k,l} c \sin(k x + \alpha_k) \sin(l y + \beta_l),$$
where ... |
Consider a tensor, $T$ of rank $(r,s)$ over a supermanifold, $M$ and take the supertrace over its indices $p$ and $q$ (DeWitt, p. 77, eq. 2.4.33):
$$(-1)^{a_q(1+a_{p+1}+...+a_{q-1})}T^{a_1...a_{p-1}a_qa_{p+1}...a_r}_{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a_{r+1}...a_{q-1}a_q...a_{r+s}}.$$
As... |
I couldn't find any information on this topic. That is why I decided to ask in here.
Can air be compressed by tides? I have an aquaponics setup next to the sea. When the high tide occurs, will you be able to compress air with the rising water? For example one end of a pipe will start filling with water while the other... |
I understand how to do this problem perfectly fine.
I am posting here however because I have a disagreement with my professor and classmates in finding the final y-coordinate of the projectile.
I am confident that to find the final y-coordinate of the projectile, the correct equation should be:
$-y = (100sin60^o )t ... |
Consider a wire of lenght $L$ and transversal area $A$ that it isn't an ideal conductor, but follows Ohm's Law. After a few computations we have
$$-\Delta\phi = \rho\frac{L}{A} I $$
where $\rho$ is electrical resistivity. Note that $\Delta\phi < 0$.
My question is if voltage and resistance are defined as:
1) $V =-\Delt... |
I have a question about the following passage from this article:
Moschidis imagined standing in the middle of AdS space-time, which would be like standing inside a giant ball whose edge or boundary lies at infinity. If you sent a light signal from there, it would travel out and reach the boundary in a finite amount of... |
In chapter 8.2.3 of Schwartz' textbook "Quantum Field Theory and the Standard Model", the author states the following,
Finally, we expect from representation theory that there should only be two polarizations for a massless spin-1 particle, so the spin-0 and the longitudinal mode should somehow decouple from the phys... |
Recently I find someone declared that: ‘Even if we write $g_{\mu\nu}=\delta_{\mu\nu }$ everywhere in some patch, we can still find a non-zero Riemann tensor if our basis vectors don't commute’ From this I find an interesting example:
If we parallel a basis $e_\mu(x_0)$ on a manifold $M$ which equipped with a connectio... |
If photons are their own anti-particles, why don't they annihilate?
Also on a side note, why do particles and anti-particles annihilate?
|
If we isolate wire with thin wire and assuming that no heat rejected by wire then does electromagnet work. If it work then it violate conservation of energy .
|
We have Maxwell's Equations (ignoring permittivity and permeability of free space)
$$
\nabla\cdot E=\rho\;;\;\nabla\times E=-\frac{\partial B}{\partial t}
$$
$$
\nabla\cdot B=0\;;\;\nabla\times B=\frac{\partial E}{\partial t}+J
$$
with $E$ and $B$ being the electric and magnetic fields, and $\rho$ and $J$ being the cha... |
Consider events A and B with coordinates $(t_A,x_A,y_A,z_A)$ and $(t_B,x_B,y_B,z_B)$ respectively.
The spacetime interval $\Delta s$ between them is given by $$\Delta s= \sqrt{c^2\Delta t^2-\Delta x^2-\Delta y^2-\Delta z^2}$$
where $\Delta t=t_B-t_A$ etc.
I am trying to prove that the spacetime interval $\Delta s$ can... |
I am currently watching a series of lectures on Nuclear Physics. One of the topics covered is the emission and absorption of X-Rays. This got me thinking about some of the physical chemistry I took as an undergraduate, in particular, about the way photons interact with electrons.
My basic photon/electron understanding:... |
In Chaikin's Principles of Condensed Matter Physics, in chapter 6 ("Generalized Elasticity"), on pg. 290, there is a formulation of what he refers to as an elastic energy associated with gradients of a variable $\theta(x)$, where $x$ is a site on a lattice and $\theta$ the angle of the order parameter for spins alignin... |
I have a response function of the form $\chi(\mathbf{r},\mathbf{r'};t,t')$ at hand. Now, the function is time-invariant so I can write it as $\chi(\mathbf{r},\mathbf{r'};t-t')$ right off the bat. After performing Fourier transform on $t-t'$, I've arrived at $\chi(\mathbf{r},\mathbf{r'},\omega)$ where $\omega$ is the tr... |
I was just learning about what happens to current inside a battery, and my professor gave an example: Let's say we have a $1$ volt battery connected to a $1 \Omega$ load. Then he claimed that the electric current will be $1A$ flowing through the positive terminal, $-1A$ through the negative terminal and $0A$ through th... |
This might seem a bit off-topic question but it comes into different physical theories. While learning quantum scattering I came across certain singular integrals but could not compute them. I am learning to compute singular integrals using the '$i\epsilon$-prescription' of complex contour integration from the book Mat... |
When a photon produces an electron-positron pair, do both these particles have mass? Why or why not?
|
I know that the density and potential (in spherycals) of a charged ring is, respectively,:
$$
\rho(\textbf{r})
=
\frac{\lambda}{a}
\delta(r-a)\delta(\theta-\tfrac{\pi}{2})
$$
$$
\varphi(\textbf{r})=
\frac{2\pi a \lambda}{r_>}
\left[
1+ \sum_{n=1}^\infty (-1)^n \frac{(2n-1)!!}{(2n)!!}\left(\frac{r_<}{r_>}\right)^{2n... |
Let there be a composite system $\mathcal{H}=\mathcal{H}_{A}\otimes\mathcal{H}_{B}$, where $\mathcal{H}_{A}$ and $\mathcal{H}_{B}$ are Hilbert spaces of two subsystems of $A$ and $B$.
Suppose the density matrix of this composite system be $\rho_{AB}$ and suppose that it is not separable.
We can find the density matrix... |
This may be quite a straightforward question, but I have a dynamical system with a high dimensional phase-space. I calculated the Lyapunov spectrum for it and saw that one third of my Lyapunov exponents are approximately zero (which is a lot and was quite unexpected).
What can I conclude from this? These do not signify... |
Heisenberg principle states that product of uncertainty in velocity (momentum but assuming mass constant) and uncertainty in position is greater than reduced Planck constant divided by 2. What happens when the system is traveling at a high velocity? Does the uncertainty in velocity increase or decrease with increasing ... |
I want to filter out any light of higher frequencies and pass only infrared. How is it done?
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