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In Wikipedia ( https://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity ) one can find the following expression for the effective gravitational potential in the Schwarzschild approximation
$$V(r)=-\frac{GMm}{r}+\frac{L^2}{2\mu r^2}-\frac{G(M+m)L^2}{c^2\mu r^3}$$
This is given without reference. Does anybody... |
In some physics problems that involve finding a second force given the total force and a first force, I've seen people's solution "letting" the math give you the sign of the missing force
Let's say we know the intuitively, or given a graph, we know that the second missing force is in the direction of the negative X-axi... |
I have seen a lot of questions here which ask why a free rigid body always rotates about it's centre of mass. The answer in most cases is like a "thought experiment". First, we prove that when a force is applied to a rigid body, it behaves like a point object where the entire mass of the object is concentrated to one p... |
Every source tells that eddy currents are produced by change in magnetic flux in conductor, but according Gauss' law for magnetism net flux over a closed surface is 0, then how magnetic flux will change to produce eddy current?
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I found this article here in which it is said that it would be incorrect to say that g is not acceleration due to gravity but local gravitational field as there is no acceleration on a block placed on a table. Please can you explain this as I am in a school and I have read only that g is acceleration due to gravity and... |
By the naming of scalar we know that it scales. When It is multiplied with a vector it changes the vector's magnitude because it only has magnitude but no direction. So then why a negative scalar rotates a vector's direction by 180 degree? For example, if the scalar is -5 then it will scale the magnitude 5 times and al... |
Every definition of the two is always very abstract to me. Like, A pure state is located on the surface of the bloch sphere while the mixed state is somewhere within.
First of all, what is an intuitively definition?
And second of all, how do you practically recognize whether a given state is mixed or pure?
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Suppose we start with a state on the Bloch sphere given by:
$$|\psi\rangle = \begin{pmatrix}\cos\left(\frac{\theta}{2}\right)\\e^{i\varphi} \sin\left(\frac{\theta}{2}\right)\end{pmatrix}$$
The Berry Connection is given as:
$$A=i\langle\psi|\nabla|\psi\rangle$$
I am stuck at taking the spherical form of $\boldsymbol \na... |
It's my understanding that many inverse-square laws can be explained as a central point emitting "interaction rays" in all directions equally. And that when another object with some area is "impacted" by those rays, it will then feel an effect proportional to the amount of rays that hit it. This amount can be found geo... |
The gas is contained within an elastic balloon of some sort. The balloon itself is in a vacuum.
I assume that adding charge to a gas would increase its volume because of atoms with same charge pushing against each other. Would adding charge to a gas really change its volume?
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I am trying to solve problem 7.43 in Griffiths, where a Superconducting Sphere is cooled below its critical temperature, and I am asked to find the induced current.
In the first few parts of the question I showed that:
a) The magnetic field is constant inside a perfect conductor.
b) The magnetic flux is constant throug... |
Can dark energy be used for the Alcubierre drive as a substitute for negative mass? After all, to make the Alcubierre drive work, it is necessary to expand the universe behind it, and that is what dark energy does. I saw a recent interview with Miguel Alcubierre where he mentioned this and said that it may be possible,... |
Two objects facing each other over a distance of 88m start moving from rest at an acceleration of 0.3m/s^2 and 0.2m/s^2 respectively, after how long do they intersect?
I've tried everything to find the answer and using brute force I found that they will intersect after 18.8 seconds because object a will have moved 53.0... |
The question is to verify that the following Dirac Bilinears obey the following transformation law:
$$\bar\psi'(x') \gamma^\mu \psi'(x') = \Lambda^\mu_\nu \bar\psi(x) \gamma^\nu \psi(x)$$
What I know so far that may be relevant to this problem:
$$ S(\Lambda) \text{ (for the topic of spinors) is hermitian and unitary. T... |
Generally in textbooks they represent spacetime as $(M,\nabla,g,t)$
where $M$ is a Lorentzian manifold,$\nabla$ a torsion-free connection,$g$ a metric and $t$ a time orientation.
But they do not talk of topology. My question is does the topology of spacetime have importance in physics?
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So I came across a question where a lamp was labelled 24 W and 12 V. 2 lamps that were identical and had this labelling were then put in series with a voltage supply of 12 V.
Obviously the individual voltage going through the lamps are 6V. But what I don't understand is that when there is this labelling of 24 W and 12 ... |
Let me elaborate for you my concerning
I am thinking of a example of a vertical mass spring system. Suppose i place my system at equator, let suppose a wall clock which uses a vertical spring mass system to measure time. Each time the mass reaches an extreme position, the clock advanced to by a second, so 1 sec is our ... |
A hypothetical signal is emitted from a known exoplanet thousands of light years away. The signal marks the occurrence of an epoch-worthy event on that planet, and we (the receivers) want to know exactly when that transmission was sent in our own local timekeeping system, so we can can set up the conversion of time bet... |
Consider a non-ideal gas passing through an isobaric process, with $C_p$ not affected by temperature.
Would $C_p\Delta = Q$? Where $Q$ is the heat the gas received?
I think it is not.
Here is my reasoning,
$$dH = C_p dT + V(1-\alpha T)dP \\ \implies dH = C_pdT $$
But $$\Delta H = W_s + Q$$
where $W_s$ is shaft work.
So... |
Increasing the angular momentum of an object will increase the mass of an object. The thought experiment I have in mind is 2 identical discs, left and right:
spin left
push right off of left
stop left spinning
spin right
pull left back towards right
stop right spinning
start over
I imagine it inch-worming along as ea... |
Mattig's formula for any k:
How to derive this equation without using General Relativity?
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I have a question about the really meaning of the fine structure constant. Actually, my doubt is why the physicist look to a meaning for this constant.
I understand the difference between this constant and the ordinary constant, that is, it carry no units with it.
But is not this just like pi or euler number? It someti... |
How far will a person travel in 15 min, driving their car down the highway at 24 m/s?
when it says how far will a person travel, is it talking about distance or displacement?
|
Consider that we have the electric field,
$$\mathbf{E}=E_0\cos(kz-\omega t)\hat{\mathbf{x}}\tag{1}$$
and the magnetic field,
$$\mathbf{B}=\frac{B_0}{c} \cos(kz-\omega t)\hat{\mathbf{y}}\tag{2}$$
These are the plane wave solution in vacuum, for an electromagnetic wave moving in the $z$ direction. The Maxwell stress tens... |
I was trying to calculate the total charge from a charge density that has a very strange form involving delta functions. The charge density is
$$\rho(\vec r) = - \vec d . \nabla \delta(\vec r)$$
$d$ is a vector in 3 dimensions. How to find the integral of such a function?
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The problem then states: estimate the minimum wavelength of the gamma ray photon.
The answer to this question is: 0.25 x 10^-11 - (binding energy of oxygen - the binding energy of F which is 0.04 x 10^-11). Then you use the hc/E = wavelength which I understand.
What I don't understand is why you would minus the kineti... |
WRT: https://www.youtube.com/watch?v=0ui9ovrQuKE&ab_channel=ArvinAsh
Now I found a paper "Why Delayed Choice Experiments do NOT imply Retrocausality by David Ellerman" on the internet but as a layman, I couldn't understand the paper but everyone on youtube is saying that this experiment shows retrocausality, can someo... |
My Grandparent asked me this question a few years ago, and I am getting around to giving him an answer, but I don't know the answer. Can anyone help?
"A pickup truck is speeding along a highway at 60 mph. One man (c) is standing on the side of the highway at point A. Two men (a and b) are standing in the bed of the p... |
Why can we ignore the magnetization $\vec{M}$ but not the electric polarization $\vec{P}$ in first order when discussing the response of a material to optical fields?
Related to this: Why is the electric polarization $\vec{P}$ only dependent on electric and not the magnetic field in first order?
Summarized: Why is the ... |
I know that atoms and entire molecules and even sets of hundreds of molecules can be in superpositions of position eigenstates.
Viruses are the smallest living organisms (if they can even be called organisms) with the smallest being 20 nanometers.
Can viruses, analogous to a set of hundreds of molecules be in a nontriv... |
Energy is often defined as the capacity of a system to do work.
How does this definition apply to thermal energy?
Work is done by displacing an object under a force. But under what force is displacement occurring on the microscopic level?
|
I am a beginner in topology and I want some help in visualizing the following statements:
"Strings arise when manifold contains non-contractible loops"
"Monopoles arise when manifold contains non-contractible 2-spheres"
"Textures arise when manifold contains non-contractible 3-spheres"
Can someone help me to understand... |
I am a student in an Introduction to Physics class, and I have the following question which I am confused about, and how two parts of the answers relate to each other. (We are doing 1d kinematics)
A car traveling 45 $\frac{km}{h}$ slows down at a constant 0.5
$\frac{m}{s^2}$ just by "letting up on the gas." Calculate ... |
In the book "Classical Mechanics Point particles and relativity by Greiner"
We calculate Forces in the motion on an ellipse as follows
we first parametrizate the ellipse $$\vec r(t)=<a\cos(\omega t),b\sin(\omega t)>$$and take second derivative and found $$\vec F=m\vec a(t)=-m\omega^2 \vec r(t)$$
Which points the center... |
Suppose you need to weight something that weights $x$ in a digital scale that reads a non zero value a when empty. There are two options:
Tare the scale and weight, giving $x \pm \Delta x_1$.
Weight and substract a from final reading, giving $x \pm \Delta x_2$.
When subtracting, error propagation must be performed, s... |
The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object's speed in the rotating frame (more precisely, to the component of its velocity that is perpendicular to the axis of rotation).
Can someone sketch a diagram... |
This problem is an example (page 26, ex. 3) from An Introduction to the Use of Generalized Coordinates in Mechanics and Physics by Byerly. The Kinetic Energy and equations of motion are given and I'm to reproduce it.
A wedge of mass $M$ having a smooth face and a perfectly rough surface, making with each other an angl... |
Suppose I have a proton and a neutron in an external harmonic oscillator potential well. Let us first neglect all interactions between the two: since they are distinguishable particles I conclude their Hamiltonian eigenfunctions to be:
$$ \Psi(r_1, r_2) = \phi_p (r_1) \phi_n (r_2),\tag{1}$$
where the $\phi_i$s are any ... |
In his book (String Theory Volume 1, pp. 66-68), Polchinski explains state-operator correspondence and derives the vacuum state through the identity operator:
$$
\Psi_1[X_b] \propto \exp \left( -\frac{1}{\alpha'} \right) \sum_{m=1}^\infty m X_m X_{-m} \tag{2.8.24}
$$
where $X_m$ comes from the expansion of the field at... |
I am studying on my own with the book by Professor Moyses Nussenzveig "Course in Basic Physics", and I decided to solve some examples from the book.
In this example, there are two infinite plates, one in the $ xz $ plane with $ \sigma> 0 $ and the other in the $ xy $ plane with $ \sigma <0 $, and I want to calculate th... |
The Unruh effect states an accelerated observer in flat Minkowski spacetime sees excited states in a heat bath with the Unruh temperature.
Then, when the initial rest observer is in a heat bath with the uniform temperature $T$ in the Minkowski spacetime, what is the temperature the observer will see after some accelera... |
I am new to quantum mechanics, and I'm trying to learn about Majorization in quantum states. These are the notes I am following http://michaelnielsen.org/blog/talks/2002/maj/book.ps by Michael Nielsen. I am stuck in an exercise that already has an answer, but I still can't understand it. It is the following:
Exercise ... |
I've made an experiment to verify Newtn's law of cooling, but while doing the analysis, my results don't fit accurately with the data collected (303 data using a sensor). According with my initial conditions such as $T_R=21.8°C$ (room temperature) and $T_o=80°C$ (initial temperature) I should obtain something like:
$\l... |
Not sure how to go about integrating the equation for this example. Any help would be appreciated.
|
On pg 72 of "Something Deeply Hidden," Sean Carroll discusses how the uncertainty principle is just a consequence of the Schrodinger equation. He writes:
Consider a simple sine wave, oscillating up and down in a regular pattern throughout space. Plug such a wave function into the Schrodinger equation and ask how it wi... |
The questions is just the title. I understand we're supposed to not use cursive wherever we write units (so if I write m as a variable, it goes like $m$, but if it indicates metres, then it goes as m).
So, if I'm writing on a LaTeX table that the mass (noted as $M$ is measured in solar masses, should I use $M_\odot$ or... |
What are the differences between bound and unbound nuclear states?
What does bound or unbound excited states mean?
Please explain in nuclear sense.
|
Consider two parallel conducting frictionless rails in a gravity free rails parallel to x axis. A movable conductor PQ( y direction) of length $l$ slides on those rails. The rails are also connected by a fixed wire AB with a resistor of resistance $R$. Suppose a magnetic field exists in region which varies as $$B = cx$... |
I see that this topic has been well covered from the perspective of a) a stationary observer dangling on the end of a rope and and b) an observer free-falling from infinity. What I'm still unsure about are the roles of velocity vs. acceleration. Is it all about velocity? Does an observer who is stationary near the ho... |
In the figure we see a typical electron gun, if the anode is at a positive potential, Why don't electrons collide with the anode in an electron gun?
Another question, if the potential of the anode is high enough to create an electric arc with the cathode, the path of the electrons will be as shown in the image? Or will... |
Recently I have been working on a problem involving a cross-flow heat exchanger (Two fluids flow orthogonal to each other on either side of a separating wall and exchange heat with each other through this wall). As a result, I have derived analytical expression to describe the temperature distributions for the hot (los... |
Maybe it sounds as very stupid but I cant understand why there is possibility to summation and synergy something. So please be patient to my question :)
We have 3 objects with own gravitation force but when they become into one single object they have single (m1+m2+m3) mass and common gravity (with one center of mass).... |
Looking at explanations of neutron stars, the neutrons towards the center of the star are stabilised by the enormous pressure, and so don't undergo nuclear decay. I am wondering if this is possible under different circumstances. Could uranium nuclei experience this sort of stability if they were put under enormous pres... |
I have been wondering for a while. Is it possible that when a body or a particle moves close to the speed of light, it interacts more with the Higgs boson? If so does that explain why moving at the speed of light increases relativistic mass?
|
I was doing research into how $G$ forces are calculated, and I was told that they show all acceleration that can be "sensed" by humans (i.e. all non-gravitational acceleration).
This confused me though, because the notion that gravitational acceleration cannot be sensed was not intuitive to me - I can feel when I am fa... |
Griffiths says
The energy of a point charge is infinite
$$W=\frac{\epsilon_{0}}{2\left(4 \pi \epsilon_{0}\right)^{2}} \int_0^\infty\left(\frac{q^{2}}{r^{4}}\right)\left(r^{2} \sin \theta\; \mathrm{d}r\;\mathrm{d}\theta \;\mathrm{d}\phi\right)=\frac{q^{2}}{8 \pi \epsilon_{0}} \int_{0}^{\infty} \frac{1}{r^{2}} d r=\inft... |
It is my understanding that
Hawking radiation is observed by external observers, and
A necessary condition for having Hawking radiation is the formation of an event horizon during a gravitational collapse.
Since the emergence of an event horizon takes infinite time for an observer far away from the black hole, how ... |
How do I go about solving this?
I know bound states require the energy to be less than the potential while scattering states require the energy to be greater than the potential.
I also know that quantum particles exist in areas where a classical particle would not.
Here is the second question, again what steps should... |
I learned that a tensor is a linear map from some number of vectors to the real numbers.
For example, $t(\vec{u},\vec{v})=\vec{u}\cdot\vec{v}$ is a rank-2 tensor as it takes 2 vectors as arguments and combines them into a real number.
I then read that a rank-1 tensor is a vector. How is that possible? If the rank-1 ten... |
A particle is trapped in the region $0 \leq x \leq \pi$ by an infinite potential well. At the initial time, the particle has a
wavefunction
$\psi(x, 0)=A(\sin (x)+\sin (2 x))$.
Find the wavefunction at all times:
$\psi(x, t)=$
The question first asked to find $A$, assuming the wavefunction is normalized.
I found $A$ to... |
I was working out the evanescent magnetic field of a perpendicularly polarized incident wave. The plane of incidence is the $xz$ plane. For the evanescent field the wave vector $\mathbf{k}_T$ is give as,
$$\mathbf{k}_T=k_T\left[\frac{n_1}{n_2}\sin\theta_I\hat{\mathbf{x}}+i\left(\sqrt{\frac{n_1^2}{n_2^2}\sin^2\theta_I-1... |
Using the uncertainty relation
\begin{equation}
\Delta x \Delta p \geq \frac{\hbar}{2}
\end{equation}
we can calculate the momentum uncertainty on a length scale of a nuclei. Assuming $r_{nucleus} \sim 1 fm$ we get a momentum uncertainty of $\Delta p = 98.66 MeV \cdot c \sim 100 MeV \cdot c$.
What is the impact of this... |
I don't speak English so edit my question if it is not accurate.
Euler's formula for a complex number is:
$$e^{i\theta}=\cos\theta + i \sin\theta$$
But when I write a plain wave as
$$e^{i\vec{k}\cdot\vec{x}}=\cos(\vec{k}\cdot\vec{x}) + i \sin(\vec{k}\cdot\vec{x})$$ I think something is not right because $\vec{k}\cdot\v... |
It is often said that special relativity doesn't handle acceleration since you general relativity for that. If I understand correctly this is incorrect just with some caveats.
Rindler coordinates are coordinates as experienced by a constantly accelerating observer such that the observer is at rest in that frame. They a... |
So I know that emf is directly proportional to the rate of change of magnetic flux linkage.
And Lenz's law is that the emf opposes the change producing it.
I am assuming the coil already has a magnetic flux (even though I don't know why but it just seems to make sense).
When the magnet is moved towards the coil, the co... |
Can anyone explain the fundamental reason of why time-independent sources cannot emit or absorb energy. Does it have to do with time-translation symmetry and Noether's theorem?
I was studying the following model of scalar field theory $$ \mathcal{L}=\frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi-\frac{\mu^{2}}{2} ... |
Introduction
Six point charges of magnitude $Q_0$ is evenly distributed on a sphere with radius $a$ and center in the origin. The six point charges have the cartesian coordinates:
$q_1=(a,0,0) \: \: \: \: q_2=(-a,0,0)$
$q_3=(0,a,0) \: \: \: \: q_4=(0,-a,0)$
$q_5=(0,0,a) \: \: \: \: q_6=(0,0,-a)$
The electric field caus... |
Why can't information be conducted out of a black hole?
Does gravity affect conduction?
What is the temperature profile in equilibrium of a metal pole half in, half out of a very large BH such that gravity is low?
What if the external half is insulated?
Similarly, what happens to electrical signal conducted into ... |
I have read this:
The live wire carries the alternating potential difference from the supply. The neutral wire
completes the circuit. The earth wire is a safety wire to stop the appliance becoming live.
My question is related to this phrase, "The live wire carries the alternating potential difference from the supply.... |
I mean we can represent plane waves using just sine and cosine functions. Why do we need to use Euler's formula to represents plane waves as complex exponentials? What is the intuition behind using $i=\sqrt{-1}$. Of course, the plane waves are solution of Maxwell's electromagnetic equations.
Please clarify my doubt!
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I came across a good website that explains how Newton derived his formula of gravitational force click here
Why is $\frac{k}{4\pi ^2}=\frac{c}{M}$ and $f=(kmM)/r^2$ not $(4\pi^2)/r^2\sqrt{MmcC}$? Which I tried myself and it seems that I can't see how they came to that conclusion.
|
I’ve solved a physics problem about acceleration with the quadratic formula and I don’t understand the solutions.
There is two vehicles A and B. A is before B of 50 meters. The velocity of A is 20 $ms^{-1}\hat{i}$ and B is 30 $ms^{-1}\hat{i}$.Then A start an acceleration of 2 $ms^{-2}$. How long do A overtake B.
I’ve c... |
Consider the Schwarzschild metric
$$ds^2 = -f(r)dt^2 + \frac{1}{f(r)}dr^2+r^2 d\Omega^2,$$
where $f(r)=1-\frac{2M}{r}$. I take it that $M$, although not really the mass of a black hole, is the coefficient that is closely associated with the mass. I'm curious as to what will happen if in the metric I directly replace $M... |
How QED eliminates the cases when
in loop corrections two fermions get created with the same momenta and spin state?
Is it done by the ladder operators?
Edit: the two fermions are in two distinct loops.
|
Surface Tension as a Line Integral
I have seen the surface tension force defined by multiple sources as the following line integral over the contact curve C (with trivial differences in notation among sources for the differential length element and surface tension coefficient, which I shall call $dl$ and $\gamma$):
Eqn... |
When airliners fly through clouds it looks like they are circulating the air sideways. See Image.
The wings are pushing the air flown through downwards, which circulates the air each side of the wings. It looks like two separate swirls of counter-rotating air centered on each wing-tip vortex. See illustration in the i... |
I read that 2 mbar of atmospheric methane = 1 x 10^13 tons, but how is this calculated? I have looked for information but can only find this for converting pressure to kgs-of-force/cm^2.
Is atomic-weight involved here, as the difference between 2 mbar methane and the same quantity of carbon dioxide doesn't seem to refl... |
In non-relativistic quantum mechanics, the normal condition for position eigenstates is
$$\langle y|x\rangle=\delta(y-x).$$
However, this condition is not Lorentz-invariant. I have never seen a textbook on relativistic quantum mechanics address this normalization issue. It seems to me like this is a very important issu... |
Given a photon gas, one can use standard statistical mechanics methods to obtain the energy
$$U=aVT^4,$$
with $a$ a messy constant whose precise details do not matter. This is a fairly involved process, but it is doable. However, my question is, can one obtain this temperature dependence from more roundabout methods? T... |
Is it possible to form a lagrangian of the TISE using the concept of Lagrange Multipliers? I am new to this topic so any help would be much appreciated.
|
I can't find an answer for whether the Double Pendulum equations can be derived solely using Newtonian Mechanics (Newton's Laws of Motion). The reason I ask for this answer is because wherever I go, I only see the Lagrangian solution. I am also aware that there are certain problems in Classical Mechanics that can't be ... |
I read somewhere that the Energy Density of Magnetic field is given by $\frac{dU}{dV}=\frac{B^2}{2\mu_0}$ where $B$ is the magnetic field in present in the space in a volume $dV$.
However, we know that the force due to magnetic field is always perpendicular to velocity of a charged particle. That means the power delive... |
I'm having some trouble understanding the formula: $Z=e^{-\beta F}$ which is sometimes used to define the partition function.
From what I understand, this $Z$, is the partition function but taken at the thermodynamic limit since:
$$Z=\sum_{E_i}\Omega(E_i)e^{-\beta E_i}=\sum_{E_i}e^{S_m(E_i)/k_b}e^{-\beta E_i}=\sum_{E_i... |
Suppose I have two operators $\hat{A}$ and $\hat{B}$, where $\hat{A}=\hat{a_1}+\hat{a_2}+...+\hat{a_m}$, and $\hat{B}=\hat{b_1}+\hat{b_2}+...+\hat{b_n}$. Is there a necessary and sufficient condition for $\hat{a_1},\hat{a_2},...\hat{a_m}$ and $\hat{b_1},\hat{b_2},...\hat{b_n}$ to make $[\hat{A},\hat{B}]=0$ ?
If so, ho... |
I am from India and in India ceiling fans have generally three wings.
Today while laying on my bed a question came in my mind.
First of all, I know that if we use just a single wing at a time of same dimensions as each wings of a three winged fans have then it will reduce the amount of air being pushed down.
But what i... |
I am reading chapter 3 of Quantum Mechanics - A Modern Development by Leslie E Ballentine, where he derives the operators for the common dynamical variables from space-time symmetry considerations.
At the start, he states that for each space-time transformation there must be a transformation of observables, $A \to A'$,... |
I've been trying to derive the result of the following dot product in position space: $\langle p|x\rangle$.
The information I'm supposed to be using:
i) Any state can be written as a linear combination of the basis vectors: $|p\rangle=\sum_i a_i|i\rangle$
ii) The dot product between two functions is given by: $\langle ... |
I am currently trying to find the focus of an IR laser beam by using a 300 $\mu$m pinhole. Now, when I am scanning the pinhole across the beam and plotting the pinhole position vs the laser spectrum amplitude at a given wavelength, on both $x$ and $y$ axes I obtain a profile which is well fit by a Gaussian whose width,... |
Let $\vec{p} = p_x \hat{x} + p_y \hat{y} + p_z \hat{z}$, and also use the notation $|\vec{p}| = p$, where $p^2 = p_x^2 + p_y^2 + p_z^2$.
What is the difference between the operator $\hat{p}^2 = \hat{\vec{p}} \cdot \hat{\vec{p}}$, and the operator
$\widehat{p^2}$? And which one is the operator that correctly represents ... |
In this wiki page we can read:
The Lagrangian density for Newtonian gravity is:
$$\mathcal{L}(\mathbf{x},t)= - \rho (\mathbf{x},t) \Phi (\mathbf{x},t) - {1 \over 8 \pi G} (\nabla \Phi (\mathbf{x},t))^2,$$
while in this other wiki page we can see:
The simplest classical field is a real scalar field — a real number at... |
Is the imaginary time just a different convention to express the time evolution to make the calculations easier? Hawking also said that
"It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless ... |
According to the Heisenberg equation of motion, the velocity operator is given by
$$\hat{v}=\frac{d \hat{r}}{dt} = \frac{1}{i\hbar}[\hat{r},\hat{H}].$$
Question 1: How can I find the velocity operator in a specific direction i.e. in the x-direction from this equation?
From Hamilton mechanics, we have
$$\hat{v_i}=\frac{... |
Many people criticize string theory for being very speculative and far fetched (since it requires extra dimensions). Nevertheless, the string landscape is often invoked to have many variations of constants in different regions of the inflationary multiverse since ordinary GUTs only allow small variations:
"The fundame... |
Looking into the options of adding and retaining heat in the outdoor pool (and saving wallet) - heat inverter, roof solar water heater, gas heaters etc. the pool cover seems to rule them all (at least here in Australia).
There is a very nice (though pretty old - 1978) paper by CSIRO on this topic:
SWIMMING POOL HEATING... |
Phys.org's The detection of phosphine in Venus' clouds is a big deal, and here's how we can find out if it really is life contains part of a NASA/JPL-Caltech image which is on the cover of Aerial Platforms for the Scientific Exploration of Venus, JPL D-102569
What caught my eye is the inclusion of what I assume is chro... |
Basic quantum mechanics told us that multiple commuting Hermitian operators have simultaneous eigenstates (as a complete basis for the Hilbert space). However, there are cases where the operator are non-commuting while they share some eigenstates (the number of which is less than the dimension of Hilbert space and do n... |
Are electrons created from a battery and then 'injected' into the copper wire?
If no, does that mean the battery loses power because the copper wire has run out of free electrons?
|
I'm pretty new to quantum computing, and I'm wondering how I can compute the outcome of a projective measurement of a spin along the +Z axis followed by a projective measurement along the -Z axis. I think that when we make the +Z projective measurement. I know that +Z axis corresponds to $(1, 0)^{T}$ and -Z axis corres... |
For this problem I am stuck on how to calculate the electric field. I know to apply Gauss' Law:
$$\oint \overrightarrow{ E} \cdot \overrightarrow {dA} = \frac{q_{enclosed}}{\epsilon_0}$$
$$E(4\pi r^2) = \frac{Q + -Q}{\epsilon_0}$$
I don't know $r$, but knowing that the $Q's$ are equal magnitude can this be stated that... |
Consider a full Hamiltonian $H=H_0 +H_1$ on a lattice with hopping terms $H_0$ of the form $t c^* c$ and attractive interaction $H_1= -V c^* c^* c c$ so that superconductivity can occur. We can then approximate $H$ with the quasi-free BCS Hamiltonian $H_\text{BCS}$ of the form $\xi c^* c + \Delta^* cc+ \Delta c^* c^*$ ... |
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