instruction stringlengths 31 24.3k |
|---|
By the Lorentz guage $\displaystyle \nabla \cdot \mathbf A = -\frac{1}{c^2}\partial_t \varphi\ $ one gets the inhomogeneous wave equations for the potentials
$$
\square^2 \varphi = -\frac{1}{\epsilon_0}\rho, \qquad \square^2 \mathbf A = -\mu_0\mathbf J \tag{I}
$$
where $\displaystyle \square^2 \equiv \nabla^2 - \frac... |
In 1D, the energy eigenvalue equation for an energy value $E$
$$
-\frac{\hbar^2}{2m}\psi''(x) + V(x)\psi(x) = E\psi(x)
$$
can have at most two linearly independent solutions, $\psi_1$ and $\psi_2$, with their Wronskian, $\psi_1'\psi_2 - \psi_1\psi_2'$ being a constant. Then it is said that
if $\psi_1$ is such that it ... |
The physical constant $\epsilon_0$ is usually called "permittivity of free space" or "vacuum permittivity". Griffiths says:
I dislike the term, for it suggests that the vacuum is just a special kind of linear dielectric, in which the permittivity happens to have the value $8.85 \space 10^{-12}\space \rm {C^2\over Nm^2... |
I am investigeting the meaning of the components of the Stress-Energy tensor:
My source also states, that this matrix is always symmetric in the General Relativity. That looks obvious on the image - except the pair of the momentum flux and shear stress. On this picture, these quantities are the same.
Why would be mome... |
This is a basic question in bosonic String Theory. Can someone explain what is the interpretation of the coefficients?
Since this is like the first quantized version of String theory, I would guess that A,B,C are associated with probabilities for the string to exist in that particular oscillatory state. Is that right?
... |
It is known that the galaxies at the edge of the observable universe are accelerating away from us and eventually they will start moving faster than light with respect to our frame. However, suppose that just before such a galaxy sped to past the speed of light, one attached a long rod to a star in that galaxy and the ... |
After doing so much research on the concepts of work and energy, I feel like Potential energy is more like a 'dummy' (I don't really know what word to use to describe it) energy concept defined so that we can say that isolated systems have constant energy, like I feel that we could interpret/treat all forces (conservat... |
engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last
compartment with velocity v. The middle point of the train passes past the same pole with a velocity of.
My thinking:
Q1 Will the values of v and u be constant since they can’t pass it with different velocities becau... |
Why does a bucket of water left outside in the cold will most likely break (it happened to me; filled a bucket for cleaning intentions, then something happened and I forgot it outside - then the winter came and when I came to retrieve it, the bottom was cracked), but the ice trays in the freezer?
I get that the water e... |
A crazy ant is standing on the origin.
It starts by walking 1 unit in the positive x axis direction and then turns 60 degrees counterclockwise and walks 1/2 units in that direction.
The ant then turns another 60 degrees and walks 1/3 units in that direction.
The ant keeps doing this endlessly.
Find the final position o... |
The wave function of a particle in a spherically symmetric potential $V(r)$ is given by: $$ \psi(\vec{r})=(x+y+3z)f(r).$$ Determine the probabilities to find $\psi$ in the different eigenstates of $\hat{L}_z$.
My attempt:
It's best to rewrite $\psi(\vec{r})$ in terms of spherical harmonics: $$\psi(r,\theta,\phi) = \l... |
So a random thought crossed my mind, I am not sure if it makes sense at all. I apologize for the very amateur question: is there a name for the specific temperature at which an object reaches an optimum state and stability, i.e. is resistant to deforming?
For instance, an iron rod, if heated enough, will bend with ease... |
Suppose the case that someone in future makes a time machine which can be used to time travel in past. Now s/he can accurately measure momentum of a particle without caring about the particle's position at that time and then s/he can use the time machine to travel back in the past at the same time when s/he measured pa... |
Suppose that 2 observers are sending light signals to each other.If each of them are stationary in relation to a nearby galaxy, but each of these are separated by so great distance, they will be moving apart at speed which is higher than light:
How's the type of violation of causality seen in the Krasnikov tube avoide... |
I had a asked a question about six months back what direction forces due to pressure must be pointing and I got a pretty good answer for it (here). Thinking a bit more deeply about the answer, I started getting confused how the pressure always wants to contract a body rather than expand it?
THe following equation is wr... |
I know that Isentropic Efficiency is a comparison between the actual performance of something(turbine for example) and the performance that would be achieved under idealized circumstances for the same inlet and outlet. Let's say a turbine has an isentropic efficiency of 0.75. What does 0.75 mean and the rest (0.25) mea... |
If one measure some object in air and then measure it in vacuum will there be any difference in weight?
|
I am a high school student and I am very confused in fluid mechanics, MY confusion is that:
we know pressure increases with depth, but I want to know what are the cause and effect here i,e actually pressure depends on height or height depends upon pressure? because in some cases if we have to explain why liquid surfa... |
In the Flow of dry water chapter of Feynman lecture, this following point is written (see here):
The law of hydrostatics, therefore, is that the stresses are always normal to any surface inside the fluid. The normal force per unit area is called pressure. From the fact that there is no shear in a static fluid, it foll... |
I understand why an object rotates about its centre of mass from a mathematical perspective but I have been trying to think how we can explain this in terms of the bonds within the object. Feel free to amend this example to help explain, but I was thinking about a linear molecule that receives a force for a brief time... |
I'm trying to solve a problem regarding two systems interacting through a coupling hamiltonian:
$$ H(x,y) = H_1(x) + H_2(y) + kxy $$
I am supposed to express the mean values $\langle x \rangle$ and $\langle y \rangle$ in terms of their independent momenta $\langle x^n \rangle _0 = \int dx \rho_1(x) x^n$ (and the same f... |
A bullet moving with a velocity of 200cm/s penetrates a wooden block and comes to rest after traversing 4cm inside it . What velocity is needed for travelling distance of 9cm in same block.
My though for this question:
Q1 By 200m/s , does it mean the speed just before it touched the block and during that time it may ha... |
I am ignorant of physics besides college, and I would like to know if it is possible that a moon rotates its mother planet for an infinite time assuming there is no resistance of any form.
I came up with this question since once a moon starts rotating, it keeps rotating according to law of gravity. Isolate the system t... |
I try to do basics computations of SR with the heavier formalism of GR to see if I understand it well.
Change of coordinates is spacetime: changes of coordinates in space time are change of coordinate maps in the $(\mathbb{R}^4,\eta)$ Lorentzian manifold. For the cartesian coordinates we have one global map and it's th... |
This question is a bit more meta and non-straight forward than it might appear on first glance.
I recently saw Why The Speed Of Light Is Unmeasurable, which is actually about why the speed of light cannot be measured one-way, but only for the round trip, and about the respective convention to say that the round-trip ti... |
It is said that light behaves like a wave until it is measured, then it behaves like a particle.
Photons (the particles) then have to be defined by the measuring device.
It is my understanding that all single photon detectors rely (at best) on light moving a single electron from one atom orbital to another (or even ej... |
Looking at special relativity (which gives a real geometry of space-time) which reduces to Newtonian mechanics when $v\ll c$, It seems that special relativity is possible without Newtonian mechanics. At least we have an explanation for things.
But is it the same for quantum mechanics? Is Quantum mechanics formalism... |
I have an LED with the following specification which I'm using for oxygen saturation measurements. Here the optical output power is given as >1.2mW for RED LED and >0.5mW for IR LED. How to convert optical output power into relative luminous intensity (mcd)?
|
This question pertains to some notation in Zee's QFT book, Section II.2. The Dirac equation is
$$ (i\gamma^\mu\partial_\mu-m)\psi(x)=0, $$
which we can write in momentum space with the Fourier transform
$$ \psi(x)=\int\!\frac{d^4p}{(2\pi)^4}e^{-ipx}\psi(p)$$
as
\begin{align}
(i\gamma^\mu\partial_\mu-m)\int\!\fra... |
We know that by $F=-dU/dx$ formula that when force is attractive in nature potential energy increases and when force is repulsive, potential energy decreases. But I don't exactly understand this concept. Whenever i think of repulsive force i feel that the potential energy between two bodies would increase but it's the ... |
I am not a physicist so I am not sure how to check my intuition. Hence my question here.
Suppose I wish to charge a sphere to the maximum extent.
Intuitively I imagine the following:
I can give the sphere an indefinite amount of negative charge by continuing to add electrons indefinitely.
On the other hand I can remo... |
it is well known that we describe electrical propagation in a conductor using the conductivity matrix $A$, through the following laplace equation:
$$div(A(x) \nabla u(x))=f(x)$$
where $u$ is the electric potential (in $\mathbb{R}$) and $A$ is the conductivity matrix. A(x) describes the local conductivity in the point $... |
I'm trying to understand what exactly is the ETH, and miserably failing. Here's what I'm reading everywhere: isolated systems are supposed to thermalize, hence "forget about their initial condition", but the infinite time average of an observable $O$ is
$$\langle O\rangle_\infty =\int_0^\infty dt \langle\psi| e^{iHt}Oe... |
$$ \delta L = L \alpha \delta\theta$$
Is the equation of linear dilatation (Approximately). Just now raise a doubt about this equation:
See this image, imagine that the bar was initially with its ends on the red lines, and so the bar expanded, by let's say L/6 in each side.
I need to use $$ \delta L = L/6 $$ or $$ \de... |
I’m dealing with non-minimally coupling Quadratic gravity in the weak field limit, and as a result of the perturbation $g_{\mu\nu}= \eta_{\mu\nu} +h_{\mu\nu}$ I get some kinetic term mixing. On doing the expansion to quadratic order in $h$ I obtain an action which has couplings between a matter field $\phi$ and the gra... |
So we were given this problem in mathematical physics (Context is that we're learning about Sturm-Liouville):
Consider the 1D Helmholtz equation with $k^2>0$
$$\frac{\partial ^2y}{\partial x^2}+k^2 y=0$$
on the interval $0\leq x \leq L$ subject to the boundary conditions
$$ay(0)+by'(0)=0$$
$$ay(L)+by'(L)=0$$
What are ... |
It is found that all known
gases cool slightly on undergoing a free expansion. This is consistent with the
kinetic theory idea that temperature is associated with the kinetic energy of
the molecules.
If the gas expands, then the intermolecular attraction potential
energy goes up as the molecules get further apart. - F... |
I am trying to design a gun barrel and simulate its fatigue properties in a FEM solver like ansys. I have the basic geometric data of the barrel and shell. I found out that using internal ballistics we can theoretically calculate the variation of pressure in time using something called Vallier–Heydenreich Empirical For... |
Huygens' principle says that points on a wave can be thought of as the sources of new waves. This makes a lot of sense to me in the context of a moving wave and diffraction. However, in the context of a wave pulse, like a single stone being dropped into a pond, it feels as if Huygens' principle would predict that the c... |
There is a big concern about loosing information inside a black hole. As far as I understand, the black hole is characterized classically by its mass, angular momentum and charge. Semi-classically, thermal radiation is added.
Lot's of effort is paid to somehow restore the amount of information that crossed the horizon ... |
Kerr metric has the following form:
$$
ds^2 = -\left(1 - \frac{2GMr}{r^2+a^2\cos^2(\theta)}\right) dt^2 +
\left(\frac{r^2+a^2\cos^2(\theta)}{r^2-2GMr+a^2}\right) dr^2 +
\left(r^2+a^2\cos(\theta)\right) d\theta^2
+ \left(r^2+a^2+\frac{2GMra^2}{r^2+a^2\cos^2(\theta)}\right)\sin^2(\theta) d\phi^2 -
\left... |
⁸You have two possible configurations to make push-ups. In both configurations our arms are placed at 90 degrees from our body. The first position is normal push-ups where. your hands are placed on the ground. The second push-up. position, you have your legs on the ground and your hands on a cube. Which one between tho... |
Lets say i have a convex lens with a focal length of 10 cm. I place a 4 cm long pointed needle ( ie the
object )vertically say 25 cm to the left of the lens; call this x = - 25 cm . The base of the needle is on the principal axis (ie x axis ) and the tip of the needle is 4 cm above the principal axis .
From the thin l... |
I was washing a spoon in the sink and this question popped into my mind:
If a ball is dropped from height H and is allowed a single deflection of any angle $0 < \theta < 180$ at any height $ 0 \leq H' \leq H$, what is the furthest the ball can land from where it would have landed without deflection? What are the value... |
So I was thinking about this post I made earlier: What is the second conserved Quantity of the Pendulum?
In which a pendulum appears two have significant properties. It's Kinetic Energy and its Phase.
I was thinking about pendulums and I wanted to characterize their trajectories (in a time forgetful way). One thought i... |
Look at a particle in a cylindrical well of radius $R$ and length $L$ with zero potential $V=0$ inside and $V=+\infty$ on the boundaries and outside the well. The time-independent Schrödinger Equation can be written as:
$$\nabla^{2} \psi=-k^{2}\psi\tag{1}$$
where $k^{2}=\frac{2mE}{\hbar^2}$
The geometry demands cylindr... |
I though I understood this concept but the more I learn advanced topics like torque, momentum, work, the more I realize that I have fundamentally misunderstood it. My original, theoretical line of thinking was that COM was that point on object or somewhere outside it where equal amount of mass was distributed that surr... |
I am looking for the best astrophysics book or combination of books given my background.
I have a PhD in nuclear engineering and I am still doing research in the nuclear field. I develop mathematical models for radiation transport, hydrodynamics, shock physics and MHD, as well as to study the interaction among these ph... |
Do the ideas of Bloch wavefunction and Bragg scattering of electrons which apply to crystals also apply to liquid Mercury ?
Why is it that electrons in the liquid are not localised by the disordered positions of the mercury ions ?
|
I am not asking for a solution of the following problem that appears in my assignment. However, I don't understand the question and I would like someone to explain the what the question actually is asking AND also hints for a solution as in where to look for or what to think in solving this,
Express the geodesic equat... |
Spontaneous thermal fluctuations occur at microscopic level in liquids. It is said that hydrodynamic description is valid in the long wavelength and low frequency limit. So, to depict the thermal fluctuations occurring at microscopic level an extension of hydrodynamics is done by retaining the basic structure of hydr... |
My textbook defines melting point of a solid as the point when the solid vapour pressure is equal to the liquid vapour pressure.
However when I search for solid vapour pressure, I get information on sublimation. This doesn't satisfy me because I know that not all solids sublime easily, but they can melt easily.
So my q... |
When we are studying harmonic oscillations, we come across with this equation:
$\ddot{x} + c^2x = 0 \tag{1}$
We know immediately that the period of the x oscillations is equal to $T = \frac{2\pi}{c}$
The question is:
I know how to prove the period is that equality AFTER solve the equation, but there is a way to disco... |
I am a high school student and I am little confused in manometers, My teacher told me that we cannot equate pressure even at same horizontal level if different liquids are there, but he doesn't give the reason, can anyone explain why we cannot equate the pressure in different liquids , if the pressure is different her... |
I am studying the Euclidean Schwarzschild metric and trying to find its isometries. It still has $\partial_{\phi}$ as a Killing vector, but I wonder if the range of $\phi$ is still $0$ to $2\pi$. The following metric,
$ds^2=dr^2+(r+2M)^2d\phi^2$
where $0<r<\infty$ and $0<\phi<2\pi$, is a constant time slice of a 3D Euc... |
We are given that there is drop of density $d_1$ and radius $r_1$ with a surface tension $T$.Next we are told that the drop is made into an ellipsoidal shape.
How do we find the time period of S.H.M of the drop?
My attempt:-
I found excess pressure acting on the drop in the deformed shape and computed the integral
$\v... |
I was reading
this question since I am still a bit rusty on the idea of Heisenberg picture.
I do believe that I follow the math given in the accepted answer, but then I have run into a problem extrapolating the idea to the following problem.
So let's consider a real scalar field theory with Lagrangian density:
$\mathca... |
Consider a thermal state for some Hamiltonian $H$ over a $D$-dimensional Hilbert space, defined by
$$
\rho_{\beta} := \frac{ e^{- \beta H} }{\mathrm{Tr}[ e^{- \beta H} ]} \ .
$$
I've seen statements that thermal states are maximally mixed. However, when I compute the purity of the above state, I find
$$
\mathrm{Tr}[\rh... |
My textbook says that viscous force is directly proportional to the velocity gradient (du/dz). But I am finding this a bit against my logic. What I understand is that viscous force tries to resist the laminar flow of a fluid. My textbook also explains that we can imagine the fluid flow as flow of different laminas of f... |
I know the temperature of the universe is decreasing due to it's expansion after the big bang but after I came up with this article in AOP(please note I don't have the access of the journal,so I have just read the abstract) after reading this I am quite confused.
A news media states that:
The study by the Ohio State... |
Electric Potential
Question 1. Is $V=W/Q$ or $V=P.E./Q$.
P.E. is electric potential energy
Potential difference
Question 2. Is $\Delta$$V=W/Q$ or $\Delta$$V=$$\Delta$$P.E./Q$.
Question 3. Is there any relationship between work and potential energy in this case?
EDIT:
Why change in Electric Potential Energy is equal to ... |
In the derivation of Bernoulli's equation
$$W_{nc} = (P_1 - P_2)V $$
$$W_{nc} = \Delta KE + \Delta PE $$
$$(P_1 - P_2)V = 1/2mv_2^2 - 1/2mv_1^2 + mgh_2 - mgh_1 $$
$$P_1V + 1/2mv_1^2 + mgh_1 = P_2V + 1/2mv_2^2 + mgh_2$$
$$P_1 + 1/2\rho v_1^2 + \rho gh_1 = P_2 + 1/2\rho v_2^2 + \rho gh_2$$
I have read that this is just c... |
I have read some physics papers in theoretical particle physics and all of them were based on computation, they had some mile long equations and the result was always the proof of some formula.
I am interested in studying physics but those endless computations are not my cup of tea, therefore I was wondering if there i... |
If a apply a force(Pull it) F ext on the wall which can move.
The wall will move which is very obvious and the spring gets elongated.
Due to Newton thirds law of motion , force applied by wall on spring = force applied by spring on wall.(Forces written on the right side)
Then we see that the end of spring also applies... |
I'm trying to compute the continuity equation for the stress-energy tensor $\nabla^\mu T_{\mu\nu}$ in the FLRW metric $$ds^2=-dt^2+a^2(t)ds^2_3$$ where $ds^2_3=g^3_{ij}dx^idx^j$ is the metric for the 3 dimensional space without time dependence. The Christoffel symbols are
$$
\Gamma^i_{jk}=\Gamma^{i3}_{jk}, \space\space... |
The task is:
A thin rod extends along the z axis from z = −d to z = d. The rod
carries a charge uniformly distributed along its length with linear
charge density λ. By integrating over this charge distribution,
calculate the potential at a point P1 on the z axis with coordinates
(0, 0, 2d).
By summing up the potentia... |
Hi I am trying to learn the concepts of angular momentum but I don't understand why in the formula for torque the radius from the line of action of the force is regarded as a vector surely distance is only a scalar so why is the cross product used?
|
The following potential is given:
$ V\left(x\right)=\begin{cases}
V_{0} & x<-a\\
0 & -a<x<0\\
\infty & 0<x
\end{cases} $
I have to find the general solution for Schrodinger equation for this potential with energy $ E>V_{0} $, and then I have to use the boundary conditions in order to find the probability of particles b... |
I don't understand why it is necessary to state the superposition principle. Reading Griffiths' Introduction to electrodynamics, the superposition principle is described as experimental fact that is not implied by Coulomb's law. Well, it is clear to me that non-linear phenomena can exist, but as far as know, Couloumb's... |
Now I am trying understand:
What are fuzzballs?
What is the difference between fuzzballs and black holes?
According to this presentation, one can construct fuzzball solution from ordinary BH solution in few steps:
Start with standart metric, for example Schwarzschild metric:
$$
ds^2 = - \left(1-\frac{r_0}{r}\right) d... |
Persistent currents can be induced in superconductors that have no decay in current over the period of observation withing the measurement errors. (see for example this book chapter)
I always thought that this is not a true "perpetuum mobile of the third kind", as one has to put in energy to conserve the superconductiv... |
A problem states that
Measurement of the electric field (E) and the magnetic field (B) in a plane-polarized electromagnetic wave in vacuum led to the following:
$$
\begin{array}{ll}
\frac{\partial E}{\partial x}=\frac{\partial E}{\partial y}=0 & \frac{\partial E}{\partial z}=-\frac{\partial B}{\partial t} \\
\frac{\pa... |
So I am having some difficulty understanding gyroscopic precession. I understand that mathematically by convention torque is perpendicular to the force and so is angular momentum but surely that force is a true force acting outwards as this is what occurs in gyroscopic precession. My question is is this torque a conve... |
Here is the question :-
Two methods came to my mind while trying to solve it, which are:
I assumed the velocity of M as v(upwards). Then, as the strings are inextensible the cosine component of v should be equal to u, if that doesn't happen then the strings will stretch or slack, which we don't want to happen.
Hence... |
I've never really understood how having treads on a tire. allows more grip in wet conditions; surfaces with water on them. What I know is that the water gets into those spaces and is forces out of the sides openings of the treads. I understand that but how does that create more grip. At the point the the tire hits the ... |
As a scenario let's take a box filled with air in empty space and no gravitational field around. As the box is opened,the air inside will rush outside and the box will move in opposite direction because of Newton's third law of motion but what is exactly pushing the box or where does the force coming from?
|
An infinite long hollow semicylinder of radius R has a uniform surface charge density P(s)
a.What is the electric field intensity (EFI) along the axis of that semicylinder ?
b.Use the result from (a) to find EFI along the axis due to semicylinder of uniform volume charge P(v) ?
I don't understand this problem
Please ... |
Given the blackhole temperature formula, $$T =\frac{\hbar c^3}{8\pi k_BGM},$$ can I use $M=E/c^2$ (where $M$ is the mass of the Blackhole) to invert the above equation to express it as $$E=E(T)$$ and use the formula $C_V=\left(\frac{\partial E}{\partial T}\right)_{V,P}$ to calculate the specific heat of the Blackhole?... |
In Ta-Pei Cheng's Relativity, Gravitation and Cosmology book, pg. 88, it was stated that the infinitesimal invariant interval $ds^2=g_{\mu\nu}dx^\mu dx^\nu$ for a spherically symmetric metric $g_{\mu\nu}$ is:
$$ds^2=Ad\vec{r}\cdot d\vec{r}+B(\vec{r}\cdot d\vec{r})^2+Cdt(\vec{r}\cdot d\vec{r})+Ddt^2$$
where $A$, $B$, $C... |
As a scenario say, If we suddenly push the ground and release the pressure we will jump off but where does the force coming from?
|
I am trying to reconcile two different ways of producing the Schrödinger equation in momentum space starting from the Schrödinger equation in abstract notation. The time dependent Schrödinger equation of course reads: $$i\hbar\frac{\mathrm{d} }{\mathrm{d} t}{|\psi(t)\rangle}=\hat H{|\psi(t)\rangle}=(\frac{\hat P^2}{2m}... |
I will consider $\textbf{spacetime}$ as $(M,\eta)$ where $M$ is a four dimensional $\textbf{manifold}$ and $\eta$ the metric which in this coordinates
$$
\begin{align*}
x \colon M &\longrightarrow \mathbb{R}^4\\
p &\mapsto x(p)=(x_0,x_1,x_2,x_3).
\end{align*}
$$
is given by
$$\eta=dx^0\otimes dx^0-dx^1\otimes dx^2... |
I read in my book that any system tends to become disorderd or tends to become more probable and this decides the spontaneity of a process.
But I would like to know that if entropy exists then why does a closed system exists ? I am asking this question because system tends to become free but we also know that close sys... |
Suppose free particle described by Gauss wave-packet. With increasing time the uncertainty in position is increasing and particle is moving in x-direction.
Does the increase in position uncertainty mean decrease in momentum uncertainty?
I would suppose that it does not decrease since uncertainty principle is satisfied ... |
I read in my textbook that the potential energy is a system property. In case of gravitational potential energy, the potential energy is a shared property of both the body and the earth. The value of potential energy increases if the earth stays fixed and body moves upward, away from earth; it also increases if the bod... |
To jump we exert force on ground and because of third law of motion the ground also pushes us but from where does the force coming or what is exactly pushing us back with such a force?
|
$$\delta^{[a_{1}}_{a_{1}}\cdot\cdot\cdot\delta_{a_{j}}^{a_{j}}\delta_{b_{j+1}}^{a_{j+1}}\cdot\cdot\cdot\delta_{b_{n}}^{a_{n}]} = \frac{(n-j)!j!}{n!}\delta_{b_{j+1}}^{[a_{j+1}}\cdot\cdot\cdot\delta_{b_{n}}^{a_{n}]}. $$
I'm trying to prove this equation and got started to see how it goes for base case of $n=2$.
It would ... |
If we increase the temperature of a volume of air it will rise up but if we look from molecular level, there kinetic energy has just changed but not thier weight so why they rise up
and do not go in any other direction?
|
Zettili's Quantum Mechanics, section 2.4.5 (p95):
$\hat A$ is an operator and $\langle\hat A\rangle$ is its expectation value with respect to a normalized state vector. Then the operator $\Delta \hat A$ is defined: $$\Delta\hat A = \hat A - \langle\hat A\rangle. \tag{1}$$
What confuses me is that $\hat A$ is a matrix a... |
I have a wire that is a steel alloy. I want to know what the alloy components are, because I like that this wire does not work harden and fatigue quickly.
|
Why is the linear magnification $m_{obj}$ defined as
$\frac{-d_i^{obj}}{d_o^{obj}}$?
|
We have the Lorentz transformation $\Lambda$ that acts on the vectors and tensors and the meaning of the $\Lambda$ is that it modifies the entries of a vector or tensors ( $V^{\mu}$ or $T^{\mu \nu ...}$ ). These transformations are special in special relativity (SR) because they leave the $ds^2$ invariant (are they the... |
I'm taking physics lessons in university and my professor described the Earth's orbit as en ellipse, where one of the focal points is the Sun (1st Kepler's law).
However, this doesn't make much sense to me, since other planets in the Solar system must affect the Earth's rotation due to gravity.
What I used to believe i... |
I am only wondering about how Newton weighed the mass of the earth if he didn't have the value of gravitational constant $G$, so how he did it? I read about some explanations but i hadn't understand it well, can someone help me? It's for a job.
|
This question originates from the definition of linear and non-linear dynamic susceptibility in Uwe Tauber’s book “Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior”.
In page 50, he talked about the dynamic susceptibilities.
For a system under perturbation, the Hamiltonian
$... |
I am designing (in my mind) an accordian / scissor crane, but have little knowledge of calculating torque, fkg/cm etc.
I've enclosed a sketch. I need to pull the apex of the triangles together to extend, or "repel" apart to shrink the mechanics. My current thinking is two gears on each beam, one fixed, one loose. The l... |
In 3+1 Minkowski spacetime, we can use the fact that the Lie algebra of the Lorentz group decomposes (I am omitting some details here to keep it short) into $su(2) \oplus su(2)$ and then use the fact that spinors are the fundamental representations of $su(2)$ to start building representations of the Lorentz group$^\dag... |
I'm trying to solve for work after 2 seconds given $v(t)=3t^2$ and mass$=1kg$. There are 2 approaches:
Just calculate kinetic energy after 2 seconds: $E_k=.5*mv^2 = .5 *1 * (3*2^2)^2 = .5* 144 = 72J$
And calculate the amount of work applied: $W=Fx$. Which is where I'm having troubles - can't get the same number.
Here... |
What was Niels Bohr's reasoning behind his second postulate (about integer angular momentum)? How did he come up with it without any knowledge of matter waves?
I only have a high school level education so go easy on me.
|
Why is the frequency of photons emitted from a laser different than the frequency of the incident photon?
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.