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The indistinguishability postulate states that any (normalized) state vector $|\psi\rangle$ for a system of $N$ identical particles should satisfy $\langle \psi | \hat{O} | \psi \rangle = \langle \hat{P} \psi | \hat{O} |\hat{P} \psi \rangle$ for any observable for the system $\hat{O}$ and any permutation $\hat{P}$ in t... |
this question comes from an exercise of Sethna's book "Statistical Mechanics: Entropy, Order Parameters and Complexity". it is in page 282 question 12.2
In 3d Ising model, the spin correlation function is measured to be in the form
$$C(r,T) = {r^{ - 1.026}}C\left( {r{{\left( {T - {T_c}} \right)}^{0.65}}} \right)$$
wher... |
I understand where the van der Waals equation originates from, but I am having trouble understanding why it underestimates liquid densities. Could someone please explain?
And when is it not appropriate to use? Only at high pressure?
|
My textbook states the following:
Voltage is the same across each component of the parallel circuit.
However I am confused on what the exact meaning of voltage is in this case, is voltage used interchangeably for potential difference?
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I found here that the Planck constant is defined as an exact number: $6.626 070 15\times10^{−34}\ \mathrm{J/Hz}$. How could this be done? Shouldn't it be a quantity with uncertainty measured by experiments?
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Suppose $A$ is a positive definite $d\times d$ matrix and $T$ is a positive map over such matrices defined as follows
$$T(X)=AX+XA$$
I'm wondering if if it possible to get a decomposition of this operator, ie, set of $V_i's$ such that
$$T(X)=\sum_i V_i X V_i^T$$
and if so, how do I go about it?
|
Why does the velocity of sound not increase with an increase in pressure? Let me take an example. Suppose there exists a gas at some pressure. With an increase in pressure, it would turn into a liquid. Sound travels faster in a liquid, and thereby won't this contradict the fact that the velocity of sound does not depen... |
There is a line of spinning top toys in Japan called Beyblades. So, there is a 'stadium' (surface) along which the Beyblades spin around after being set to spin at high RPMs by the players, and the first Beyblade to stop spinning is said to be the winner.
Out of all the Beyblades, there was this one particular Beyblade... |
When a sound source moves, frequency perceived by the observer is changed due to the doppler shift. Does this apply to intensity too? If yes then how.
Thanks!
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Consider a uniform beam that is supported by 3 pivots that are the same distance from each other (shown below). What will the normal force exerted by each pivot be?
The situation seemed rather paradoxical to me because depending on the order you place the pivots in the normal force exerted by each pivot will be differe... |
Can it be in any unit ?
Can it be in grams,
Kilograms or
Unified atomic mass( to calculate centre of mass of a compound)
Or should I convert them to kg and then proceed?
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Consider the partition function for a scalar field $\{\phi:\mathbb{R}_{\geq 0}\to\mathbb{R}\}$, $Z=\int D\phi D\lambda\exp(-S)$ with the action $$S=\underbrace{\int_0^\infty dx \frac{1}{2}(\partial_x\phi)^2}_{S_0}+\underbrace{\int_0^\infty dx \hspace{1mm}i\lambda(\partial_x\phi-c\phi)\delta(x)}_{S_\lambda},$$
where $\l... |
Maxwell equation's in differential form: $dE = 0 \ and\ \ (\ast d \ast)E = p$ in static situation.
Where $E \in \Omega^1(U)$, $p \in \Omega^0(U)$, $\ast$ is hodge star operator, $U= \mathbb{R}^3$
what does $E$ looks like in open subset $U = \mathbb{R}^3 \backslash L$ where L is a line ($z$-axis)?
Edit: If U = $ \mat... |
I am simulating a free fall with a function that needs to calculate the time it takes for a particular object to reach the surface, I got this program working without accounting for air resistance.. the force of air resistance(drag) is: 0.24 * v^2
Im not sure what I'm doing wrong or how I can make it work, any help wou... |
Let's say I have an electron in an infinite potential well. The Hamiltonian is given by:
$$ \hat H | E_n \rangle= \frac{\hat p^2}{2m}| E_n \rangle $$
with $p$ being the momentum and $m$ being the mass. Now, suddenly turn on an electromagnetic field with gauge $(\phi, \vec A)$. Then the Pauli equation holds:
$$ \hat H' ... |
Hello, I'm an undergrad CS student that somehow got a physics class in my lecture.
So, I got homework from my lecturer about this [5] footnote. My lecturer wants me to find an interval of $F$ in this problem for which no motion occurs and $μ_km_1 \gt m_2$ (as mentioned in the [5] footnote).
But, I don't quite understa... |
In my text book they stated:
As an example, the wave function of an electron that is in position $2p$ in a hydrogen atom given by:
$$
\varPhi(r,\theta,\varphi)=\frac{1}{4\sqrt{2\pi}a_0^{3/2}}\frac{r}{a_0} e^\frac{-r}{2a_0}\cos\theta
$$
If we want to calculate the average electrostatic force of the electron (Assume tha... |
My understanding of siphons is that air pressure is able to lift (because of lower pressure at the top of the siphon) the liquid up the shorter arm and then gravity pulls it down the longer arm.
However, siphons can work in vacuum under special conditions. Wikipedia states that the liquid siphons because of cohesion an... |
How is the change of radius of a dancer spinning around their axis different from the change in the radius of orbit of a satellite revolving around a body? Why doesn't angular momentum remain the same in the latter?
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It's a very silly question, but sill: Can metals have an energy gap in their bandstructures?
I would say yes, because the band gap is just $E_g = E_{c} - E_{v}$, I thought, where $E_c$ is the minimal energy in the conduction band and $E_{v}$ the maximal energy in the valence band.
But Wikipedia doesn't have anything ab... |
The Problem
I have been given the following Lagrangian of a series of $N$ one-dimensional coupled oscillators, with distance a. I have also been given the boundary conditions: $y_0=0=y_{N+1},$ but have been given little explanation on where this came from.
$$L=\sum_{i=1}^{N}\frac{1}{2}m\dot{y_i}^2-\sum_{i=0}^N\frac{1}... |
The scattering, in two dimensions, of a particle of mass $m$ by a central potential $U(r)$. The hamiltonian of the system is $H= p^2/2m + U(r)$.
Then the radial wave function $ϕ(r)$ is obtained as a solution to
$$((d^2/dr^2)+1/r(d/dr)-(v^2/r^2)+K^2)ϕ(r)=0.$$
where $v^2(L)=L^2+2mλ$, $K^2=2mE$, if $U(r)=λ/r^2$.
My firs... |
I'm studying about the Stern–Gerlach experiment. I'm having some hard time to figure out how the Stern–Gerlach apparatuses work. I have the following question:
Transfer a beam of electrons through the next series of experimental machines (Stern - Gerlach):
Given that in all Stern apparatuses - your electrons with the... |
For the coating, it is necessary to pour 40 ml of liquid in a closed container with a volume of 80 ml and place it in an oven at a temperature of 200-300 °C .My question is whether, given the high temperature and low volume and high gas density, the pressure to temperature ratio at a constant volume is the same as the ... |
let me explain my question with an example. Say we put a charge at the centre of an metallic hollow charged sphere and measure electric field at a distance larger than the radius. It is easy to calculate.
What if I move the charge so that it is not at the centre but at half the radius. Is the charge distribution on sph... |
Probably the most well known property of metals are that they are shiny. Ultimately arising from the high density of conduction electrons capable of carrying current, this shinyness is means that metals are broadband reflectors of light from radio frequencies to visible light (until about the plasma frequency). The que... |
Water at temperature $T_s$ is added to a lake at temperature $T_0 > T_s$ until the total system reaches equilibrium. What is the change in entropy of the Universe?
This is a homework question but I believe it touches on something very general. The lake is a heat bath and the water added is our small thermodynamic sys... |
I’m referring to an instant in time where the velocities of two different particles are identical. One particle experiences a force and the other does not. I think their states of motion are different even if the velocities are identical. Am I correct?
In Figure 1 below, Particle 1 has a velocity to the right and is ex... |
Why does Einstein's theory of specific heat of solids work well at high temperatures but fail at low temperatures?
|
I was watching a video lecture which talked about how the doping level is varied across the Collector and the various reasons behind doing this.
There was also the question about why Intrinsic semiconductor isn't used for the collector region? Like, because of no doping, the free charge carriers will be less. So, the ... |
Before I say any further, this is just a thought experiment, it's a crazy idea and I'm not suggesting otherwise!
A key pro/anti nuclear argument goes like so: nuclear waste storage is hard, but on the flipside, coal-fired powerplants get to dump their waste (CO2, soot and all the chemicals) direct into the atmosphere. ... |
I am trying to write a sort of "universal" equation sheet that all instructors can use on closed-book exams (with minimal modification.) Since it is not a teaching tool I can be extremely concise. But it needs to be 100% accurate (within a certain context). Are the following definitions valid all the time? I used t... |
Let me clarify my question by explaining my thought-process to you:
We all know that in order to explain gravity, Newton introduced the concept of a gravitational force to explain the phenomenon of masses being attracted to other masses. Of course there are also other forces not related to gravity, i.e. when you tug a ... |
Reading Curtis' book Orbital Mechanics I found this relation that confused me.
$$
\underline{r}\cdot\underline{\dot{r}}=r\dot{r}
$$
What happens, say, for a circular orbit where $\underline{r}$ and $\dot{\underline{r}}$ are orthogonal? Shouldn't the scalar product be zero?
Thank you!
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In Nakahara section 4.9, "Defects in nematic liquid crystals", it is discussed that the order parameter for a nematic should be the real projective plane $\mathbb{R}P^2$, which has fundamental group $\pi_1(\mathbb{R}P^2) \cong \mathbb{Z}_2 = \{0,1\}$. The real projective plane's fundamental group is generated by two ho... |
Let's say we have a scalar theory with an $O(N)$ symmetry, for which the scalar fields $\phi_{nm}$ transform as a rank $2$ tensor. I can write down an action which spontaneously breaks the symmetry
$$S=-\int d^dx\Big(\frac{1}{2}\partial_{\mu}\phi_{nm}\partial^{\mu}\phi^{mn}+\lambda(\phi_{nm}\phi^{mn}-v^2)^2\Big)$$
At t... |
I'm running into some confusion understanding rotations as being instantaneous cross products of angular velocity vectors. I would like to highlight two approaches which seem like they contradict each other, in the hopes that somebody can explain the conceptual error being made.
Approach 1
Don't think about frames. Jus... |
Given a large mass and a smaller mass at infinity, the total amount of work done on the object due to the force of gravity is -Gpe, for a given radius (r) end point. All fine there.
But a thought experiment: What if, at the instant the smaller object reaches point r, the larger mass, due to external force, accelerates ... |
Wikipedia "Time dilation" shows the formula $\sqrt{ 1-v^2-v_e^2-v_r^2.v_e^2/(1-v_e^2) } $
where v is (perhaps) the 3D speed, $v_e$ is the Newtonian escape speed, $v_r$ is the radial speed.
However "Proper time" seems to show the formula $\sqrt{ 1-v_e^2-v_r^2/(1-v_e^2)-v_p^2 }$ where $v_p$ is the speed perpendicular to... |
For a range of LEDs I'd like to model their performance and predict the flux density across an area using manufacturers datasheets. Eventually I'd like to take various power measurements and calculate efficiency when it either isn't provided or isn't fully trusted.
Looking at a specific LED such as the Luminus SST-20-B... |
This question is related to the Michelson-Morley experiment. See below an illustration of the setup:
When looking at this image, I am wondering where and how exactly the interference occurs. Is it only at the intersection point, or are the two beams cancelling each other out when travelling back together in the same p... |
I watched a video on khan academy(https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/centripetal-acceleration-tutoria/v/visual-understanding-of-centripetal-acceleration-formula) it said (around 3:29) that the radius of a circle is equal to the magnitude of the velocity. I am not exactly sure ... |
One of the simplest QFT model is $\lambda \phi^4$ theory.
$$
S = \int dt d^dx\; \left(\frac{1}{2}(\partial_\mu \phi)^2 - \frac{1}{4!}\lambda \phi^4 \right)
$$
Equation of motion:
$$
\Box \phi = -\frac{1}{3!}\phi^3
$$
The equation is non-linear.
What is known about solutions of such e.o.m.?
What is physical interpretati... |
The problem
I'm trying to show that the Euler-Lagrange equations for the Lagrangian $\mathcal{L} = \frac{1}{2}m(\dot{q} \cdot \dot{q}) - U(q,t)$ can be written as
$$
m \ddot{q}^{l} + m \Gamma^{l}_{ij} \dot{q}^i \dot{q}^j = -g^{kl} U_{,k}
$$
A couple of things to note:
I'm using the notation $U_{,k} \equiv \frac{\partia... |
When deriving the turbulence kinetic energy equation $k$ by taking the trace of Reynolds stress transport PDE, this term appears :
$$ 2\nu \overline{\frac{\partial u'_i}{\partial x_k}\frac{\partial u'_j}{\partial x_k}}$$
Where $\nu$ is the kinematic viscosity and $u'$ is velocity fluctuations.
This term is turbulence k... |
For finding a quantity in rotational dynamics, we need a reference point around which we define it. Once, the reference point is chosen, rotational quantities are generally described as the cross product of the vector which connects the reference point to where translational quantity is applied with the translational q... |
I understand that all living beings have the same proportion of carbon 12 to carbon 14 and that this is an assumption used to carry out carbon dating but I do not understand how this is possible. As isotopes are not evenly distributed, how can it be that the proportion of carbon 14 is the same in all living beings?
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I know that when we prove the centripetal acceleration we use similar triangles that are isosceles. How exactly, can we prove that they are similar, after all those 2 similar triangles could have different angles?
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Why did Kaluza-Klein need an additional dimension and not just treat the fourth dimension as a description of both time and space?
Assume that you can exchange the time dimension to a space dimension and vice versa with $cdt=dx_4$. In other words you treat the fourth dimension as a representative for both space and tim... |
I have seen a video saying a stationary (from our frame) charge should radiate, because is accelerated, the falling charges are the ones with no acceleration.
But he says we cannot test it due some technical challenges, what are those challenges?
// Video: https://www.youtube.com/watch?v=XRr1kaXKBsU
|
We know that to measure the if the n-dimensional manifold is curved or not, we look at the Riemann Tensor. If it is 0, then it is flat otherwise it is curved positively or negatively (which each of the sign has its own geometric meaning).
Ricci tensor help us track the volume changes along when we move in the direction... |
A box made of 6 conducting plates as sides has vacuum inside. The plates are joined by an insulating layer, allowing for different plates to be set to different potentials. Initially, all sides are grounded. At a certain time $t_0$, one of the sides is connected to a DC generator set to $V_0$. What is the electric fiel... |
A small concept I'm a tiny bit confused about. Sakurai in the introduction to quantum mech introduces the Stern Gerlach experiment. According to his discussion, an $S_{x}+$ particle that goes into a SG apparatus with $B\hat{z}$ will split 50-50 into $z+$ and $z-$ directions.
However, if we consider time dynamics of the... |
I'm currently writing a paper on underdamped oscillatory systems where I'm using the logarithmic decrement equation:
$\delta = \ln\frac{x(t_n)}{x(t_n+T)}$
Where $T$ is the period of the system. I then substituted the equation for initial displacement "$x(t_0)$":
$x(t) = Ae^{-\zeta\omega_n t} \sin(\omega t + \Phi)$
(w... |
We know the well known relation in General Relativity.
$G=\kappa T$
Where G is the Einstein Tensor and T is the Energy-Momentum Tensor and K is the constant.
I wanted to ask how did Einstein got to know where to place a particular element of a energy-momentum tensor with respect to the corresponding curvature tensor?
I... |
I'm working with the 1-dimensional Euler Bernoulli beam described by the PDE:
I am wondering if reducing $EI$ as my time-advancing scheme solves the equation is an acceptable model of wear and tear (a very simple one). If you have any references it'd be great.
Thank you!
|
I’m trying to understand the derivation of the Maxwell stress tensor in Heald and Marion. Im confused how they go from 4.101 to 4.102 in the image above. I can't seem to see how 4.101 is the divergence of the tensor described in 4.102. I think my misunderstanding might stem from the fact that I'm not sure how to take ... |
(For context, I originally thought of this question in the context of electromagnetic Doppler shift, but I'm also curious if the same logic applies for acoustic Doppler shift.)
Assume you are watching an object approaching you at relativistic speeds, for example fast enough that the measured frequency of its emissions ... |
A Lie algebra is a vector space $\mathfrak{g}$ over some field $F$ together with a binary operation $$\mathfrak{g}\times\mathfrak{g}\to\mathfrak{g}$$ called the Lie bracket satisfying the following axioms: Bilinearity, Alternativity, Jacobi identity, Anticommutativity.
(Correct me if I am wrong)*
A real Lie algebra is ... |
This is probably a dumb question, but does anyone know whether both Wigner and Wigner's friend observe the same result once both have been in the room and measured?
|
Calculated event horizon using Schwarzchild radius for 10 Earth mass primordial black hole and get a diameter of 17.7336cm. Using spherical gravity calculation of
g=GM/r^2, I get gravity at 1 meter of 3.984 x 10^15m/s^2. Given speed of light is c=299,792,458m/sec, how is it that light can escape the gravity outside o... |
I want to get the equations that model free energy for a given phase in a given alloy system (see attached image). I do not just want to get values of free energy for specific compositions. Is it possible to extract the equations themselves from a Thermo-Calc database? Ideally, I'd like to be able to do this in TC_Pyth... |
You are driving a SUV with constant velocity of 22m/s. At a moment, you notice a truck 200 meters ahead of you, moving in the same direction with constant velocity 18 m/s. How far your car should travel until you catch the truck?
|
The Scwarzschild metric describes any Spherical body untill its surface, so any object may be considered as a black hole, untill we reach the surface i.e. if we can't observe the planet, there should be no difference between the planet and a black hole.
A Photon-Sphere is defined as a sphere of photons orbiting around ... |
I know some aspects such as the extra dimensions have been used in String Theory, but is it possible to make a Quantum Field Theory out of Kaluza-Klein Theory, and how does it differ from Quantum Gravity as an effective field theory & Quantum Electrodynamics?
|
I'm going through "Advanced Quantum Mechanics" by Franz Schwabl, and he calculates the electron energy levels from the Coulomb interaction in a perturbative way (section 2.2.3). In the course of this, he calculates that:
$$
\left< a^\dagger_{k + q, \sigma} (t) \: a_{k + q, \sigma} (t) \right>
= \left< \phi_0 \right| a... |
A questions goes like this:
X and Y are large,parallel conducting plates close to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Points A, B and C are as shown in the figure.
To find the field at A, the solution goes; $E_A = E_1 + E_4 = \frac{Q}{4A\epsilon_0}$X$2 = \frac{Q}{2A\... |
Strictly speaking, it is "wrong" because it does not describe spin-1/2 particle like an electrons. Why in every QM textbook is it taught, not as a historical equation, but as a current equation?
|
Background:
I think it would be helpful for laypersons like myself to understand how, in practice, a "real" force differs from a pseudo-force. Virtually all explanations (eg, on this stack, Wikipedia, Quora, great Veritasium video) of the difference between a pseudo-force and a real force that use the freefalling/acce... |
We know from the Theory of Relativity that there is an upper bound on velocity, namely the speed of light $c=2.99792458\cdot 10^8\frac{m}{s}$. Is there an analogous upper bound on acceleration? I don't think there is an upper bound, and it can be as large as possible, but is it really true that there is no upper bound?... |
What are the two metals that cause the repel force of a north side magnet, and the attract force force of a south side magnet?
|
I am doing this problem for practice, and I am not sure what I am doing wrong.
A $2.0$-ton truck provides an acceleration of $3.0 \frac{ft}{s^2}$ to
a $5.0$-ton trailer. If the truck exerts the same force on the road
while pulling a $15.0$-ton trailer, what acceleration results?
My logic is that because the $5.0$-ton... |
There's a problem that I've been working on in physics for a couple of days now, and I'm just wondering if my thinking is wrong here. Say you're given the velocity of an object (with an x- and y-component) relative to another object's velocity (with only an x-component). If I'm trying to determine the first object's y-... |
I've been studying about capacitive accelerometers, and basically how they work is by detecting the change in capacitance or as a result of change in the distance between the conductive plates, small capacitive changes can be measured. And they further imply that by measuring the voltage, we can get the motion informat... |
Given a boson field described by $\psi(\vec{x})$, conserved momentum from the Lagrangian (which isn't relevant here) is $\vec{P} = \frac{\hbar}{2i} \int d^3 x \left( \psi^\dagger \nabla \psi - \nabla \psi^\dagger \psi \right)$. Question claims the commutator of $\vec{P}$ and $\psi(\vec{x})$ is $\frac{\hbar}{i} \nabla \... |
I am 195 pounds, 71" tall, standing reach of 92”.
Currently, I can jump to touch 115" in height (finger tips).
I'd like to jump to 123" in. to grab the basketball rim. (Note: 10ft/120" is the height of the basketball rim.)
Assuming that I maintain the same jumping power, how much weight/mass do I need to lose in order ... |
$$v_g\equiv\frac{\partial\omega}{\partial k}.$$
The above equation is for Group velocity of waves, so what is the Physical Interpretation of this Equation? As we know $k$ is wave number which shows how many times the wave repeats itself and $\omega$ is the angular frequency which means the number of rotations per secon... |
I'm trying to understand how the intermediate axis theorem works. And in one of the works that I found, they used a pendulum phase diagram, but idk how to read it. Can anybody help please?
The work that I'm looking at is https://arxiv.org/abs/1606.08237 and the diagram I'm looking at is on page 8.
But it looks similar ... |
The radiation dominated era is described as a universe full of photons and ultra-relativistic particles with little slow moving matter. Ideally it has w = P/ρ = 1/3.
But didn't the actual value of w move down and up over this era?
My reasoning is as follows: When the temperature gets within an order of magnitude of a p... |
The flux and angular position of the graph has been recorded as shown in the graph.
and so is induced voltage and angular position.
and my teacher derived the relation between induced voltage and angular position as such:
My question is how he came to this relation. All he said was flux and angular position has a li... |
I am having an issue with the definition of work. I know there are several questions already posted which seem the same as this one but the issue is that all of them either haven't been answered or they have been answered in a tricky way which indirectly fools us. That's the reason I am posting this question again. I d... |
I'm following the discussion on the page 290 of Mathematical Methods of Classical Mechanics by V. I. Arnol'd (you can download it here), and I've encountered the fact that in a nondegenerate system, the resonant and nonresonant tori are dense - even if the former have Lebesgue measure zero and the latter are of full me... |
In curved spacetime, 1.) a photon is supposed to move along a null-geodesic, i.e., a trajectory $x^{\mu} = x^{\mu}(\lambda)$ satisfying $$\frac{d^{2}x^{\rho}}{d\lambda^2} + \Gamma^{\rho}{}_{\mu\nu}\frac{dx^{\mu}}{d\lambda}\frac{dx^{\nu}}{d\lambda} = 0$$ and $$g_{\mu\nu}\frac{dx^{\mu}}{d\lambda}\frac{dx^{\nu}}{d\lambda}... |
I am asking question which definitely will be considered as duplicated but I want to ask it more explicitly to prevent empty speech.
Suppose we have "closed" system which is consists of alone planet and its gas atmosphere. Planet gravitation sorts gas particles, cold are near the ground hot are on top. So $T$ distribut... |
While ago I was studying drag coefficients (or pressure coefficients, as we call them in the context of wind loads in structural engineering) and I wondered how can they be more than 1, for example a small cylinder can have a drag coefficient of 1.15 according to Wikipedia. This seemed weird to me, since pressure upon ... |
In my textbook it said the following:
Photons with wavelengths in the spectral range of $[94\mathrm{\ nm},104\mathrm{\ nm}]$, interact the hydrogen atom in the basic state. Photons having those wavelengths can stimulate the hydrogen atom to $n=3,4,5$ levels.
I'm trying to figure out why it's true. Given some waveleng... |
The following is written in my notes:
Let $\hat{O}$ be a hermitian operator associated with an observable $O$, with eigenvectors $\mid\phi_n\rangle$ and eigenvalues $\lambda_n$: $$ \hat{O}=\sum_n \lambda_n | \phi_n\rangle\langle\phi_n|$$ and let $|\phi\rangle=\sum_n a_n|\phi_n\rangle$ a state vector of a quantum system... |
An object moving in a circular path as observed from the ground frame is moving with some constant velocity along a non-smooth surface, my question is we know that Static Friction provides for the centripetal force for the body, but why doesn't the kinetic friction act since the body is moving with some velocity?
I app... |
I am a high school student and I am very confused in a concept related to rotational dynamics , we know that
1)"$Γ=Iα$" and also**
2)"$Γ=\text{rate of change of angular momentum}$"
it means that if moment of inertia does not changes about an axis these two expressions are same but when I solve all problem then I get th... |
So, we know that
$$\text{Relative Humidity(%)}=\frac{\text{Actual Water Vapor Pressure}}{\text{Saturation Vapor Pressure}}$$
Now, we can find saturation vapor pressure only from the ambient temperature [1]:
$$e_S=0.6113\text{ exp}\left(5423\left(\frac{1}{273.15-T}\right)\right)$$
The problem for me begins when I want t... |
My professor gave us a formula for absorption cross section, but he said he did not remember where he found it.
The formula is given by
$$\sigma_a =\frac {1} {|\mathbf E_i|^2} \int_V k \epsilon^{''}_r |\mathbf E|^2 dV = k \epsilon^{''}_r |\frac 3 {\epsilon_r +2}|^2 V .$$
Where does this formula come from? I want to kno... |
According to wikipedia, one can get the S pararemeters from an impedance matrix $Y$ as follows:
$S = (\mathbb{1}_N - \sqrt{z} Y \sqrt{z})(\mathbb{1}_N + \sqrt{z} Y \sqrt{z})^{-1}$ where $\mathbb{1}_N$ is an identity matrix and $\sqrt{z}$ is a diagonal matrix having the square root of the characteristic impedance $Z_{0n... |
Something always bugged me about Newton's equations (or, equivalently, Euler-Lagrange/Hamilton's):
Determinism, which is the philosophical framework of classical mechanics, requires that, by completely knowing the state of a system at a given instant, $\textbf{x}(t_0)$ and the law by which the system evolves, which, in... |
What is the difference between the Luminous intensity and intensity of illumination? Please explain with units and dimensions as well! I googled but I partially understood it!
|
We have two concepts that are energy and momentum. To me, momentum is more fundamental than energy and I think that momentum was the thing which we wanted to discover as energy.
Now momentum can describe several things that that energy does and if it is not able to describe it then it can be somehow extended to describ... |
How can I prove these two relations? Assuming $\mathbf{D}$ is defined as $$\mathbf{D}=\sum\frac{\partial\mathcal{L}}{\partial\dot{x}_i}\delta x_i-\mathcal{L}=\mathcal{H}t-\frac{1}{2}\mathbf{p}\cdot\mathbf{r}$$
we have
$$\{x_i,\mathbf{D}\}=\dot{x}t-\frac{1}{2}x_i\{\dot{x}_i\,\mathbf{D}\}=\ddot{x}_i t+\frac{1}{2}\dot{x}_... |
Is it true that things that are hard, such as diamonds, wear out more slowly? Does abrasion depend on the hardness of the material? If so, why can diamonds in alluvial deposits survive for thousands of years? Does that mean they wear out so slowly that you hardly notice it? If I had a diamond and was rubbing it with a ... |
The closing paragraph of Julian Barbour's review of Penrose's Cycles of Time contains the following (emphasis mine):
Despite his great attraction to conformal geometry, Penrose still
accords length a real physical role. But in fact we only ever
observe angles, never lengths as such.
Would someone kindly explain what ... |
I am studying a semiconductor. My System has n-type dominating character.
I am getting effective mass for top of the valence band (VBM) as 5.04 while for bottom of conduction (CBM) band it is 0.20.
My question is:
Is it okay to have higher effective mass for the VBM where my system is showing n-type character?
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According to this source, there are $5077$ visible stars in the night sky, and a full sky area of $41253$ square degrees of sky. This makes for a density of $0.12$ stars per square degree of the sky. Suppose I hold up a square picture frame that is $1$ square meter in size ($1\ {\rm m} \times 1\ {\rm m}$), $2$ meters a... |
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