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Let us consider Lagrangian
$$ \mathcal{L} = \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2} m^2 \phi^2 $$
with $\phi$ being a scalar field, and Minkowski signature $(+,-,-,-)$. My question is concerning the calculation of the energy density, which is given by
$$ \mathcal{E} = \frac{\partial \mathcal{L}}{... |
Alright so I'm trying to figure out how to find the operator $XP$ in the $x$ basis, knowing that the elements of $X$ and $P$ are $x \delta(x-x')$ and $-ih \delta'(x-x')$ respectively. I know how to do it by assuming $X=x$ and $P=-ihd/dx$, but I don't want to do it that way, I want to actually calculate the elements of ... |
Is it correct to say that the field exiting the conductor is less than the field entering the conductor as the internal field of the conductor due to the induced charges is opposite in direction?
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I am reading heat and thermodynamics by Zemansky and while defining heat capacities at constant pressure and volume, it is said that heat capacity at constant pressure is a function of $P$ and $T$. Why not V? and likewise for heat capacity at constant volume is a function of $V$ and $T$, why not $P$?
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Studying the experiment of a magnet falling down through a copper tube, the problem gives me the graph of the surface current density, as a function of $x$, $x$ varying on the longitudinal axis of the tube (the center of the graph corresponds to the center of the magnet).
The function is:
$$
y= \frac{3x}{x^2+4}
$$
It ... |
In p-type semiconductors, when the acceptor gains an electron, it creates a hole in the valence band of the semiconductor. From what I understand, the holes create the current in this case. Does it mean that the current flows in the valence band as opposed to the conduction band?
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In this Wikipedia article there are interesting statements:
A quantum field theory is said to be trivial when the renormalized coupling, computed through its beta function, goes to zero when the ultraviolet cutoff is removed. Consequently, the propagator becomes that of a free particle and the field is no longer inter... |
Or instead of bodies, let's say have two massive point particles. Does their being local to each other mean that they're infinitesimally close in space and infinitesimally in time? OR does it mean that the spacetime separation between them is infinitesimally small?
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Looking at the Particle Data Group tables of the $\Lambda$ baryon, I find that the rate of the hadronic decay $\Lambda \to p \pi^-$ is 64% while the semileptonic decay $\Lambda \to p e^-\nu_e$ has the rate of $8 \times 10^{-4}$.
I cannot explain what is the reason for such large suppression of the semileptonic decay of... |
In R. Shankar book "Principles of quantum mechanics" $2$nd edition on page $170$ he states that for a step potential the following is energy eigenfunction, where $k = \sqrt{2mE/\hbar^2}$.
$$ \Psi_k (x) = A \left( \left( e^{ikx} + B(k) e^{-ikx} \right)\theta(-x) + C(k) e^{i\sqrt{k^2 - q^2}x} \theta(x) \right) $$
Here, $... |
Suppose that $M$ is a manifold with a metric $g$, and three independent (independent in the sense of Killing vector fields) Killing vector fields $K_1,K_2,K_3$ are given with commutation relations $$ [K_i,K_j]=\sum_k\epsilon_{ijk}K_k. $$ Here $\epsilon_{ijk}$ is the standard (algebraic) Levi-Civita symbol. This setup ... |
Apologies in advance if this is a naive question. I'm learning the fundamentals of gravity and from what I've understood, it's not particularly meaningful to talk about it as a force, since it induces the same "acceleration" (classically speaking) in everything.
This means that whatever device or accelerometer we use, ... |
This is a very rudimentary question, but I thought I would have to ask here because I don't discern any site better.
Given the formula that $t$ equals the square root of $2h/g$, calculate the theoretical and experimental time needed for an object to reach the ground. For the experimental time, add a random amount of e... |
I know that, in vacuum, the electrostic energy is:
$$
U_E = \frac12 \int \rho(\mathbf r)\varphi(\mathbf r) d^3\mathbf{r}
$$
But I don't know how to pass to the matter version? The formula would be the same, but what is $\rho(\mathbf r)$ now?, Is it free charge or total charge (free plus bound charge) density?
P.D.: I ... |
Background
So I was trying to make as much sense out of kinematics through intuition after having taken my first semester of university physics, and I've stumbled onto a dillema that I can't seem to work around.
Specifically, I'm stuck on the issue of average velocity. From what I understand, in kinematics, there are t... |
I want to measure the absorbance spectrum of some solutions, in the 400-700 nm range. I've always used regular "optical glass" cuvettes for this. But I've been wondering, is this really necessary?
If the glass looks transparent to the eye, then its absorbance in the 400-700 nm range is negligible. And if the surface lo... |
In this reference $[1]$ the author created a Inflating Morris-Throne Wormhole (IMTW) given by:
$$ds^2=-e^{\Phi(r)}dt^2+e^{2\xi t}\Biggr\{\frac{1}{1-\frac{b(r)}{r}}dr^2+r^2d\theta^2+r^2sin^2\theta d\phi^2\Biggr\} \tag{1}$$
Which is slightly different from canonical Morris-Thorne Wormhole (MTW):
$$ds^2=-e^{\Phi(r)}dt^2+\... |
We know that earth is neutral in charge. It has zero potential and this is the reason why electrons move towards earth while lightning or earthing.
If we manage to transfer a considerable amount of charge inside the earth enough to cause polarity what would happen? Will the earth explode?
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Dark energy seems like the explanation for the expansion of the universe. Are there any physics models where it is included? Is it possible to control it in those models? I was thinking because the expansion of the universe seems anisotropic it might be possible to control the expansion.
(might need to revisit question... |
I have read in a text that if potential is nowhere infinite and $\psi$ and $\psi '$ is $0$ at given point then $\psi$ will be zero everywhere. How do we prove the statement?
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The question comes from writing an oversimplified version of a physics in a 2D world as a computer simulation. I know that I can make something that looks not too horrible, but it'd be great to use this as a learning opportunity.
Let's say we have a 2D object (a polygon) that is falling with a specific acceleration. He... |
If two weak EM beams consist of waves with an irregular distribution of light quanta does it mean that if that photons are not uniformly distributed in a wave regarding the time when they arrive and hit the meeting point that in that case they can't cancel out? If this is very hard to understand then I will ask this wa... |
My understanding of Inflation Theory:
Before $10^{-35}$ seconds the universe began to cool and the Inflaton Field approached a false vacuum. When it reached this false vacuum, there was a constant energy density in the universe which cause the universe to expand (for some reason? I don't really understand why a consta... |
I have been searching for a table of nuclear mass for a long time, but what I got are mostly data of atomic mass. The mass of electrons and the atomic binding energy might bring error to the calculation involving nuclear mass.
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Solving the particle in a box problem considering boundaries 0 and L leads to the energy equation
$$\frac{n^2\pi^2\hbar^2}{2mL^2}$$
but doing the same with center at the origin (from -L/2 to L/2) I get
$$\frac{2n^2\pi^2\hbar^2}{mL^2}$$
shouldn't I get the same answer?
I used the solution
$$A\sin (\frac{\sqrt{2mE}}{\hb... |
Suppose that there is a hovercraft floating a few centimetres above the Earth's surface. As it is disconnected from the Earth, which is spinning from West to East, shouldn't it appear to move East to West to observers on the ground? Does this happen? If not, why not?
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Why is the time component of the stress energy tensor $T^{00}$ associated as energy density?
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My question is really very simple, how can one see that a spin 1/2 particle in a definite projection in z(say, up) is in a superposition of Sx states?
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Two simultaneous events are happening in a stationary inertial frame of reference ($S$), but they are happening at different positions. First event is happening at $x=x_1$; $t=t_1$, second event is happening at $x=x_2$; $t=t_2$.
$$t_1=t_2$$
$$x_1\ne x_2$$
The question is what is the time difference of these two events ... |
I was reviewing past exams and I found a question where I could give no satisfactory answer. The core of the question is the following:
If there are boundary conditions, does this necessarily imply, that the solutions to the time-independent Schrödinger equation are quantized, i.e. there are only countably many solutio... |
I'm new to special reltivity theory and length contraction. I can't figure out the logic or algorithm of calculating lengths in length contraction problems. Let me explain where I am stuck.
There is a simple and first given example. There are two inertial frames of reference, one is $S$ and another one is $S^{'}$. $S^{... |
This problem has been bugging me for a long time now.
It states that given an insulated cylinder which contains a spring and an ideal gas, you must calculate the work required to compress the gas, work required to compress the spring, work done by the atmospheric pressure $p\ $ ($p=1\ bar$) the work done by the block ... |
Aluminium (-containing) foils are used for insulation, eg. in emergency situations where injured people are covered in them, to prevent heat loss. On the other hand, aluminium is used for heatsinks, since it conducts heat well. So, how come it works both ways? How come, that in the first use case, the AL foil does not ... |
Could any of you help me understand what I'm doing wrong, when solving this line integral? I believe I'm getting the wrong sign and the issue is probably the limits.
Consider an equilateral triangle with sides $a$, and a current $I_1$ running through it. The triangle is placed above a infinite wire with the current $I... |
I am trying to simulate Ising model, and have learnt that we get more accurate results when we take correlation time $\tau$ into account. I.e, decrease the correlations between observing samples only at intervals after time $2\tau$. and $\tau$ can be found using this equation. $\chi(t) = e^{-t/\tau}$. That is taking lo... |
I was trying to solve two questions from problem book on relativity and gravitation by lightman.Questions are
Calculate the nonzero components in an inertial frame S of the stress-energy tensor for the give system: A ring of N similar particles of mass m rotating counter- clockwise in the x-y plane about some point fi... |
I am confused in a term while reading spin orbit interaction from Sakurai. He said whenever a moving charge is subjected to an electric field, it feels effective magnetic field given by $$B_{eff}=-\frac{V}{C}\times E$$ eq 5.3.14 in the book. How one can obtain this expression?
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Looking for explanations of what electromagnetic waves (light, etc.) are, I found apparently contradicting explanations. According to the first, which seems wrong to me, EM waves are explained using the following two facts:
A changing electric field causes a magnetic field, and
a changing magnetic field causes an elec... |
I'm studying FEM. My book says that "the work of internal forces is equal the the work done by external forces" and it states it in an equation Wi=We.
But then it somehow starts discussing potential energy of external and internal forces, and somehow it turns out their sum is not 0. I'm having trouble understanding thi... |
I have a sheet of paper, clad with a half-circle shape of conductive material. The half circle is not filled to the center. The inner radius is about 8cm, and the outer radius about 12cm, not that the measurements are very important here, but you get the idea. The area between the radii is filled out with the conductiv... |
Consider electron-positron interaction :
$$e^-e^+\rightarrow\mu^+\mu^-$$
when peskin book come to compute Non relativistic limit of this process said that, because we are in Non relativistic limit we have conservation of total spin(In picture below,And page 147 of the book). My question is that, what is special thing a... |
When we solve Schrodinger equation with potential goes to 0 at large distance, if $E>0 $, the wave function dies away to zero (as this shows).
My idea to prove this fact is using curvature, since normalizable it must vanish as the curvatual show.But there is a possibility that curve of wave function can look like a bow... |
I'm looking for a way to circulate water through a DIY pool heater without a pump. The problem is, the pool heater itself is elevated above the pool, and I don't know of a way to get the water to flow up through the tube without a pump. The only thing I can think of is capillary action, but don't think that that would ... |
I need guidance if i can do this or is there any error in doing this? Consider the equation,
$dP=\frac{\beta}{k}dT-\frac{1}{kV}dV$
$\beta$=Volume expansivity
$k$=isothermal compressibility
In heat and thermodyanmics by zemansky, the case of constant volume is taken, and integrated between two temperature $T_i$ and $T_f... |
The standard Friedmann equation is defined as
$$H(z)=H_{0}\sqrt{\Omega_{m}(1+z)^3+\Omega_{r}(1+z)^4+\Omega_{\Lambda}}$$
So, this equation is only defined in $z>0$?
If this is the case what how do I know what will happen in the "future"?
As far as I understand that $z=0$ is the actual state of the universe and $z>0$ is ... |
I am a little puzzled by einselection models. I followed those two papers (Environment-induced superselection rules Decoherence, einselection, and the quantum origins of the classical) to understand it and I end up in some contradiction with two different explanations.
Global summary of decoherence theory with a spin m... |
How can I formally show (or at least argue) that, given the crystal Hamiltonian expansion around a Weyl node in a three-dimensional Brillouin Zone located at $\vec{k}_{0}$,
$\hat{H}=f_{0}(\vec{k}_{0})\mathbb{I}+\vec{v}_{0}\cdot\vec{q}\mathbb{I}+\sum_{a=x,y,z}\vec{v}_{a}\cdot\vec{q}\sigma^{a}$
with $\vec{k}=\vec{k}_{0}+... |
This is high-school physics, and the answer is "south". I cannot comprehend however why it would point to the south.
My understanding of the question is that it is asking for the direction of the magnetic field, for finding which my textbook has supplied me with the right-hand rule for a simple straight cable (as well ... |
I've become really interested lately in the Wolfram Language and using it to work through problems in physics. I'm in a first year course in classical mechanics right now, and I was wondering if anyone had any insight into how these types of problems (easy kinematics and dynamics) could be modelled in Mathematica.
I've... |
I guess this is a pretty basic question, but I am not certain about its answer (since I am still studying in high school).
Let's say we are given the equation of the following sound wave and we are also asked to find the velocity of a particle whose x=1 m and t=8 s. The equation is given in SI units:
$$
y( x,t) =3\ sin... |
In the Srednicki's textbook, Chapter 35, the author states (Equation 35.28):
$$
U(\Lambda)^{-1}[\psi^\dagger \bar\sigma^\mu \chi ] U(\Lambda) = \Lambda^\mu_{\,\,\nu} [\psi^\dagger \bar\sigma^\nu \chi ]. \tag{35.28}
$$
When I tried to derive this myself I got $\Lambda^{-1}$ instead of $\Lambda$ on the right hand side.
M... |
Will connecting, 6x1.5v(non recharge) cells (in series) to a 9v battery(non recharge) through parallel combination, increase circuits capacity while keeping the voltage same?
If yes, then will this be true if the 9v battery was rechargeable?
|
Suppose an electron beam hits a positively charged plate, what is the force on the plate?
I was thinking that the force on the plate is equal to the sum of the electric field produced by the plate at a distance d where an electron is found, times the charge of each electron
Assuming that there are n electrons in the be... |
Many books including the book (Hamamatsu, "Photomultiplier Tubes", link to PDF) says that a photocathode of a photomultiplier tube is damaged by intense light.
Do not expose to strong light. The photocathode of photomultiplier
tubes may be damaged if exposed to direct sunlight or intense
illumination. Never allow stro... |
I'm trying to study renormalization in QFT in curved spacetime. So let's say we have a fixed de Sitter background and we have an interacting theory (e.g. massive $\lambda \phi^4$) and I'm going to calculate the one-loop correction to the $\phi$ propagator in the in-in framework.
If I regularize the amputated amplitude ... |
Let me start with an analogy, namely a mass on a spring. If I am not mistaken,
first quantization consists of replacing the dynamical variables by their operators and then solving the Schrödinger equation so as to obtain the stationary, energy eigenfunctions of the Hamiltonian, namely the various modes $\psi_k$ the wa... |
Theorem: Suppose $A_{\mu}$ is a $4$-vector and $B^{\mu}$ is an object with $4$ components. If $A_{\mu}B^{\mu}$ is a scalar then $B^{\mu}$ is a $4$-vector.
I have been stuck on trying to prove this theorem for quite a while (See Ref.1) and haven't made much progress. I think this is due to my lack of understanding on wh... |
I'm trying to understand the Galilean Transformations, as shown in my book. Here's the situation, first and foremost: Two observers, R (uses Roman Coordinates for its Reference Frame) & G (uses Greek Coordinates for its Reference Frame) are traveling towards each other at a constant velocity $v<<1$. They synchronise th... |
I thought that since a conductor as a whole, an electrically neutral medium, $\vec{\nabla}\cdot\vec{E}=0$ inside a conductor. But while reading Ashcroft and Mermin's Solid state physics, I found out that at equation $1.31$ they assumed $\vec{\nabla}\cdot\vec{E}=0$ but at $1.43$, they assumed $\vec{\nabla}\cdot\vec{E}\n... |
I am trying to understand string theory. In elementary quantum mechanics, one objective is to calculate $<X_{f},T|X_{i},0>$, the propagation kernel. I imagine two ways to accomplish this: 1) by directly calculating the matrix elements of $e^{-iH/\hbar}$ between the initial and final positions ,and 2) Representing this ... |
Question: Is it possible to express the effect of a simple 50% beamsplitter on photon number states using matrices, such that the output can be computed by matrix calculations rather than manual substitution of equations?
To explain the problem, consider a 50% beamsplitter and define: $a_{1,2}^{+}$ = creation operators... |
The potential of the inner shell is 10V and that of the outer shell is 5V. The potential at the centre is given in the book to be 10V. I know that inside the shell potential should be constant but how can we neglect the potential due to outer shell? In the same book I read how to calculate potential at the surfaces of ... |
If I solve the Klein Gordon equation in the Poincare patch with the boundary condition that the field vanishes at infinity I get a continuous set of solutions.These are normalizable solutions and I can quantize scalar field theory on Poincare patch. I then have a continuously infinite basis.
On the other hand if I solv... |
Is it mathematically correct to say the following:
1 inch = 2.54 cm
1000m = 1 km
100°C = 212°F
Here is my justification for what is true and false:
is in a somewhat grey area for me, it seems to be true but I think it is just because our initial statement is our definition so no real contradictions are to be made, ... |
This graph shows the binding energy per nucleon which is the energy required for extract a nucleon from a nucleus. From the fermi gas model of nucleus I know that both protons and neutrons are in a potential well and, due to Pauli principle, protons and neutrons have different energy. The question is, how can the bindi... |
This is a problem from Heat and thermodynamics by zemansky. A thin-walled metal container of volume $V$ contains a gas at high pressure.Connected to the container is a capillary tube and a stopcock.When the stopcock is opened slightly,the gas leaks slowly into a cylinder equipped with a non-leaking,friction less piston... |
How do I obtain the absolute value of a Feynman diagram's amplitude if I do not have values for the components of this amplitude?
If the amplitude of a process such as $e^+(p_1) + e^- (p_2) \to \phi (p_3) + \phi^* (p_4) $ is given as:
$$\require{cancel} \mathcal{A}=ie^2 \frac{\bar{\nu}(p_1)(-\cancel{p_3} + \cancel{p_... |
I came across this article in my book where they had related the velocities of earth at the aphelion and at the perihelion . Their approach was
$1)$ conservation of angular momentum at the desired points
$2)$ conservation of energy at the desired points.
This method is completely fine but I tried to think about it on m... |
In decoherence theory, the basic situation is the following (I illustrate with two level system for simplicity). I want to measure a system $S$ by the mean of an apparatus $A$. Around it there is the environment $E$.
I assume the system is initially in $|\psi_S \rangle = a |0 \rangle + b |1\rangle$, the apparatus and e... |
Hello
My question comes from my interest in antennas i suppose:
I understand that antennas utilize alternating current to generate EMF Waves along a particular frequency depending on how quickly the AC current is alternating and changing between the two ends.
My question is more so to do with voltage, so that if the vo... |
In a material about radiometric dating, it is said that:
As fast as this background $\bf{_{}^{210}Pb}$ is lost by radioactive decay, new $\bf{_{}^{210}Pb}$ is created by the decay of $\bf{_{}^{226}Ra}$.
This sentence seems to say that the $\bf{_{}^{210}Pb}$ loss rate is the same as the creation rate, so the backgroun... |
By the Born rule in Quantum Mechanics, a state's complex wave function $\Psi(x,t) \in L^2$ gives probabilities when we take its complex norm $\overline\Psi(x,t)\cdot\Psi(x,t) = |\Psi(x,t)|^2$. In this case, since I'm using the cartesian spatial wave function, the probability of finding the particle that is in the state... |
Historically slits have been invaluable in teaching, research, and theory validation in both electromagnetic and quantum mechanics but conceptually they differ from what we can actually build based on the physical properties of matter because the canonical slit perfectly absorbs an incident wave in an infinitely thin l... |
The laws of physics are reversible and quantum information is never destroyed.
Given this, how do I time reverse the $U_{235}$ fission reaction, n which
${}^1_0n + {}^{235}_{92}U \rightarrow {}^{141}_{56}Ba + {}^{92}_{36}Kr + 3 {}^1_0n + \gamma +$ 202.5 MeV (in kinetic energy plus gamma ray energy).
That is, would reve... |
For delta well $V(x) = -a \delta(x)$ we have the solution for TISE as $$\psi_1(x) = A e^{ikx} + B e^{-ikx}$$ for $x<0$ and $$\psi_2(x) = F e^{ikx} + G e^{-ikx}$$ for $x>0$
where $k>0$
after adding the time dependent term,it's the travelling wave solution.
When we consider the wave scattering from left,we will set $G =0... |
$$
\oint_C \vec{E} \cdot d \vec{l} = -\frac{d}{dt} \oint_S \vec{B} \cdot d \vec{A}
$$
where $S$ is a surface and $C$ is its boundary.
Why is there no negative sign in front of the left-hand side? I thought that
$$\xi(\text{or EMF}) = \Delta V = -\int_{initial}^{final} \vec{E} \cdot d \vec{l} $$
instead of $ \int_{initi... |
I'm a physical chemist so bear with me. We are going over quantum statistical mechanics, and to motivate and derive the density matrix, my advisor used the following explanation:
We have a system of interest in contact with it's surroundings. The system + surroundings are isolated, and are described by the state $|\Psi... |
I am an MD, I am studying the fluid flow of the tears through the tears duct system of the eye. The newer view suggests that the first part of the system is a funnel or a cone. I cant seem to understand (without equations), what are the main advantages of fluid flow through a funnel?
|
In QFT is it possible to quantum entangle the polarization of a photon with the spin of an electron? How could this be done? Would it be possible, for example, to use the flipping of the electron spin in the hyperfine structure process?
|
I recently read in Polchinski's textbook on string theory (Volume One, page 229) that an orientifold of the 26-dimensional bosonic string can be considered. Investigating further, I found that after computing the cylinder and Mobius strip partition functions for such orientifold a divergence due to massless states can ... |
I understand that the equation for kinematic displacement is:
$x = v_{0x}t+\frac{1}{2}a_xt^2$
Perhaps my understanding is naive, but it seems like this leaves out higher order rates of change. Why wouldn't the equation be like:
$x = v_{0x}t+\frac{1}{2}a_xt^2+\frac{1}{6}j_xt^3+\frac{1}{24}s_xt^4+\frac{1}{120}c_xt^5+. . ... |
According to this wikipage,
The cross product only exists in three and seven dimensions as one can always define a multiplication on a space of one higher dimension as above, and this space can be shown to be a normed division algebra.
There was an answer on math.stackexchange.com by riemannium and another related po... |
Imagine I have a 1D wavefunction $\Psi(x)$. If I sample this wavefunction at $n$ points, I will have a $n*1$ vector $\left|\Psi\right>$. Now, if I take an outer product of this vector with itself, i.e $\left|\Psi\right>$$\left<\Psi\right|$, I will get a $n*n$ matrix. Is this matrix guaranteed to be a density matrix cor... |
Yesterday, I observed an unexpected rainbow in the sky. There was no forecast for rain, neither was it raining anywhere nearby. I have been trying to find an explanation but don't seem to find any. Can someone please explain what this rainbow is?
Note:the colours were way more vivid as compare to the picture I have tak... |
I am following this paper on simulating a room impulse response (RIR). The wave of a single frequency $\omega$ point sound source in location $X$ as it is viewed by a microphone located at $X'$ is:
$$P(\omega,X,X')=\frac{e^{i\omega(\frac{R}{C}-t)}}{4\pi R}$$
Where $i=\sqrt{-1}$, $R=|X-X'|$ and $C$ is the speed of sound... |
In wikipedia of ESD and PSD, there is a pair of equations, one is
$$\hat x(f) = \int_{-\infty}^\infty e^{-2\pi ift}x(t){\rm d}t$$
We know $\omega= 2\pi f$. How can we obtain then the other
$$\hat x(\omega) = \frac{1}{\sqrt{T}}\int_0^T e^{-i\omega t}x(t){\rm d}t$$
where does the $\sqrt{T}$ come from?
|
I believe the answer to this is quite simple, perhaps so simple that I cannot find it in any book.
Usually, if there is a gauge symmetry in the theory, we add an interaction term in the covariant derivative, like:
\begin{equation}D_\mu = \partial_\mu +i \frac{g}{2} V^i _\mu t_i\end{equation}
where, in this general case... |
Using the Carter-Lichnerowicz equation of motion $\Omega_{\mu \nu}u^{\nu}=T\nabla_{\mu}s$, we obtain $Tu^{\mu}\nabla_{\mu}s=0$, where s is the specific entropy, $u^{\mu}$ the velocity of the fluid and $\Omega_{\mu \nu}=2\nabla_{[\nu}w_{\mu ]}$ is the vorticity tensor of the fluid ($w^{\mu}=hu^{\mu}$ with $h$ the specif... |
First of all, let me say that this question is for a High School project, so a classical approach in 1D is enough.
I guess that the first question is, can a Lennard-Jones potential be used to (roughly) study distance between atoms in a metal?
Second, how can I calculate the force between to atoms in a metal using Lenna... |
If I have a cylinder filled with an ideal gas and a piston and if the pressure of the gas is greater than the surrounding pressure how can the gas do work if the net force on the gas is 0 i.e. the forces acting on the gas are the force due to the piston and the sides and bottom of the container which all cancel out so ... |
I have been doing a physics depth study on the topic of "how gravitational waves affect the phase shift of light (in a vacuum)" and have found it difficult to find a source, at least one I am able to understand, on what factors affect the strength of gravitational waves. I am sure that strength is inversely proportiona... |
Context:
For instance, the quantity Torque, $\vec{\tau}$ is defined about a point: by the formula $$\vec{\tau}=\vec{r}\times\vec{F}$$
We can use this defintion to define torque about an axis. Let the axis be along the vector $\vec{n}$. If the torque of a force about a point on the axis,=$\vec{\tau_1}$=$\vec{r}\times\ve... |
Say a particle is in state
$\Psi(x, t)$.
Then what is the meaning of
−i$\hbar \partial_x (\Psi(x, t) )$ . I know we have operated the wave function by the momentum operator but what is the significance of the whole result?
|
Find the force required to separate two plates with water between them water wets the plates and area of contact of water with each plate is A.
Distance between the two plates is 't'.(Surface tension of water: 'S')
I have tried the problem by pressure difference approach but I am getting the answer as
$$
\frac{4 s A}{t... |
As we know, the Coulomb potential is in the form
\begin{equation}
V(\mathbf{r}) = Q/\mathbf{r}
\end{equation}
Mathematically, as $\mathbf{r} \rightarrow 0$, $V(\mathbf{r}) \rightarrow \infty$. But is this [as $\mathbf{r} \rightarrow 0$, $V(\mathbf{r}) \rightarrow \infty$] physically true? I can’t imagine at an extremel... |
In Philippe Di Francesco's book on Conformal Field Theory in section 11.2.3 on the Infinite Strip, the one point function of a primary operator (with scaling dimension $\Delta$) is calculated by considering a conformal mapping from the upper half plane.
For an infintie strip of width L this is found to be:
$$ \langle \... |
$$\delta S=2\int dx^+dx^-\left(\frac{\partial\delta \phi}{\partial x^+}\frac{\partial \phi}{\partial x^-}+\frac{\partial \phi}{\partial x^+}\frac{\partial\delta \phi}{\partial x^-}\right)=-4\int dx^+dx^-\frac{\partial^2\phi}{\partial x^+\partial x^-}\delta\phi \tag{1}$$
This variation leads to the equation of motion.
C... |
I'm trying to solve this task. The body moves in a uniform field of gravity of the Earth. Resistance force
the medium is proportional to the square of the velocity. In the initial moment of time, the body was at a height of H, and its speed was zero. To find the dependence of speed on time, speed on height, and height ... |
For getting the density of states formula for photons, we simply multiply the density of states for atoms by 2 (due to two spins of photons).
I am getting the 2D density of states formula as :-
g(p)dp = 2πApdp/h^2
I think this is the formula for normal particles, and so for photons I need to multiply it with 2.
But var... |
The general definition of causality is that the principle of the 'effect never occuring before the cause', as in Wikipedia.
The book 'Picturing Quantum Processes' (pg: 262) defines causality as states or processes having the following property:
Discarding the state or process is equivalent to them never having occured.... |
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