instruction stringlengths 31 24.3k |
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The interaction energy for Potts model (on an dicrete interval with periodic boundary condition, i.e. a $\mathbb{Z}_N$- model) is of the form
$$E(\{\sigma\})=-\sum\limits_{\langle n,m\rangle} \delta_{\sigma_n,\sigma_m},$$
with $\sigma_n=\pm 1$. In one place I found an information that the transfer matrix for such a mod... |
I am trying to find the amount of electrons in a conduction band in Si (Silicon), all I've got is a graph similar to this one:
I've tried to integrate like this:
$$ N = \int_{1}^{\infty} \frac{1}{1+\exp(E-E_f)} \cdot D(E)\text d E$$
However, I have a hard time finding what $D(E)$ is supposed to be. If i put is as:
$D(... |
Here I have added a section from Griffith's Book. It says that H need not be zero when the free current is not zero. I can't wrap my head around this. With the example of an electromagnet, I can imagine H to be the Magnetic intensity due to the current in the wire, but what about in the case of a bar magnet. What is t... |
I noticed that there are a lot of similarities between momentum and energy, and it's almost like momentum is the time-like version and energy is the space-like version of the same thing.
For example, energy and momentum are both the integral of force, just energy is with respect to space and momentum is with respect to... |
I would like to ask a question about hyperloop's inner air pressure, how would air pressure inside the semi-vacuum tube affect the acceleration of the cabin? Is there any functions or equations to calculate such relationships?
Thank you
|
On the Wightman axioms Wikipedia page, the W2 axiom describes the effect of Poincare transformations on the quantum field. It states:
$$U(a,L)^\dagger A(x) U(a,L)=S(L)A(L^{-1}(x-a))$$
where A is the quantum field, $a$ is a spacetime translation, $L$ is an element of the Lorentz group, $U$ is a unitary representation of... |
When two trains cross inside a tunnel, the velocity of the air around the train increases so the pressure decreases (Bernoulli's Principle). Using that logic, the windows are pushed outwards because the pressure outside is inferior then the pressure inside the train (which continues to be $P_{\rm atm}$, right?).
The p... |
Consider two wires of length $L$ and resistivity $\rho$, and consider a fixed voltage source with voltage $V$. The first wire has cross sectional area $A_1$ and the second wire has cross sectional area $A_2$ such that $A_1 > A_2$.
If we connect the first wire across $V$, Ohm's law gives:
$$V = I_1\rho\dfrac{L}{A_1}... |
If I had two coherent point sources of visible light, above a piece of paper maybe, would you expect to see an interference pattern?
Then, if one had a slight shift in phase, would you then expect to see a different pattern, but still an interference pattern?
Then, say you had a strip of point sources with constant spa... |
As far as i know, in a nuclear reaction we "go" from a binding energy $B_1$ to a binding energy $B_2$ with $B_2$>$B_1$ because a bigger binding energy means more stability for the nucleus.
If we consider the nuclear fission $n+^{235}U=^{141}Ba+^{92}Kr+3n$ the binding energies $B_1$ and $B_2$ are the sum of all the bind... |
What is the tangential force and radial forces in a particle of mass m at the end of a string of length R (where G is acting downwards)?
And how to find the radial and tangential force(i.e radial force=-(T+W sin theta) and -(W cos theta) where theta is the angle between the string and the horizontal;T being the force o... |
In this paper and another, the Dirac equation for an uncharged fermion is written as $$i\gamma^{\mu}D_{\mu}\psi + \frac{m}{\hbar}\psi=0 $$
where $D_{\mu} = \partial_{\mu} + \Omega_{\mu}$, $\quad \Omega_{\mu} = \frac{1}{2}i\Gamma^{\alpha \ \ \beta}_{\ \mu}\Sigma_{\alpha\beta} $, $\quad \Sigma_{\alpha\beta} = \frac{1}{4}... |
The questions I ask are based on the peculiarities of quantum physics that I except but don't necessarily understand.
Thought experiment: If you are able to place a single static electron in a vacuum (ignoring the possible effects of virtual particles) with the understanding that there are virtual photons surrounding i... |
Why is mass a very concentrated form of energy? Does it have to do something with photons, phonons or nucleus?
|
Suppose, an observer is on a train which has only platform to stand but no walls. The train is moving with a constant velocity with reference to railroad. While moving, the observer feels strong wind against his face (if he faces towards front). If he puts a light ball on the platform, it automatically goes backwards d... |
I am working on a "tensor gymnastics" exercise, and have arrived at the following line to simplify:
$\delta_{ik} y^{i} X_{ij}$
where $\delta_{ik}$ is the Kroenecker delta. Does this simplify to:
$y^{k} X_{kj}$, i.e., replace all of the $i's$ with $k's$, or just apply to one of the $y^i$ or $X_{ij}$?
|
What is the Spin-flip of electrons in non-neutral hydrogen atoms in water and fat molecules?
I know there is known spin-flip RF of electrons in neutral hydrogen atoms (hydrogen line).
Thanks,
Cheers
|
I'm doing a risk assessment of space debris in low Earth Orbit (about $1000-2000$ kms). While working on a simplified model, I couldn't correctly predict the outcome of a random collision, so far we've only dealt with $1$-Dimensional collisions in our curriculum.
Let us suppose object $1$ collides with object $2$, they... |
Assume a multilayer with high and low refractive index layers. Now imagine that the high refractive index layers are successively made thinner and thinner. At what point would a single layer no longer be seen as one interface, that would reflect light, and instead be considered as part of the entire structure? I.e., th... |
Say I have a charge density $\rho(\vec{x})$ in some finite volume $V$, such that all of the multipole expansions apart from the monopole moment (meaning dipole, quadrupole and so forth) are zero. Does this mean that $\rho(\vec{x})$ is spherically symmetric? I know the opposite is true - meaning, if $\rho(\vec{x})$ is s... |
( Question will be: why modulus of obtained four-velocity is not $c^2$ ? )
In Schwarzschild metric, the trajectory of an object falling directly ($h=0$) into a planet from infinite, with no initial speed ($E=mc^2$) is, according to this wikipedia page:
$ \tau = \text{constant}\pm\frac{2}{3}\frac{r_{\rm s}}c\left(\frac... |
My questions are:
1) Does a gluon always have no charge?
2) Is the W-boson always positive or negatively charged?
I thought these two statements were correct, but I came across an exercise that makes me doubt it.
In the exercise I have to make a feynman diagram for the reaction :
u + $\bar{u}$ $\rightarrow$ d + $\bar{... |
Mimicking the process for finding the Christoffel symbol in terms of the metric (and its derivatives), see box 17.4 on page 205 of Moore's GR workbook, we can use the torsion-free (gauge local translations curvature set to zero) condition and some non-trivial index gymnastics to solve for the spin connection in terms o... |
I'm searching about the experiments, which Faraday has done in order to discover the electromagnetic induction phenomenon. I didn't find what I need on google scholar nor google books. Can you recommend me a certain textbook?
|
Consider the following scenario:
I am alone in space with a ball. I threw the ball at a certain speed such that i am propelled backwards (like a rocket is) as to conserve momentum. Now, since my momentum changed, so does my kinetic energy. By Work-Kinetic Energy Theorem, if there is a change in kinetic energy, there sh... |
This question sits at the crossroad between economics and physics.
Given that
The Earth receives a finite amount of light from the sun every day
It can dissipate a finite amount of heat and reflect a finite amount of light
The amount of matter exchanged with space is comparatively irrelevant
The set of all dissipativ... |
Consider a cell. It has more efficiency than a human being even though a human being is a bulk of cells: The cell has fewer losses when it converts the food it ate for nutrition to do some sort of work.
Does this mean that the entropy of organisms increases as they get more complicated? WOuld a higher life form produc... |
Let $(M,g)$ be a $d$-dimensional Lorentzian manifold and let $\Sigma \subset M$ be a null hypersurface, which therefore has dimension $(d-1)$. We know that its normal vector $k^\mu$ is null and since it is null, this normal vector is also tangent to the hypersurface. Its integral lines are null geodesics which are the ... |
Consider the following state for some bosons represented in Fock space:
$$|2\rangle_{k_1}|1\rangle_{k_2}$$
where $k_i$ is some distinguishing index. You may think of these as the two different wavevectors for photons.
Now, if we use the Hilbert space representation of each individual boson, the same normalized state is... |
I do understand this from a energy point of view. However, let's consider a system with two small mass point in a classical case. The total mass of the system should be $M=m_{1}+m_{2}-\frac{E}{c^{2}}$ where $E$ is the gravitational potential energy between $m_{1}$ and $m_{2}$. I know this effect is very small and can b... |
I started with evaluating the following derivative with respect to a general element of an $n\times n$ matrix,
$$\frac{\partial}{\partial X_{ab}}\left(\mathrm{Tr}{(XX)}\right)$$
I wrote out the trace in index notation in order to get a sense of how I might take the derivative term-by-term:
$$\mathrm{Tr}{(XX)} = X_{ij}X... |
What does the plot of the entire universe's Entropy versus Time starting from the big bang look like?
Is it even possible to create such a figure?
|
I'm studying the formalism of gravity with torsion, the Einstein-Cartan (EC) theory, and i've encountered this book by H. Kleinert "Gauge fields in condensed matter", in which he derives the basic framework of EC theory [in part 4].
When defining the basic differential geometric quantities, he does it all in term of a... |
I have a Hamiltonian $H$ on a periodic lattice, which is expressed as, say:
$$H = \sum_{n} (A_n a^\dagger_n a_n + B_n a^\dagger_{n+1} a_n + h.c.)$$
where $A_n$ and $B_n$ are periodic in space (over the lattice) with a period of $\beta$. Now, in order to get the momentum space representation of the Hamiltonian, I expres... |
The Openstax Astronomy book talks about stars converting mass into energy via fusion reactions:
So far, we seem to have a very attractive prescription for producing the energy emitted by the Sun: “roll” some nuclei together and join them via nuclear fusion. This will cause them to lose some of their mass, which then t... |
This is the problem itself. It is from David Morin's Introductory Mechanics.
This is the solution to the problem (or part of it)
|
McNamara and Vafa have recently conjectured in their paper Cobordism Classes and the Swampland that any vacua in string theory can be reached from any other one (possibly by a process that require an infinite amount of action) i.e. the cobordism class of string theory is trivial.
The motivations for the new swampland c... |
I've learnt that the Young's modulus of elasticity is defined as the ratio of stress and strain when the material obeys Hooke's law. So it has no significance beyond the proportional limit in the stress-strain graph.
Image source: Stress–strain curve - Wikipedia
However, my book1 says that out of two materials, the on... |
I am confused by the Feynman lectures Vol1Ch28-29. In all the pictures, there is an electric dipole oscillating vertically. We're assuming the intensity is $E^2$ and that in the far r limit $E$ depends only on the perpendicular component of the acceleration. So the logic in the first picture is that since the E field o... |
The horizontal component of the reaction force responsible for forward movement of person while walking is regarded as frictional force. But when a person pushes the ground backward, the supposed relative motion is person moving forward. Then the frictional force should act backward opposing that relative motion. But t... |
I am a bit confused regarding the nature of surface tension. Now, it can be defined as energy (E) per unit area (A). This basically means that surface tension (T) relates a scalar (energy E) with a vector (area A) as
$$E = TA$$
So, surface tension cannot be a scalar I guess.
Another definition of surface tension is fo... |
I am thinking of the now easy-to-obtain speakers where a spherical speaker is suspended above a platform. If this was in a vacuum and the sphere was spinning, why would it ever slow down? What is the source of the friction?
|
I am thinking about a way to design a process which makes a extremal Reissner-Nordström black hole out of a non extremal one, i.e. it would violate the third law of black hole thermodynamics.
Consider the case $\vert Q \vert < M$. To achieve extremality of the black hole I either need add charges or get rid of some of... |
Here is the Full Question:
A monoatomic gas is expanded adiabatically from volume $V_0$ to $2V_0$ and then is brought back to the initial state through an isothermal and isochoric process respectively. Plot the P-V diagram of the complete cycle and find the efficiency of the cycle .
My general understanding of a heat e... |
I am looking at a special class of space-time where the Christoffel symbols obey $$\Gamma^a_{bc} = g_{bc}g^{ad}\partial_d\ln \sqrt{g}$$ I wish to know if such class of space-times have been seen or studied before?
|
This is all the information given in this question. I have no idea how to build these Loerntz invariants. How would I go about answering this?
|
Suppose I have a wave-function over a Hilbert-space of (complex) dimension $N$. It has $2 N-2$ real degrees of freedom, after normalization and removing the phase. It seems to me that I can measure these degrees of freedom with $2N-2$ measurements, first by projecting on each of the basis states, and then by making a m... |
A common example how to write a rank-2 tensor in the spherical basis is an outer product of two vectors,
$$ T_{ij} = a_i b_j $$
such that
$$ T_{ij} = \frac{\textbf{a}\cdot\textbf{b}}{3}\delta_{ij} + \frac{1}{2}\epsilon_{ijk}(\textbf{a}\times\textbf{b})_k + \left( \frac{a_ib_j+a_jb_i}{2}-\frac{\textbf{a}\cdot\textbf{b... |
I am learning the Faddeev–Popov path integral formlism with Schwartz's QFT textbook. In the section 25.4.2 "BRST invariance", I came across the Lagrangian as:
$$\mathcal{L}=-\frac{1}{4} F_{\mu \nu}^{2}+\left(D_{\mu} \phi_{i}^{\star}\right)\left(D_{\mu} \phi_{i}\right)-m^{2} \phi_{i}^{\star} \phi_{i}-\frac{1}{2 \xi}\lef... |
As I understood the highest possible value for a magnetic moment of a point charge having the same amount of charge as an electron and rotating with same electron velocity and confined in the same area around a pivot point is a half of the electron magnetic moment. Does it imply that the electron could posses that kind... |
Pulsars rotate very fast.
Its axis of rotation may be or may not be aligned with the axis of the radiation beam.
But, you see with respect to the Dzhanibekov effect, the pulsar should be rotating with its maximum moment of inertia.the Dzhanibekov effect states that The spinning body ends up in the spin state that mini... |
We learnt magnetic field is electric field but viewed from a different frame of reference. Then why do we need to worry about B. We could very well take a frame where it is E?
|
This almost seem counter-intuitive to me as if a object is such as a Galaxy is moving away from me at a constant velocity and the space between us is accelerating so should the velocity.
Any help is much appreciated
|
Consider this situation:
A ball is moving forward and undergoing rotation. Assume that it is not slipping. Eventually, the velocity and rate of rotation of the ball decrease, and it comes to a halt.
But if you observe the direction of friction (when the ball is rotating clockwise), you will see that the friction shoul... |
Consider a sphere of radius $R$ on a rough surface. Let it be rotating with angular velocity $\vec{\omega}$ and let it be moving with velocity $\vec{v}$. Then what happens after a very long time? What is the magnitude and direction of both its velocity vector and angular velocity vector after a long time?
EDIT: Let co... |
I know $E = mc^2$ says that inertial mass of a system is equal to the total energy content of a system in its rest frame. My friend told me the $c^2$ can be omitted from this equation because that's just an `artifact' when measuring inertia and energy in different units.
Is he right?
|
I hope this picture helps out on understanding the system. Here is the exercise:
Hold a spoon next to a water stream from the faucet. Observe the spoon getting attracted to the stream of water. Explain why does this happen?
According to the Bernoulli principle the pressure will decrease on the bottom of the spoon beca... |
Assume a almost perfect black body at temperature zero and consider pointing a signal, let's say a laser beam (pure state), on this body. What happens with the information of the beam?
My thoughts go like this: The described body will absorb and scatter the beam and will heat up. Now the scatter part is still pure but ... |
I have been looking at a formula which is supposed to calculate the lean angle and turn radius which is
$$\theta=\arctan\left(\frac{v^2}{gr}\right)$$
I do not understand how velocity effects turning radius at a fixed lean angle. I would think that turn radius is proportional to lean angle regardless of velocity (within... |
I am trying to convert $\frac{dB\mu A}{m}$ to $\frac{dB\mu V}{m}$
So, I know that;
$\frac{dB\mu V}{m}$ = $\frac{dB\mu A}{m} + 51.5$
However, I cannot find a source explains where 51.5 comes from. Is it related with air impedence? Thank you for explanations in advance.
|
If we have two measurements of the same quantity, say, $m_1=a\pm c$ and $m_2=b\pm d$, how many sigma away are these values? In other words, when we say that two measurements are in e.g. $3$ sigma tension, which measurement sigma ($c$,$d$, or combination thereof) do we refer to?
|
I am studying Special Theory of Relativity from the book "Special Relativity And Classical Field Theory" by Leonard Susskind. I am not being able to understand the following:
The three space components of a 4-vector may equal zero
in your reference frame. You, in your frame, would say that
this displacement is p... |
I would like to know if there is a procedure to completely fix a gauge, which I believe we must do in order to make sense of the path integral?
In chapter 74 Sredniki introduces the Lagrangian
$$
\mathcal{L} = \mathcal{L}_{YM} + \delta_B \mathcal{O}\ .\tag{74.17}
$$
The operator $\mathcal{O}$ has to be Grassmann-odd, t... |
All QFTs that I come across have vector fields appearing as gauge-bosons. Is there any problem with vector fields that are not gauge-bosons? I am not so concerned about the theory producing results that match observations at the LHC, I just want to write down a Lagrangian which does not belong to a guage theory, yet ha... |
Suppose we have a lagrangian quantum field theory, thus a theory where we can write an action in the form
\begin{equation}
S = \displaystyle \int d^4 x \; \mathcal L \, \left( \partial_{\mu} \phi , \phi \right) \ .
\end{equation}
In classical field theory, we define a symmetry as an action on the fields and/or on space... |
In any nuclei, if it is even-even or odd-even we can determine ground state spin and parity just by single particle shell model. But if in a odd-odd nuclei, we consider residual interaction to determine ground state.How can one define this residual interaction physically?
|
I found, that magnetic moment is measured by $\rm J/T$, and equals magnetization times volume:
$$\vec{m}=\vec{M}V$$
Magnetization, also equals magnetic susceptibility times external magnetic field:
$$\vec{M}=\chi\vec{H}$$
$\chi$ doesn’t have units, $\vec{H}$ has $\rm T$. How does equation below, gives $\rm J/T$ units?... |
I'm going over some problems with a solution manual in order to brush up for a coming exam and one of the problems I came across was this:
What is the charge density related to the field $E=A\frac{e^{-br}}{r}\hat{r}$?
Now obviously here I would use $\nabla\cdot E=\rho/\epsilon_0$, however taking the divergence of th... |
Below is the result of a single-slit experiment of light.
Alternate bright and dark fringes can be observed, where they represent the maxima and minima caused by constructive and destructive interferences respectively.
Below shows the diffraction of water waves.
The degree of diffraction increases as the gap size dec... |
Let's consider laminar flow of normal liquid from a tap with round opening of radius $r_0$. The liquid leaves the opening with vertical velocity $v_0$ (for simplicity, let's assume this velocity is the same across entire liquid flow at the level of the opening). Will it be correct (at least within first approximation) ... |
Consider a reversible polytropic process :$$PV^x=K$$ where $K$ is a constant. We can easily derive , By differentiating this and using the gas laws, that for such a process: $$PdV=\frac {(nRdT)}{(1-x)}$$.
Consider the First law for a reversible process: $$dq=du+P_{gas}dV$$ (since $P_{ext}=P_{gas}).$ Substituting
$$Pd... |
knowing that energy is given by $E_{n}=\frac{n^{2}\pi^{2}\hbar^{2}}{2ma^{2}}$
and that $$|\psi(t=0)\rangle=\frac{1}{\sqrt{6}}|\phi_{1}\rangle+\frac{1+i}{\sqrt{12}}|\phi_{2}\rangle+\frac{1-i}{\sqrt{4}}|\phi_{3}\rangle+\frac{i}{\sqrt{6}}|\phi_{4}\rangle$$
I want to calculate the probability of finding the value $E_{1}$ w... |
Original Post : here
On the accepted answer , it was said that the Normal Force is more on the right side of the centre of mass which provides an anti-torque to the rotation of the body which slows down the rolling.
I also found some similar explanations on "Why a rolling Body Slows Down" in the book "Concepts of Physi... |
I've done an experiment to study a capacitor's discharge time and calculate an unknown capacitor's capacitance.
With the help of an oscilloscope, I measured the time it took for the capacitor's voltage to reach half the maximum voltage. I repeated this procedure for different resistors and I got this graph:
I've spent... |
Does a term for non-QM physics exist - in the sense of classical physics including relativity?
|
Given a small solid body like a small asteroid or satellite and some initial slow spin, for example 1 rotation every hour.
If placed in a perfect vacuum with no external forces will this spin forever?
The classical solution (where we approximate the object with a rigid body) will conserve angular momentum.
Is this true... |
Could someone help show that in special relativity, conservation of momentum is independent of inertial frame by applying Lorentz transform.Or better, can you derive the formula for relativistic momentum under the requirement of conservation of momentum for inertial
Here’s what I’m hoping you can help me with. Your na... |
Ok, my colleague and I are having a debate that we need help with. Neither one of us works in this space (chemist and materials scientist) and we understand this should be pretty straight forward intro physics or fluid dynamics, but we are struggling to convince each other that one of us is right.
Here is the scenario... |
When we think about electric charge, one particle namely Photons is responsible of two important feature in particle physics:
The property we call electric charge of an electron is statement about how the electron field interacts with the electromagnetic field (statement from David Tong in: https://www.youtube.com/wat... |
For context, I am reading this paper.
Basically, the paper makes reference to "evolving with respect to the time-reversed Hamiltonian". I'm slightly unclear as to what this actually means. Here is my logic:
Let $H$ be some Hamiltonian with eigenstates $|E_n\rangle$. Let $H'$ be the time-reversed Hamiltonian, with eige... |
Why does adding a photon to the system, gives a vertical transition in the reduced zone scheme?
Considering me, it's due to the fact that a photon does not change de $k$-vector, is that correct? And why is that?
|
Consider two charged balls in space with radii $R_A$ and $R_B$, and total charge $Q_A$ and $Q_B=\rho_B\space V_B$. They are separated by a distance $D = \|\overrightarrow{AB}\|\geq R_A + R_B$.
I was wondering if it was possible to determine the force exerted by one ball on the other, e.g. $\overrightarrow{F}_{A\to B}$.... |
We know the Gravitational Waves (GW) provide a new way to observe the Universe. Now, we face a new era for cosmological and astrophysical researches. I know that it is possible to obtain the gravitational redshift from some astrophysical phenomena like merge of black holes and other sources. Furthermore, I understand t... |
We have that $\gamma_5 = -\frac{i}{4!} \epsilon^{\mu \nu \rho \sigma} \gamma_\mu \gamma_\nu \gamma_\rho \gamma_\sigma$. Using this, what approach would be suggested in showing that $\gamma_5 \gamma^\sigma = \frac{1}{3!} \epsilon^{\mu \nu \rho \sigma} \gamma_\mu \gamma_\nu \gamma_\rho$? You would think that the solution... |
The Setup
Suppose I know, in some particular coordinate system, three components of the four-velocity vector $u^{\alpha}$ with $\alpha = \{0, 1, 2, 3\}$. For this question I'm going to assume the known components are the spatial components $u^{i}$ with $i = \{1,2,3\}$.
I then use the constraint
$$-\epsilon = g_{\mu \nu... |
Gravitation page 325 section 13.5, From (1) the Riemann curvature tensor $$R^\alpha{}_{\beta\gamma\delta},$$
one could construct (2) the double dual of Riemann
$$G^{\alpha\beta}{}_{\gamma\delta}\equiv \frac{1}{2} \epsilon^{\alpha\beta\mu\nu} R_{\mu\nu}{}^{\rho\sigma} \frac{1}{2} \epsilon_{\rho\sigma\gamma\delta},$$
(3... |
I am working in the context of quantum chemistry. Given this expectation value in second quantization
$$
\langle 0 \vert [p^\dagger q, \kappa] \vert 0 \rangle
$$
with
$$
\kappa = \sum_{ai} k_{ai}(a^\dagger i - i^\dagger a)
$$
Indices $i,j,\ldots$ indicate occupied orbitals, $a,b,\ldots$ virtual orbitals, and $p,q,\ldot... |
When a pointed cathode and a plane anode are subjected high voltage dc and there is air between them, and spark is formed and the spark is allowed to sustain for few micro seconds, how the electrons and ions of gas will move in the plasma formed(the path of electrons and ions in plasma)?
|
When calculating the rate of spontaneous emission in the Weisskopf-Wigner theory the time derivative of the excited state is related to a sum of couplings to all modes (directions and polarizations) of the electromagnetic field. See for example.
The sum is converted to a 3D integral which can be expressed in polar coor... |
I do know the satellite's tangential velocity is always perpendicular to gravity, therefore its speed must remain unchanged, however, I have some confusion.
If I separate both the tangential velocity of the satellite and the gravitational force of the earth, things becomes different.
For example, lets say point O is th... |
Two spin-1/2 particles either are part of a spin-1 triplet or a spin-0 singlet. The singlet is antisymmetric but bosons need to be symmetric wave functions.
So does the spatial part of the wave function need to be antisymmetric in the singlet and symmetric in the triplet? What if we're only considering the spin state,... |
Problem
I want to calculate the time it takes for a particle living in a spherical spiral to fall under de force of gravity down to the bottom. So far I've sketched the procedure but when I tried to solve the equations, they've seemed too complicated to solve analytically so I'm stucked. Let me introduce my attempt:
F... |
According to law of conservation of angular momentum, the merry-go-around is expected to rotate at constant angular velocity, while the man walks along it's rim with constant speed relatively to the merry-go-around.
But I was thinking about it, and I noticed that each step the human takes produces a force which pushes... |
I've been going through Kardar's book and, in the chapter on probability, I found this expression (numbered as $2.13$ in the book):
$$
\sum_{m=0}^\infty \frac{(-ik)^m}{m!} \langle x^m \rangle = \exp \left[ \sum_{n=1}^\infty \frac{(-ik)^n}{n!} \langle x^n \rangle_c \right] = \prod_n \sum_{p_n} \left[ \frac{(-ik)^{np_n}... |
I am currently doing some research for my university thesis and I am dealing with plates.
Right now I am trying to figure out the potential (strain) energy of a plate under bending.
So basically I found a paper which explains exactly this but the following part is confusing me:
My question is:
Usually the bending stra... |
Surface tension makes liquid surfaces smooth, but how smooth? How rough?
This question has an Experimental version and a Theoretical version:
E : Optics manufacturers quote specs like $1/4$ or $1/8$ wavelength ($100-400$ nm), which seems to be RMS surface deviation. How does a calm liquid surface compare? How would on... |
I'm working on the following problem, I am not quite sure how to proceed.
Consider a fermion isotriplet $\psi ^a$ for $a=1,2,3$. And
$$S_{\psi} = \int d^4x \ (i\bar{\psi}^a \gamma^{\mu} (D_{\mu} \psi)^a - f\epsilon^{abc}\bar{\psi}^a\psi^b \phi^c) $$
$$ (D_{\mu} \psi)^a$ = \partial_{\mu}\psi^a + g \epsilon^{abc}A^a_{\mu... |
Can Electric field line form a right angle ? something that look like the letter L..
please be as rigorous as possible.
Thanks in advance.
|
I was going through this article about Doppler formulas and what it says is, that we only really have 1 Doppler formula, not 2. I only want if someone can confirm if I am understanding what it implies correctly.
Here goes:
The classical non-relativistic formula for sound where $f_e$ is emitter frequency, $f_a$ is abso... |
I have a question regarding how to express forces and moments with respect to a different point.
Assume I have a measuring point $A$ where I obtain forces $F_x$ $F_y$ $F_z$ and Moments $M_x$ $M_y$ $M_z$ acting on that point $A$.
Assume we have a point $B$ which is connected to point $A$ via a rigid body with known dime... |
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