instruction stringlengths 31 24.3k |
|---|
The wave function of an electron has the well known statistical interpretation.
Does the classical electromagnetic field have a similar meaning as a wave function of a photon?
If yes, what is the precise interpretation?
A reference will be very helpful.
|
In Quantum Mechanics an electron (or any fermion) wave function changes by a negative sign or -1 under a rotation of 360°. And if we
rotate the electron in physical space we would need to rotate it twice around or $2 \times 360° = 720°$ for
it to come back to its original state. Apart from the unphysical?
and bizare to... |
With the 2020 Nobel Prize in physics being awarded for the proof and discovery of supermassive black holes, I started doing some research and came across the star closest to our own galaxy's supermassive black hole, S2.
S2 seen from Earth makes one orbit in 16.0518 years. How long time would one orbit take in the refer... |
Why is magnetic flux conserved in a magnetic field?
What rule tells this?
|
It's well known that classical mechanics is a crude approximation of reality, and that it can be derived from quantum mechanics. But if this is so, why is it not a linear theory, like quantum mechanics? And why does it not require complex numbers like quantum mechanics does?
|
I have been trying to find a good reference to understand the motion of vortices in type-II superconductors. While most textbooks on superconductivity talk qualitatively about this subject, I have been looking for advanced material, that actually discuss the intricacies of arriving at equations of motion for Abrikosov'... |
Quoting from my text book - "a blackbody is a perfect radiator of radiant energy. It is in thermal equilibrium with it's surroundings and radiated as much energy per unit area as it absorbs from it's surroundings at any given time"
Is a blackbody always in thermal equilibrium with it's surrounding temperature? What is ... |
According to No-Nonsense Quantum Mechanics:
How is it that $p_1 \in \mathbb{R}$ given that momentum of, e.g. a particle in space has to require a 3-dimensional vector to be fully described? For example in classical mechanics, momentum can often be written as $\vec{p} = m\vec{v}$.
|
I tutor some high school students, mostly in math but occasionally in Physics as well; I love the science but only took it through the high school level plus a couple of first-year university courses. I've noticed that nowadays almost all texts use the concept of a lever arm when introducing the idea of torque. This wa... |
We have laminar flow and the equation of velocity is:
$$U_r=K(R^2-r^2)$$
Where $U_r$ is velocity at radius $r$ and $R$ is radius of the pipe and $K$ is constant.
I tried to draw the figure:
In this figure $(R^2-r^2)$ lies on the shaded area.
$$\alpha=\frac{\int v^3 . dA}{V^3.A} \quad \beta=\frac{\int v^2. dA}{V^2.A}$... |
Why do Xe-135 and Zr-88 have surprisingly large thermal neutron capture cross-sections?
The probability that a nucleus will absorb a neutron—the neutron capture cross-section—is important to many areas of nuclear science, including stellar nucleosynthesis, reactor performance, nuclear medicine, and defense applicatio... |
If particle of spin 0 decays in rest frame decays in 2 particles the angular distribution will be uniform. How it will change for particle with spin 1 decaying in pair of $e^{-} e^{+}$ for example?
|
Can the big bang theory be applied to individual galaxies?
If 'yes', then this raises questions about a progressive initiation of galaxy bangs in a developing unniverse.
|
We can argue that internal forces on a body add up to zero by saying that forces are created in pairs (third law) inside the system and hence the net sum must be zero. Similarly we by the third law of rotational dynamics, we should be able to argue the same for rotations.
However, it is written in the book of Kleppmer ... |
I was curious about the following point: let's say we have a left circularly polarized light wavepacket travelling from left to right. We will call its polarization vector $\epsilon_{L}$ while the polarization vector for the right polarized light will be called $\epsilon_{R}=\epsilon^{*}_{L}$. What will the polarizatio... |
I have the following Hamiltonian for bosons in a lattice model with on-site interactions
$$H = H_0 + gV,$$
$$H_0=\sum_{n=1}^3 \left[ \omega_0 a_n^\dagger a_n + \Omega \right( a_n^\dagger a_{n+1} + a_{n+1}^\dagger a_n \left)\right],$$
$$V= \sum_{n=1}^3 a_n^\dagger a_n^\dagger a_n a_n.$$
I want to do a Schrieffer-Wolff t... |
My textbook says that we can't apply the Parallelogram Rule of vector addition for two parallel vectors. Why can't we apply the rule?
|
It is said that wave theory couldn't explain this effect and yet we shamelessly associate a frequency with light ($E = h\nu$) and call photoelectric effect as a failure of wave theory. Associating a frequency and calling it particle nature seems contradictory to me. Where is this wrong?
|
My question can be asked in either Einstein GR or Maxwell electromagnetism. Suppose we have a system which is localized in space (enclosed in a sphere of finite radius). For example two point masses(charges) orbiting each other. The system starts to radiate due to the acceleration of masses(charges).
What I know:
For t... |
Let $g_{bh}$ $[kg·\frac{m}{s^2}]$ be the force caused by the gravity of a black hole.
How do we calculate the force $g_{bh}(r)$ outside event horizon $R_{Sch} = \frac{2GM}{c^2}$ onto a satellite with mass $m$ at a given distance $r$ from that black hole?
And with that formula, is it possible to also derive the speed $... |
I have a problem understanding what exactly is non-equilibrium steady state. Let's say the system starts with an equilibrium state at remote past. We should have the density operator given by: $$ \hat{\rho}_{eqm}=\frac{\prod_{i}e^{-\beta_i\hat{K}_{0,i}}}{\mathrm{Tr}(\prod_{i}e^{-\beta_{i}\hat{K}_{0,i}})} $$ where $\hat... |
my mechanics sir was telling us the other day that when the relative velocity is zero between the surface and the object then the object starts sliding, eg in rolling motion without slipping, the v rel is zero at the bottom most point .how does kinetic friction come into play here. I understand that since the object ha... |
I'm trying to understand the connection between The Equivalence principle and the Rindler space. According to Einstein the inhabitants of the elevator should feel the acceleration. However, for an observer in outer space (far the homogeneous field) should observe the elevator (and its inhabitants) as free-falling objec... |
The question reads, "A positive point charge of mass m is projected with a velocity inside the tunnel as shown. The tunnel has been made inside a uniformly charged non conducting sphere. Find the minimum velocity with which the point charge should be projected such that it can it reach the opposite end of the tunnel."
... |
The picture I see in documentaries is a flat piece of cloth depressed downward by the large mass, say a star, and objects falling into the depression. But this is one side of the star.So if I were to look on the other side of the star, there would be another depression going on the opposite side. So, these two depressi... |
I'm working on creating a pool of physics questions for my students, and I came up with one whose solution made me stop and think. I'm not asking for checking/proofing of my work, I think it's correct. I just want some help/confirmation of my analysis of the results.
The problem has a mass hanging in the corner between... |
Quoting from my text book - "several attempts were made to predict intensity as a function of temperature/wavelength". This line was preceded by the explanation for blackbody radiations and about how the intensity of radiation of a particular wavelength would be maximum at a particular temperature.
This was followed by... |
I'm currently doing a bit of quantum mechanics, and I can't figure out how to pick out eigenvectors. Let me explain through an example.
An operator $A= \begin{bmatrix}
1 &0 &0 \\
0&0 &-i \\
0 &i &0
\end{bmatrix}$ acts on a state $|\psi(t) \rangle$. For the time being, the exact value of the state is not our con... |
Bremermann's limit, as maximum possible computation power or CPU total computing frequency, is known to be on the order $10^{50}~\text{Hz}/\text{kg}$.
Why max computation frequency for unit mass can exceed Plank frequency, which is on the order of $10^{43} ~\text{Hz}$ and how it is related to it?
|
Now see, photons travel through space and they don’t travel through time. And for any particle the limit to travelling through space is $c$. And at that limit it cannot travel through time.
Now my question is, what if we did it’s reverse. I mean the particle is moving more through time and less through space. So does a... |
If I want to know the expectation value of an operator O in the quantum trajectory formalism, I average over $N$ trajectories, where I call one such trajectory $\Psi_n$:
\begin{equation}
\langle O \rangle = \frac{1}{N}\sum_{n=1}^N \langle \Psi_n | O |\Psi_n \rangle,
\end{equation}
correct?
If so, my question is: Is th... |
My book states that the wavefunctions for the quantum harmonic oscillator are
$$\psi_n(x)=(1/2)^{n/2}H_n \left(\sqrt{\frac {m\omega}\hbar}x \right) \exp \left( -\frac{m\omega}{2\hbar}x^2\right)$$ where $H_n$ are the Hermite Polynomials. It also says that $\Psi_n(x)$ are the energy eigenstates, would these be vectors in... |
In my QM book I often see partial derivatives mixed with kets, like
$$
\frac{\partial}{\partial a} |\psi \rangle
$$
where $a \in \{x, y, z\}$. Here I'm assuming that $| \psi \rangle \in \mathbb{C}^n$ for some arbitrary $n > 0$ (in particular $n$ can be much larger than $3$).
Question: What is a partial derivative of a... |
I am learning QFT, and we discussed that to quantize a complex scalar field, we do this:
$$\begin{align*} \phi(x) &= \int \frac{d^3k}{(2\pi)^3} \frac{1}{\sqrt{2\omega_k}} \big( a(\vec{k}) e^{-ikx} + b^\dagger(\vec{k})e^{ikx}\big) \\ \phi(x)^\ast &= \int \frac{d^3k}{(2\pi)^3} \frac{1}{\sqrt{2\omega_k}} \big( b(\vec{k}) ... |
In my professors notes, there is a function representing charge in terms of time, however there is absolutely no explanation to why this function holds true. It seems like he skipped the whole part on showing the workings on how he arrived at the function of maybe it does not seem so obvious to me. Here is the function... |
I would like to have the steps to do part (a) only.
I tried using [P.E. at h1]=[(K.E.+P.E.) at h2] to find the expression but the mass m will be removed in the end, not fulfilling the requirement of expressing with m.
So how do I solve this question?
|
On page-5 of this paper1 by E. Minguzzi titled "A geometrical introduction to screw theory", he writes:
Who adopts this point of view argues that it should also be adopted for forces in mechanics, which should be treated as 1-forms instead as vectors. This suggestion,
inspired by the concept of conjugate momenta of La... |
I was reading about of entangled states and I encountered a concept which is called "fully entangled state" according to the following definition:
Consider a two-qubit state $|\Psi\rangle$. We say that $|\Psi\rangle$ is fully entangled if there exist two one-qubit unitaries $\cup, \vee \in \mathbb{C}^{2 \times 2}$ such... |
With reference to the Nambu (or famously, Nambu-Gorkov) transformation in this paper, could someone explain the reason behind using the 3rd Pauli matrix in the Lagrangian after equation (2.3) (would essentially like to understand how to do a Nambu-Gorkov transformation for any arbitrary (Lorentz-invariant)Lagrangian)?
... |
I mean, in such a way as to make it feasible to have a collectible sample of an element like astatine, francium, or protactinium (ignoring their chemical toxicity, which could probably be contained in the same way as that of arsenic, thallium, or lead). I've never heard anything about this (and of course I am aware of ... |
The force near a black hole (outside event horizon $r=3r_s/2$) onto a mass $m$ can be calculated by General Relativity:
$$F=\frac{GMm}{r^2}\frac{1}{\sqrt{1-\frac{2GM}{c^2r}}}.$$
However, there must be a distance $r$ where the black hole's gravity basically becomes Newtonian only:
$$F=\frac{GMm}{r^2}.$$
At which distanc... |
All types of clocks I know of, are based on some entropy system (oscillating quartz crystal, spring , pendulum etc.). Is there any other way of measuring time then this type of systems?
|
energy conservation equation(1st order) in density perturbations and on superhorizon scales( $k<<aH $) implies
$\delta \dot{\rho } = -3H(\delta p + \delta \rho) + 3 \dot{\Psi} ( \rho + p) $
we have
$\delta p = \delta p_{\alpha} + c^2_{s} \delta \rho$
and $c^2_{s} = \dfrac{\delta p_{\beta}}{\delta \rho}$
where we defin... |
In this lecture-pdf by Carnegie Mellon (here)1, the following quote is said:
You cannot measure force, only its effects: deformation of structures, acceleration.
I thought about this statement a bit and thought it to be accurate as 'force' is some abstract quantity which we say should be mathematically equal to $ m \... |
I was chatting with my kids about how incandescent lightbulbs work, clarifying that they don't so much "burn very slowly" (their original understanding) so much as they emit photons "just like everything does when it gets hot" (my understanding of thermal electromagnetic radiation). Somehow water came up in the ensuing... |
I have read this Wikipedia page, but I can't understand it.
In this picture from that page, in the formula, there is just one flux density, but what about the flux density of the second magnet? What if the magnets aren't identical?
Also, why do we have both area and radius in the formula? Aren't the two terms proportio... |
While thinking about Will "water" glow at very high temperatures? it made me realize another gap in my understanding of physics/chemistry. To mean these two things seem paradoxical:
if you add heat to hydrogen and oxygen atoms, they will combust, i.e. combine into water molecules
if you add heat to water molecules, th... |
What is the mathematical cause of the "quantum" in quantum mechanics? What causes some observables to take on discrete values? There seem to be two different causes, compactness of symmetry Lie groups, and bound states. I haven't been able to find a full explanation of either cause, and am also wondering whether they a... |
I have to solve the following differential equation:
$$ \partial _t u(x,t) = D \partial ^2_x u(x,t) $$
with the initial condition $$ u(x,0)=\exp \left( -100^2 \left( x-\frac{1}{2} \right) ^2 \right) .$$
The $x$ and the $t$ Interval is [0,1].
The Boundary Conditions are $$u(0,t) = u(1,t) = 0.$$
I tried to use Fourier Tr... |
I found this image on Wikipedia under Bell's theorem. I understand the blue curve generated by quantum mechanics, but couldn't understand how the classical curve (red curve) is generated (I don't understand how correlation changes with angle, classically). This has been asked here before but I didn't find any relevant... |
The Rényi entropy is defined as:
\begin{equation}
S_\alpha = \dfrac{1}{1-\alpha}\log(\text{Tr}(\rho^\alpha))
\end{equation}
for $\alpha \geq 0$. This can be rewrited in terms of $\rho$ eigenvalues, $\rho_k$, which verify $0 \leq \rho_k \leq 1$, as:
\begin{equation}
S_\alpha = \dfrac{1}{1-\alpha}\log(\sum_k \rho_k^\alph... |
First off I apologise if these questions have been asked numerous times before.
I’m having trouble visualising the flow off electrons in an AC circuit, particularly with a grounded neutral at earth potential.
My understanding is that during the positive cycle of AC electrons flow through the neutral and load towards th... |
For a pion minus hitting a stationary proton, what are the other particles if an antiproton is to be created among them? A positive pion is possible but the total rest mass energy of the final state is comparable to the initial particles.
|
Assume I have a uniform ball, heat transfer is solely governed by the heat equation ($\dot{u} = \alpha \Delta u$). It has an initial temperature distribution solely dependent on $r$, ie $T=T(r)$, where $T(r)$.
If I start to heat my ball up from all directions uniformly, will the radial temperature gradient in the exact... |
I don't need any super specific answers. But I would it appreciate alot if someone could either confirm or correct my thought process.
I know that for many of you this will sound super obvious but for me this is new knowledge.
So electrostatics usually implies that electric charges are not moving.
In the case of a lens... |
Does Hubble's constant apply to galaxies that are moving towards Earth with a velocity and does Hubble's constant also able to different systems such as binary stars, stars in another galaxies or black holes?
Also, why is there such as large uncertainty in the Hubble's constant?
It is because:
for further away galaxies... |
Convection driven compressional warming is accepted here on Earth by scientists( Chinook winds, Santa Anna winds) when there is such low pressure, 1 bar = 14 psi. Scientists also agree that Jupiter’s lower atmosphere is as hot as the Sun for the same reason, convection driven compressional heating.
My question. With 9... |
In classical mechanics, the angular momentum $\textbf{L}$ of a particle is
$$
\mathbf{L = r\times p}
$$
where the $\mathbf r$ is the position of the particle measured from some origin. That means that $\mathbf L$ is dependent on the choice of the origin. Indeed the angulur momentum $\mathbf L'$ wrt the point $\mathbf{r... |
Let's consider Maxwell theory:
$$
\mathcal{L} = -F_{\mu\nu}F^{\mu\nu} = 2 A_\mu (\Box \eta^{\mu\nu} - \partial^\mu \partial^\nu) A_\nu
$$
Is it possible to fix gauge $A_0 = 0 $ and concider Lagrangian:
$$
\mathcal{L} = 2 A_i (- \Box \delta^{ij} - \partial^i \partial^j) A_j
$$
And do quntization of such theory in L... |
Maybe a bit of a stupid question, but I'm imagining that my room is effectively a cavity with no leakage of light and minimal reflection. If I get a spectrometer and hold it out will it have the Planck shape?
I'm trying to rationalize how certain thought experiments allow you to consider being in a radiation that has a... |
For a universe that is flat, has matter and a cosmological constant, we can write the Friedmann equation in the following way:
$$\frac{H^{2}}{H^{2}_{0}} = \frac{\Omega_{m,0}}{a^{3}} + (1 - \Omega_{m,0})$$
I understand that if the second term is negative ($\Omega_{m,0}>1$) then the final fate of the universe is that it ... |
When I see depictions of the electron orbital of a hydrogen atom, I see a static proton in the center surrounded by an electron cloud. What would it look like if we shifted the reference frame to the electron and observed the proton? That is, what would it look like if we assumed the electron was statically positioned ... |
Consider a chain around two gears, one of of radius $r_1$ and the other of $r_2$. Say the gear $r_1$ is attached to a rotational device that delivers torque $\tau$ . After a quarter cycle of rotation you have input energy $E = \tau\cdot\pi/4$ rotational energy into the system.
Say you have the same system but this tim... |
Background information
Let $\beta$ be the inverse temperature 1/T, and $H$ be the Hamiltonian.
$H = H_0 + H_I$, where $H_0$ is the free Hamiltonian.
Also $S(\beta) = e^{\beta H_0}e^{-\beta H}$
Let $\phi_H(\tau)$ be a field in Heisenberg picture, and $\phi$ in Schrodinger
picture and $\phi_I(\tau)$ in interaction pictu... |
This is a paradox I'm trying to understand. I'm not tackling relativity yet. I'm still working through Walter Lewin's lectures on electro magnetism. However, I understand base and derived units pretty well and in preparation, there's something that's picking on me.
Consider distance (aka length, in meters) is a base un... |
Are the Maxwell equations written with the derivatives of the EM field strength tensor not generally covariant? I can't seem to prove that is.
The Maxwell equations in 4-tensor form:
$\partial_{\mu}F_{\alpha\beta}+\partial_{\alpha}F_{\beta\mu}+\partial_{\beta}F_{\mu\alpha}=0\tag{1}$
Transforms like this:
$J^{\theta}_{\... |
We define two operators:
A = $i (p/\sqrt(2)) + W(x)$ and $A^+ = - i (p/\sqrt(2)) + W(x)$.
And two Hamiltonian operators:
$H_{-} = AA^+ $, and $H_{+} = A^+A$.
Show that if $|n^- >$ is a normed eigenstate for $H_{-}$ with the eigenvalue $E_n$, then $A|n^->$ is the eigenstate for $H_{+}$ with the same eigenvalue.
How do I... |
I was working on this interesting problem I came up with for a couple hours and got stuck - decided to ask here.
A rocketship with is accelerating upward with constant thrust. Ignoring air resistance and the change in mass due to loss of propellant, what would the graph of $j(t)$ (the jerk of the rocket at a given time... |
A force field $F_i(x)$ is conservative if for every curve $C$ from a point $y_1$ to a point $y_2$, we have $\int\limits_C F_i(x)\mathrm{d}x^i$, so that the energy difference between $y_1$ and $y_2$ is independent of the curve taken from one to the other. Equivalently, the integral around a closed curve must be zero, $\... |
There are different types of masses like inertial mass, passive gravitational mass, active gravitational mass, relative mass, et cetera. does Are there different types of gravitational forces that is exerted on them?
|
I have just started my quantum mechanics course for school (homeschool), and I was using No-Nonsense Quantum Mechanics by Jakob Schwichtenberg, I have since discovered that the book sucks. I have now narrowed down my textbook search to Griffiths Introduction to Quantum Mechanics and Shankar's Principles of Quantum Mech... |
A supersymmetry is a symmetry that transforms fermions into bosons and bosons into fermions. What's the physical interpretation of it? I could notice a symmetry between the boson sector and fermion sector, since if we exchange then into each other the theory we hold is the same. Is this interpretation correct and is th... |
In every text/ physics book that I've read, Protons are mentioned as particles that are bigger, way bigger 2000 times to be precise, than electrons...I believed that until a few minutes ago when I googled "what is the radius of an electron" and then I read somewhere that it was 2.5 times bigger than the radius of a PRO... |
Given the potential $\phi = \alpha/r^n$, I want to find the second virial coefficient of my system. My integration limits are from some cut-off length $D$ because the particles don't experience a self-force.
This was my procedure:
$$B_2(T) = -2\pi \int_{0}^{\infty} (e^{-\beta \alpha /r^n} -1) r^2 dr \\
= -2\pi \int... |
I have an arbitrary magnetic field that varies with time, and I'm trying to numerically model the induced current in a resistive loop over time. Details below.
I'm building an electromagnetic accelerator for fun & learning: it's a coil that I'll fire high current through, to induce an eddy current on a projectile. It'... |
As a concrete example, consider boiling water. As water boils, bubbles form which rise to the surface. I know that things rise because of the Archimedes principle, however as far as I understand it, it works because water from below pushes the bubbles upwards.
My question is, (*) how did the water get below the bubble ... |
We know we give a battery connection. current wiil be determined by the resistance. if the resistance is too high then current will be low. but current will pass through.
then in potentiometer , why potential drop per length is fixed? different voltage should have diffrent voltage drop per length.
please answer it.
|
An external resistance $R$ is connected to a cell of internal resistance $r$, then the current is maximum when:
a). $R<r$
b). $R=r$
c). $R>r$
d). Any other value of $R$
As $V= I (R+r)$, I think the current will be maximum when $R+r$ will be minimum. So, I think its 'a' because $r$ is a constant. So, the less the ex... |
Almost all optics like microscope, telescope.. require observer putting their eyes very close to the optics to see.
Can the same optics designed so observer can see like viewing TV screen, i.e. from a larger distance like 30cm from optics? Or is it impossible?
|
I understand that in physics, for a converging lens, the focal length is based on the refractive index of the lens material and its curvature. However, I started reading a bunch of photography articles and got to the topic of FOV. All of the articles I have come across provide a similar visual and formula to the one b... |
I realize this might be a silly question but it is plainly true that, for example, a lighthouse beacon or any powerful light source, produces a much larger "spot" the farther it falls from the origin. So why don't distant objects also look bigger than closer objects, just the opposite as in experience things occur.
|
In `Hidden Quantum Groups Inside Kac-Moody Algebra', by Alekseev, Faddeev, and Semenov-Tian-Shansky, a relationship between quantum groups and affine Kac-Moody algebras is shown for the WZW model.
Towards this end, the authors show that a certain exchange algebra (that is implied by the quantum group relations) implies... |
Imagine we have a system of atoms in the canonical (NVT) ensemble. For this system, we know that under thermal equilibrium, the probability distribution $P(E)$ of the system's total energy $E$ satisfies the Boltzmann distribution $P(E) = \exp(-E/kT)/Z$. Is it true that the probability distribution of each atom's energy... |
My question pertains to part (ii) of the following question:
In part i, I found that the speed at point B is $ 7 m/s$.
Now, in part ii, there are two ways to approach the question. The first uses the work done formula to find the force of friction, and then proceeds to use the $Fnet = ma$ formula to figure out $\theta... |
I know that QED is some kind of second quantized version of the Maxwell-Dirac theory. But why is it that this modification to a second quantized version is just to replace the scalar function $\Psi$ by a field operator $\hat{\Psi}$?
|
In the Chapter/Section 36 of Srednicki's Quantum Field Theory, he argued that the terms of $\partial^\mu\psi\partial_\mu\psi + h.c.$ cannot be included in the Lagrangians for spinor fields because of that these terms would yield a Hamiltonian with unbounded below. I cannot understand this argument, so I try to write ... |
Suppose the Higgs field goes back to its initial unstable state, as it was before electroweak symmetry breaking. Or, in other words, suppose the electroweak symmetry is restored. Since, the physical photon that we observe today was, before symmetry breaking, a linear combination of $W^{0}$ and $B^{0}$, would it "decomp... |
I want to show that the Taylor expansion of $\frac{R\vec{e_1}-\vec{y}}{|| R\vec{e_1}-\vec{y} ||^3}$ at $\vec{y}=0$ is equal to $\frac {\vec{e_1}}{R^2}+\frac{3y_1 \vec{e_1}-\vec{y}}{R^3} + O(y^2)$. I think I should begin with calculating the Taylor expansion of $\frac {\vec{x}}{||\vec{x}||^3}$ at $R\vec{e_1}$ and then s... |
You know how energy is converted into mass in the sun, in particle accelerators and in nuclear bombs...Well mass gets converted into energy only in those situations (relativeley) and it doesn't happen in our day to day life...This makes it look like there needs to be a circumstance that the particles are in to get conv... |
I want to decompose the Coulomb potential $W\left(\mathbf{r}\right)=1/\left(4\pi r\right)$, in a periodic 3d space of size $L^3$ into a Fourier series
$\hat{W}(\mathbf{k})=\int_{\left[-L/2,L/2\right]^{3}}\text{d}\mathbf{r}\text{e}^{-i\mathbf{k}.\mathbf{r}}W(\mathbf{r})$ such as
$W\left(\mathbf{\mathbf{r}}\right)=\frac... |
Is every first order phase transition related to a second order phase transition by the tuning of some coupling? In practice is the expectation that the this tuning can usually be done in the lab. (By playing with the temperature, density, magnetic and electric fields and/or particle numbers.)
|
For a single position and force vector, it is easy to just use the curling hand, as shown in the below picture where we expand our hand in the direction of position vector and curling it in the direction of force vector.
However, it is not lucid if we have a plethora of position and force vectors as shown below.
The ... |
I have recently taken an interest in energy conversions and how it is connected to motion in classical mechanics. Sadly, I'm not really up to speed when it comes to the mathematics and derivations of the various energy formulas such as kinetic energy, rotational energy, moments of inertia, etc. With this question, I'd ... |
If we have two electrons in a state $|\psi\rangle=\frac{1}{\sqrt2}[|\uparrow\downarrow\rangle+|\downarrow\uparrow\rangle]$ and we measure the spin of the first electron to be up, does the wavefunction collapse into the state $|\psi\rangle=|\uparrow\downarrow\rangle$? If so, how is this consistent with the notion that f... |
Three equal masses are connected by two light inextensible strings. The middle one is imparted a velocity $v$. All collisions are elastic. Find the tension in the thread as a function of the angle $\theta$ made by the vertical and the strings.
I have no idea how to proceed in such a question.
(Only hint in my mind is ... |
I am solving dynamics and unable to digest author's views regarding apse. Help from the community is needed.
Theorem :- If the central acceleration p is a single valued function of the distance,
every apse line divides the orbit into equal and symmetrical portions
Author's goes on to prove the below result
v2 = C - ... |
I think I am a bit confused if I look at the following image of Fermi-surfaces for different metals:
Li, Na, K, Rb and Cs have only one valence electron. Hence, if one calculates the Fermi-vector $k_F$, it is the same for all those metals, isn't it? But then, why does it in the case of Cs overlap with the boundary zon... |
I'd like to ask a few questions about photons, not as a professional of physics.
Frequency:
Since it's connected to the frequency of the wave composed by the stream of photons but can be defined for a single one, what is the best way to picture this quantity?
Is this physical quantity related only to photons, or at le... |
Consider a 2D lattice model like this
Assuming the mass of atom and force constant is 1, we could easily calculate the dispersion relations of the system. As there are four atoms per unit cell, there should be eight eigenvalues for every wave-vector $k$. The dispersion relation is like below
We see that there are two... |
I started to develop a molecule modeling application. The early results show that quantum effects are negligable in most cases. (I mean bond orbit superpositions, effect of antisymmetrization).
Is this true?
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.