instruction stringlengths 31 24.3k |
|---|
Can somebody explain how to establish the connection between Miller indices $(h,k,l)$ of a crystal plane and the triplet of integers $(m_1,m_2,m_3)$ that appear in the linear combination $$\vec{G}=m_1\vec{b}_1+m_2\vec{b}_2+m_3\vec{b}_3.$$ Here, ${\vec G}$ is the reciprocal lattice vector.
|
So it takes a single microgram or less of pure Polonium-210 to be lethal. Which according to basically all sources makes it the most toxic material or at the very least the most toxic element. But why is this the case?
Radon-222 has roughly the same energy per decay and the same type of decay, and yet the half life is ... |
I am a student of Physics doing masters in it and I am looking forward to study on my own. By own I mean with video lectures, books etc. It would be really kind of you all if you could recommend me some good books and video lectures on each subjects I will come across.
|
In Peskin's QFT book chapter 11.5, the author gives a graph(see below) and claims that the third functional derivative for effective action $\Gamma$ gives the 1PI (one-particle-irreducible) 3-point Greens's function.
When computing the electron propagtor, I learned that the full electron propagtor is a geometric serie... |
I am reading the chapter in Griffth's introduction to elementary particle.
By solving the momentum space Dirac equation and requiring the solution of the spinor to be the eigenspinor of the helicity operator, see the questions below.
I worked out the math but I don't understand the solution completely. For example,
If... |
Let's take into consideration a system of two charges, with magnitudes $q_1$ and $q_2$.Let's assume that the charge with magnitude $q_1$ is placed at the point $A$ and also assume that a point $B$ is at the distance of $r_1$ from $A$ and another point $C$ is at a distance of $r_2$ from $A$. Points $A$, $B$ and $C$ are ... |
I'm trying to write an equation which shows a compressible fluid entering a cone with radius R and length L, where the pressure (density) and velocity of the compressible fluid increases as the exit radius R' narrows, a huge bonus would be given the mass of the fluid to also be able to calculate the overall mass of the... |
Okay so there's a car again around a roundabout, radius $8.5\ m$ at a speed of $\frac{100}{9} ms^{-1}$. There is a man of mass $72.5\ kg$ who is going to hold onto the back of the car. What force does he need to hold onto the car with?
I have been told in my physics lesson to use $\frac{mv^2}{r}$(which is the centripet... |
After reading many books I now understand that the combination of two conductors having equal and opposite charge placed close to each other forms a capacitor and their Capacitance is defined as the ratio of charge on the capacitor(i.e. the charge on the positive plate) to the potential difference between the two condu... |
As well known in the theory of quantum optics, the photon coherent state is defined by
$$\hat{a}|\alpha\rangle = \alpha|\alpha\rangle$$
where $\hat{a}$ is the annihilation operator. Explicitly this state can be written as
$$|\alpha\rangle = e^{-\frac{|\alpha|^2}{2}}
\sum_{n = 0}^{\infty}{\frac{\alpha^n}{\sqrt{n!}}|n\... |
This is my first question in this community and I hope to get a good answer.
I'm reading a book about the principles of electrical machines and it is in English while my first language is Arabic, so I need some clarifications.
I read this theory:
"the line integral of the magnetic field intensity $H$ around a closed p... |
I was reading about bounded operators, and I was wondering that if we assume a "position" operator $A$ that acts on $\psi(x)$ and here $x$ is bounded in the interval $[-1,1]$ for example. What can we say about the operator $A$ in this case? Is it defined in the whole Hilbert space $L^2(\mathbb{R})$, or just $L^2[-1,1]$... |
1) I know electric dipole is the strength of the polarization but I really wonder that what it means actually.
For example;
When we consider the following situations.
The electric dipole moment magnitudes of the first situation and the second situation are the same but I wonder What this actually mean?
2) Why is the e... |
When reading the introduction to Sterile neutrino hot, warm, and cold dark matter I came across the following definition of sterile neutrinos:
We can define sterile neutrinos generically as spin-$\frac{1}{2}$, $SU(2)$-singlet particles which interact with the standard $SU(2)$-doublet (“active”) neutrinos $\nu_e$, $\nu_... |
Suppose there is a Boltzman system, where $N$ particles are distinguishable, and we are counting the available microstates of a given energy $E$. We have
$$\Omega_{M.B}=\frac{N!}{\prod_l a_l!}\prod_l \omega_l^{a_l},$$
where $\omega_l$ is the degeneracy and $a_l$ is the number of particles in energy $E_l$ state.
Here, e... |
To study a skyrmion system, I study the continuum free energy functional \begin{equation}
F[\vec{m}] = \int d^2 r \mathcal{F}(\vec{m})
\end{equation}
The anisotropy term is:\begin{equation}
\mathcal{F}_{aniso} = (A_c/2)[(\partial_xm^y)^2 + (\partial_ym^x)^2] - A_c[(m^x)^2 + (m^y)^2] + A_s(m^z)^2
\end{equation}
... |
I'm reading the book Introduction to superconductivity by Michael Tinkham and encountered a small math problem.
In page 44, we need to substitute the spin-singlet two electrons wave function $\sum\limits_{|k|>k_F}g_k\cos k(r)(\uparrow\downarrow-\downarrow\uparrow)$ into the Schrodinger equation $[-2\frac{\hbar^2}{2m}\n... |
In an exercise it asks to prove why certain processes cannot happen in the Standard Model. One such process is the following:
$$ p + p \to K^+ + K^+ + n + n $$
This process conserves baryonic number and charge, which are the main laws dictating whether a process involving mesons and baryons can happen. It doesn't conse... |
Three concentric thin spherical shells are given their radius are $R$, $2R$ and $3R$. Outer most sphere can't radiate in outer space. The inner most and the outer most shells are maintained at $T_{1} K$ & $T_{2} K$ respectively. Assume the three shells behave as black body. The steady state temperature of the middle s... |
Ridiculous question but...
If these equations are true:
Moment of force = force * perpendicular distance from pivot to force
(M=Fd)
And
Work done by force = force * distance moved by force in the direction of force
( W = Fd)
Does that mean...
Moment of force = work done by force
(I am aware that the distances here are ... |
A really elementary question:
Solutions of the single particle, non-relativistic, time-dependent Schrödinger equation for a spinless particle of mass $m$ alone in space, with no forces acting on it, with the potential function $V(r,t) = 0$, include all constant frequency, wavelength, and amplitude plane wave functions ... |
I am confused about the first law of thermodynamics when applied to an isothermal process for an ideal gas. In my textbook it says that for any process involving an ideal gas:
$dU=dQ=nC_V∆T$
Then doesn’t this imply that since temperature doesn’t change, there is not heat added either. However, if $∆U = 0$, then $Q = W$... |
Could you explain the highlighted equality, please? Why is there the second derivative? It is from the derivation of the Virial Theorem. The derivation starts with multiplying 2. Jeans equation with $x_k$. $\bar{v}$ means mean velocity. Thanks
Moment of inertia tensor:
$$I_{jk}=\int \rho x_j x_k \,\mathrm{d}^3 x$$
Chan... |
If I have a tank of water 2 meters high x 1 meter square.
And I use a half inch outlet from the bottom of the tank going vertical, how high would the water reach in the pipe.? What would be the relationship with adding another meter in head pressure.
Or how do I calculate what I would need in head pressure given the ab... |
What is the meaning of non-resonant production in the following context:
They assumed a negligible primordial lepton number,or asymmetry, so
the neutrinos are produced non-resonantly. [1]
I thought that this meant that the reaction would not resonate, meaning that it would only "go one way". But I don't believe this ... |
How do I find the radiation pressure exerted on a perfectly reflective flat surface that is moving along the normal of the mirror?
|
When imposing local gauge invariance for a simple lagrangian describing a free Dirac fermion field:
$$\mathcal{L}=\bar{\psi}\left(i\gamma^{\mu}\partial_{\mu}-m\right)\psi$$
Is there a particular reason for choosing the local gauge transformations to be:
$$\psi\rightarrow \psi'=e^{-i\alpha(x)}\psi'$$
$$\bar{\psi}\righta... |
I recently had a haircut, and have noticed that water in my air dries up faster when I short hair. I assume that hair loses water due to evaporation. We have been taught that evaporation is faster when the surface area is increase (which is the reason why behind drinking tea off a saucer)
But, when we have longer hair,... |
I'm reading through Tinkham's Super Conductivity and I am having some issues with getting to equation (3.97).
Beginning with the perturbing Hamiltonian the relevant equation is:
$$
\hat{H}=\frac{ie\hbar}{2mc}\sum_i (\hat{A}\cdot \nabla_i +\nabla_i\cdot \hat{A})
$$
We Fourier Transform the vector potential ( $A(r)=\sum_... |
There seems to be 2 ways of calculating tidal forces that are contradictory. Either:
By calculating the difference of Io's gravitational acceleration on a point on Jupiter's near side and the gravitational acceleration felt by a point on Jupiter's far side, using the equation:
$$\frac{GM_{io}}{(d-r_{jupiter})^{2}}-\f... |
A Ruby laser emits 1W pulses of light with wavelength $6940 ± 10 \overset{\lower.5em\circ}{\mathrm{A}}$.
What is the coherence length of the ruby laser?
My question is that what would be the value of $∆λ$ in the formula of coherent length i.e.
Coherence length $=(λ^2) /(∆λ)$.
Will it be $10$ or $20$?
|
I am reading the lecture notes in https://arxiv.org/abs/hep-th/9902115 and in it, it says that the Lagrangian
$$\mathcal{L}_{\mathrm{CS}}=\frac{\kappa}{2} \epsilon^{\mu \nu \rho} A_{\mu} \partial_{\nu} A_{\rho}-A_{\mu} J^{\mu}$$
is invariant under a gauge transformation because the transformation $A_\mu \to A_\mu + \pa... |
According to the figure, pendulum $OA$ is released from position $A$ and it collides with another pendulum $OB$ at point $B$ and after the inelastic collision, they continue their oscillation. (Mass of each bob is $10\ gm$). Can they reach at point $C$ together, Explain with mathematical expression.
I have tried to so... |
When I increase the potential energy of a system, does that mean that I have also increased the internal energy of the system since I’ve done some work on it although the heat of the system remained unchanged? I'm trying to fill every possible gap in my understanding of internal energy.
|
The stationary phase approximation can be used to find an approximate value for the path integral
\begin{equation}\int Dx e^{-S[x]} \approx e^{-S[\bar{x}]} \left(\det{\frac{\hat{A}}{2 \pi}}\right)^{-1/2}.
\end{equation}
Found by expanding around the stationarity of the functional $S$.
\begin{equation}
S[x] = S[\bar{x}+... |
Consider a system of two electrically charged particles. Their charge doesn’t matter for my question but suppose they are both positive.
I am confused about what the correct way to calculate forces on particles is, based on information of the field, when those particles themselves contribute to the field and are at an ... |
I understand that the parabolic trajectory is an approximation of a more elliptical trajectory, since acceleration due to gravity is taken to be a constant for a projectile. However I'm intrigued to know that what changes in kinetic and potential energy contribute to the question? What I mean is I read that for a traje... |
I was reading the book of Barbara Ryden "Introduction to cosmology":
In the chapter number 9, in the page 203. She says:
"The photons, electrons, and protons together make a single photon-baryon fluid, whose energy density is only about a third that of the dark matter.
Thus, the photon-baryon fluid moves primarily un... |
The Planck 2018 results give the Baryonic Density as: $\Omega_B h^2=0.0224$. I want to calculate the actual density based on the parameters. The same report tells us that $H_0=67.4$. We know that the critical density is:
$$\rho_c=\frac{3 H^2}{8 \pi G}$$
$$\rho_c=8.53\times 10^{-27}\space kg\space m^{-3}$$
So if I wa... |
Page 191 of Weinberg Vol.1. Break the Hamiltonian operator up into two parts $H=H_0+V$, where $H_0$ is the free Hamiltonian and $V$ is the interaction. Write the interaction operator $V(t)$ as a local integral of some interaction density $h(x,t)$ (Eq. 5.1.1 of Weinberg)
\begin{equation}
V(t)=\int d^3 x^i\,\, h(x^i,t)
\... |
My derivation is as follows.
The total KE, $T_r$ for a rigid object purely rotating about an axis with angular velocity $\bf{ω}$ and with the $i$th particle rotating with velocity $ \textbf{v}_{(rot)i} = \textbf{r}_i \times \textbf{ω}$, (summing over the i'th particle) is $T_r = \frac{1}{2}m_i|\textbf{r}_i \times \tex... |
I am looking to understand how the age of the universe is calculated according to modern physics.
My understanding is very vague as the resources I have found do not seem to state consistently whether inflation is part of the standard model.
For example, starting at the Age of the Universe wikipedia page, the age is ca... |
There are two common misconceptions regarding the Terrell "rotation" :
it's a pure rotation
the Lorentz-Fitzgerald contraction is not detectable by a single detector, in which the past light-cone of the detector intersects with the history of a relativistic object. Instead, the detector sees a purely rotated object, w... |
I am reading through the derivation of the Gross-Pitaevskii equation in the Heisenberg picture, and I am having some trouble interpreting the following identificiation. In the derivation the field operator $\psi(r)$ is defined as the position space equivalent of the creation/annihilation operator $\hat{a}_k$. $$\hat{\p... |
When any operator is written in its matrix form, do the individual rows and columns of the matrices have any physical meaning to them? For example, the rows and columns of momentum and position operators $\textbf{x}$ and $\textbf{p}$ in Simple Harmonic Oscillator?
|
Assume we want to describe a statistical system. And assume we are working with the constraints of a canoncial ensemble
$$U\overset{!}{=}[H]:=\textrm{tr}(\rho H) \quad \wedge \quad 1\overset{!}{=}\textrm{tr}(\rho)$$
Under these constraints one finds by minimizing the Von-Neumann entropy of the system
$$S=-k\cdot\textrm... |
In Section 2.3.1 of Griffiths' text on electrodynamics he defines the scalar potential $V$ as $$V(\mathbf{r})=-\int_{\mathcal{O}}^{\mathbf{r}}\mathbf{E}\cdot d\mathbf{l}.$$
In Section 2.3.2 he states
The word ''potential'' is a hideous misnomer because it inevitably reminds you of potential energy. This is particular... |
If we define spacetime as a Lorentzian manifold $(E^4,g)$, how can we define the property that
$$\iiint_{E^3}\Psi^*\Psi\ d^3\mathbf{x}=1$$
for a wavefunction $\Psi$? Because there's no global sense of time.
With my approach, I started with a Lorentzian manifold $(M,\,g)$, the frame bundle $LM\xrightarrow{\pi_{LM}} M$, ... |
The continuity equation, where $\rho$ is a conserved density advected by the velocity field $\mathbf{v}$,
$$
\partial_t \rho(\mathbf{x},t) +\nabla \cdot [ \mathbf{v}(\mathbf{x},t) \rho(\mathbf{x},t)]=0
$$
can be derived in several ways. I wonder if it can be derived as an opportune limit of a certain number $N$ of tra... |
Suppose a magnetic dipole (e.g a magnet, not a current loop) is immersed in an electric field.
What are the forces acting on it?
What about an electric dipole immersed in a magnetic field?
|
Is it possible to derive the equations of motion from the energy of a system alone, without knowing canonical coordinates or the Lagrangian?
I'm confused about which parts of the fundamental specification of a physical system can be derived, vs. have to be known in advanced. Given a specification of a system where tota... |
It is said that light is a disturbance or oscillation in an electromagnetic field. If light passes through a certain point in space, would the oscillation cease to exist at the given point instantaneously once the light has passed through it, or would the oscillation or disturbance gradually decrease to zero? In the pi... |
Assuming a pure Yang-Mills theory, how exactly does one get that, for appropriate $\beta$ for confinement, the expectation value of the Polyakov loop $<\Phi>$ equals zero? I do not seem to get the integration right.
|
My question concerns changing variables in the calculation of the Klein-Gordon equation for a scalar field given two different "guesses" for the metric.
I consider the following Einstein tensor, which describes an action with a scalar field $\phi(r)$ with potential $V(\phi)$:
$$
R_{\mu \nu}-\kappa \left(\partial_\mu \p... |
How do I find the equations of motions of a Lagrangian of this type:
$$
\mathcal{L}=\sqrt{\frac{1}{2}F_{ab}F^{ab} }
$$
And are they equivalent to $\mathcal{L}_{EM}=-\frac{1}{4}F_{ab}F^{ab}$?
$$
\begin{align}
0&=\partial_\mu \frac{\partial \mathcal{L}}{\partial (\partial_\mu A_\mu)}\\
&=\partial_\mu \frac{\partial }{\p... |
If I have a single cell (phytoplankton) or a small piece of sediment in a lake that is neutrally buoyant, how can I calculate the change in buoyancy due to changes in barometric pressure?
For example, my single cell is close to neutrally buoyant at a barometric pressure of $1020\ hPa$. Later in the day, the barometric ... |
I have stumbled upon pair production recently and it intrigued me,but i need help understanding the subject further.
If i understood correctly you can produce a pair of a particle and an anti-particle by striking gamma rays at an object like a plate and depending the enegry of your gamma ray you can produce electrons/a... |
I'm postulating a natural fission reactor, like Oklo in Gabon. My understanding of Oklo is that the reaction occurred entirely underground. Would it be possible for a Uranium deposit nearer the surface to interact with a lake or river in a similar manner to Oklo, so that the bottom of the body of water glowed blue with... |
Usually when one derives the variation of the Chern-Simons action in 2+1 dimensions, one has a term that is proportional to the winding number. Then one argues that the coupling constant must be an integer for the whole term to be a multiple of $2 \pi$, so that the partition function is gauge invariant.
Can we instead ... |
The breaking stress of the wire is $3.5\times 10^6 \,N/m^2$. It is observed that the minimum cross-sectional area of the wire so that it does not break is $18.67 \,cm^2$. Now I need to find out if the observation is right or not.
At first, I have calculated the acceleration of the blocks. It is $3.267\, m/s^2$. I don'... |
Let's assume we have a circuit without a battery,the wire in the circuit is not an ideal wire and the free electrons will have to do work to cross them. Now let's assume that as there is no battery connected electric potential at a point is $0$. As it is not an ideal wire the electrons will have to do work and hence th... |
In this differential equation,
$$ \ddot{x} + \frac{k}{m}x = 0 $$
We assume that
$$ \frac{k}{m} = w^{2}$$
Why is that? And how one can prove it?
|
Has the John von Neumann projection, or the wave function collapse, been used in the experimental preparation of quantum states? As an illustration, for a pair of EPR-type entangled 2-level atoms
$$|\psi_{12}\rangle = \frac{1}{\sqrt{2}}(|+\rangle_1|+\rangle_2 + |-\rangle_1|-\rangle_2)$$
or equivalently $|\psi_{12}\rang... |
This is an easy question, but I'm looking for an intuitive explanation for why the total emf of a series circuit is distributed among its resistors in proportion to their resistances.
Or in other words, why isn't the potential difference equal across all resistors if they have different resistances, since the total res... |
I'm not a physics expert, but this question really intrigued me, so I thought "why not ask those who are"!
Let's suppose there is only one object in this universe. May that be a quark, an atom, etc. What will be the consequences?
In terms relating to, Gravitational force, Electrical force, etc. individually, and in t... |
This might be a dumb question but i am not so familiar with the word voltage:
What does the textbooks really mean when they say high voltage?. Does that mean:
There are more charges so more voltage, or
If the negative charge (electron) is at a large distance from the nucleus (positive charge) as we derive for point c... |
I'm looking for a short explanations describes the difference between the magnetic flux and magnetic flux density in the most easiest way.
|
This is my Hamiltonian. $\psi_{\alpha}$ is a bosonic field.
$$H_{\alpha}=\int \mathrm{d} \mathbf{r} \psi_{\alpha}^{\dagger}(\mathbf{r})\left(-\frac{\nabla^{2}}{2 m}\right) \psi_{\alpha}(\mathbf{r})+\frac{V_{0}}{2} \int \mathrm{d} \mathbf{r} \psi_{\alpha}^{\dagger}(\mathbf{r}) \psi_{\alpha}^{\dagger}(\mathbf{r}) \psi_{\... |
In archery, we measure the weight of a bow in pounds. It's measured at 28 " from a pivot point + 1,75 ".
There is also an essential measure for the arrow, which is "grain per pound". It has a certain mass weight measured in grains and this is set into relation to the draw weight. To make this question a little less com... |
I am following a derivation of the Gibbons-Hawking action term, and in it the trace of the extrinsic curvature $K_{ab}$ is found by
\begin{align}
K & = {n^\alpha}_{; \alpha} \\
& = g^{\alpha \beta} n_{\alpha ; \beta} \\
& = \left (\epsilon n^\alpha n^\beta + h^{\alpha \beta} \right ) n_{\alpha ; \beta} \\
& = h^{... |
I am looking for the material with the lowest possible refractive index. Googling did not help much, the best I found is this article suggesting that n can be as low as 1.39, but not giving any reference which material this refers to. Other than that, the lowest numbers I found are around 1.5 for fused silica and 1.31 ... |
Suppose we have an infinite set of positive and negative charges next to each other:
$$... + - + - + - ...$$
I am wondering if this a position of equilibrium.
Intuitively I would say that it is a position of equilibrium since the negative charge on the left of $+$ repeal $+$ in the right direction as much as the $-$ on... |
If at light speed time doesnt exist do photons not move from their point of view? If they dont, what would happen if you took a photon and somehow stopped it would it be at the same point at its POV that it is at your POV?
|
Since its the spin of electrons that makes iron magnetic (along with the convenient arrangement of the atoms in the crystal structure) by arranging neutrons in the right way is it possible to make a substance only made of neutrons magnetic?
|
In the laboratory frame of reference, when a moving object collides elastically and obliquely with a stationary object of the same mass, the objects always move off at a right angle. The proof is very straightforward. However, is the opposite also true? (i.e. when two objects collide and move off at a right angle, they... |
I've seen many times the angular momentum operators $\hat L_x, \hat L_y,\hat L_z$ expressed in spherical coordinates but I've never seen the components operators $\hat L_\rho, \hat L_\theta, \hat L_\phi$. What is their expression and what Is their physical interpretation?
|
In discussions of sun spots and auroras on Earth, magnetic field lines are often described as "snapping" or "breaking", with the result of releasing charged particles very energetically.
My understanding is that field lines are just a visualization tool. I don't understand, intuitively, how a field line could snap or b... |
I have been told that few models in statistical mechanics can be solved exactly. In general, is this because the solutions are too difficult to obtain, or is our mathematics not sufficiently advanced and we don't know how to solve many of those models yet, or because an exact solution genuinely does not exist, i.e. it ... |
There are already lots of questions (and great answers) regarding Schrodinger's Cat (and Wigner's Friend, which is the same concept) on here. For example, this post is a great explanation of how decoherence with the environment causes a coherent superposition to reduce to an incoherent mixture.
I have read dozens of p... |
Usually when discussing renormalization in statistical physics, some transformation $R$ of the Hamiltonian is defined, and it is supposed that such a transformation has a fixed point $H^*$ such that $R(H^*)=H^*$. I don't understand what this might mean in finite dimension. Suppose I have an Ising model on $N$ spins
$$ ... |
I'm a senior high school student. I want to learn particle physics as a hobby. I did some research about it ,and I learned that I should learn Quantum Field Theory for entering Particle Physics. QFT needs some high degree math. How can be a possible learning path in math/physics for me?
|
To derive the master equation under a continuous measurement we first define the two measurement operators
$$M_0=\mathbb{I}-\left(R~/~2+iH\right)dt \tag 1$$
$$M_1=c\sqrt{dt}, \tag 2 $$
where $M_0$ is known as the no-measurement measurement operator and $M_1$ the measurement operator, i.e. the detection of an event a... |
How free neutrons with a certain kinetic energy are produced in laboratory? For example in nuclear fission $n$ free neutrons are produced, are there other methods?
|
The definition of density of state per unit volume stated in Girvin and Yang's Modern Condensed Matter Physics is $$\rho(E)=\int \frac{d^3k'}{(2\pi)^3} \delta(E-E')$$
I would like to gain more intuition on this definition. Why is it defined this way?
On a related note: naively, I would think that $\int dE \space\rho(E)... |
I want to find the matrix representation of $S_z$ operator in terms of the eigenkets of $S_y$ operator.
( It's Problem 1.24 (b) of Sakurai Second Edition )
One simple way to solve this problem is to map (relabel) axes [x,y,z] to [z,x,y] ( note that the order of the axes is still a right-handed system ). With these new ... |
How does the attraction between two metal plates support a new effect (or force)?
Isn't it expected that two plates attract each other due to the London dispersion?
If so, how does the experiment differentiate between the two?
|
$$g(f)=g(t)e^{-2 \pi i f t}$$
For a frequency of 5 Hz.
To calculate the real component, $2 \pi f t = 2 * 3.14 * 5 * 1$ (setting time to one) $= 31.4$, so
$$e^{2πft} = 4,333,579,136,8684 \, .$$
Would that be a correct method?
Otherwise what would be the correct way to calculate it?
And what are the conditions that would... |
I am trying to understand the solution of the electromagnetic waves equation dervied from maxwell's equations.
I have been told that every function that is $f(\vec{k} \cdot \vec{r}
+\omega t)$ is the solution, and I can understand that, but I do not understand what each variable in the function is represent.
|
I saw this video by George Hart recently:
https://www.simonsfoundation.org/2014/03/20/mathematical-impressions-the-bicycle-pulling-puzzle/
Hart attached a string to the pedal while it was on the bottom position and pulled on it. The bike then started to move backwards. The explanation was that given a forward moving bi... |
Suppose that the positive side of battery is connected to a wire, so that the electric potential of the wire converges to that of the battery.
My question is: suppose that we say that wire with zero charge has zero voltage, and one particular wire has $50\ \text{Volts}$. What exactly does that say about the electric po... |
Lets assume that there is static electromagnetic field that has $E=17mc^2$ and $p=8mc$.
At some time $t=t_0$, the field is turned off. (e.g. the electric current of coil went to zero by resistance, and the capacitor is fully discharged.) As a result, electromagnetic wave (a.k.a light) will be emitted. If we gather thes... |
As we know the diffraction pattern from a circular hole looks something like
Intuitively I would think the "bessel function like" pattern on the right would be due to poynting flux through the screen but every single resource (text book and papers) that I have seen seems to indicate that the bessel function is due to ... |
I'm trying to understand the different formulas to calculate magnetic fields, it looks like Ampere’s law is an easier way than the Biot-Savart Law, but only works under certain conditions (similar to Gauss’ law and Coulomb’s law in electrostatics). Under what conditions can we use Ampere’s law instead of the Biot-Savart... |
How do I show that in this eigenvalue problem, the perturbation series for $E(a)$ has vanishing terms of order $a^n$ for $n>=3$, also that perturbation series for eigenfunction $y(x)$ is convergent for all a?
$$(-\frac{d^2}{dx^2} + \frac{x^2}{4} + ax )y(x) = E(a)y(x).$$
$E(a)$ is a perturbation series in terms of small... |
In a homework exercise i am asked why is the spin wave function (for the H-Atom) expressed as a product between the wave function and the spin function (spin function has the spin vector operator as a "variable" ).
So i used probability in order to explain it :
There is a probability to find an atom at a certain place ... |
I am in high school
and my textbook says that
"a body is said to be in pure rotation if every point on that body moves in a circular path about a fixed axis of rotation"
but my doubt is that at any moment, I can define a linear velocity as $V=R\omega$ for any particle of that body, where $R$ is the distance of the pa... |
I am following David Tong's notes on QFT. On page 58, he applies Wick's theorem to $\psi\psi\rightarrow\psi\psi$ scattering for a scalar field with a Yukwara interaction term. The claim is, that by Wick's theorem, the only contribution to
$$\int d^4x_1d^4x_2 T[\psi^\dagger(x_1)\psi(x_1)\phi(x_1)\psi^\dagger(x_2)\psi(x_... |
I am reading about the Brown-York formalism in https://link.springer.com/article/10.12942/lrr-2004-4. The document says that if we consider a deformation of our end points $(q,t$) in position and time, then the classical mechanics action varies by (equation (65) on p.76)
\begin{align}
\nonumber \delta S^1[q^a(t... |
I'm trying to reproduce Boltzmann distribution by simulating an abstract gas, i.e. a system of particle-like objects that can randomly exchange energy between each other.
The simulation is arranged as follows. The state of the gas is a collection $\mathcal E$ of energies of $N$ particles:
$$\mathcal E=\{E_n\}_{n=1}^N.\... |
Let's say we want the expectation value of $\langle S\cdot L\rangle$.
How can one multiply a $3\times 3$ matrix (angular momentum) and $2\times2$ matrix (each $S_x$, $S_y$ and $S_z$) ?
What is the physical meaning of this expectation value?
Thank you
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.