instruction stringlengths 31 24.3k |
|---|
What I have learnt in school is that, we are able to see images behind a mirror(virtual image) because our brain assumes that the diverging rays that our eyes see, are coming from a point behind the mirror but in reality, there is no such point. So, my question is if there is no such point, how can a camera capture it?... |
I heard that there are some physicists trying to figure out, out least hypothetically, how things with positive and negative mass may interact with each other.
I'm really confused about how this can even be a possibility at all. I don't know much about relativity, so please bear with me if I'm completely wrong (I'm not... |
I need some help with this problem.
I have to find the natural frequency of this system, the problem says that the cylinder has a mass of $m$, spring constant is $k$ and the string to the right is inextensible.
I am currently trying using the energy method but apparently my answer is wrong, I came up with the followin... |
Does the expression $$ C_{p} = \left ( \frac{\partial H}{\partial T} \right )_{p} $$ still work when the work done by other things than expansion (by chemical reactions, electric work etc) is not zero?
|
Consider the following problem:
A frictionless tube lies in the vertical plane and is in the shape of a function that has its endpoints at the same height but is otherwise arbitrary. A chain with uniform mass per unit length lies in the tube from end to end. Show, by considering the net force of gravity along the curve... |
Across a surface the potential is continuous so:
$V_{\text {above }}=V_{\text {below. }}$
Taking the negative gradient both sides we have
$-\nabla V_{\text {above }}=-\nabla V_{\text {below }}$
,hence
$\mathbf{E}_{\text {above }}=\mathbf{E}_{\text {below }}$. Which is wrong.
The correct expression is $\mathbf{E}_{\tex... |
I am doing this problem and I realized the wavefunction is real. But we also already showed that the wavefunction needs to be complex. Why is it that the wavefunction given here is real? I first taught $N$ could be complex, but it cannot since when you compute it to normalize $\Psi (\mathbf{x})$, it is a function of $a... |
From what I understand, inertial frames are the ones in which the momentum of every particle in the universe gets well accounted for. Like if there's any particle losing momentum, another particle somewhere must gain the same momentum, and this exchange of momentum can always be attributed to one of the four fundamenta... |
I was reading Zettili’s Quantum Mechanics book. There I have seen
when a ket (or bra) multiplied by complex number, we also get a ket (or bra)
But how do we infer this by mathematics?
|
Ring with magnetic flux
Assuming a particle locates in a ring which circle a magnetic flux,
the Hamiltonian is:
$$\hat{H}=\frac{1}{2 m}(\hat{p}-A)^{2} \rightarrow \frac{1}{2 m}\left(-i \partial_{\phi}-A\right)^{2}$$
and the energy is:
there exists ground state degeneracy for $\pi$ flux.
Square lattice with magnetic f... |
I know that spin is needed for defining the magnetic moment of any particle, and I have also read that the spin actually is the reason why some materials are magnetic. What I want to know is whether spin is necessary for the some interactions in the electromagnetic field.
Let me expound a bit: in classical electromagne... |
Tsytovich et. al. 2007 proposed that some interaction of dust and plasma might produce inorganic lifelike structures. Has there been any development regarding such theories?
|
In the lecture notes by Beisert on integrability, it is stated that integrability is a property mainly in two-dimensional field theories, with some higher-dimensional examples. As higher-dimensional examples he explicitly quotes the following two theories:
$$\begin{align}
&\bullet ~ ~ \mathcal{N}=4 ~ ~ \rm{super-Yang ~... |
I have read in Wikipedia that quasiprobability distributions in phase space quantum mechanics may fail to be $\sigma$-additive, but I don't know in which sense this is true. If I have a Wigner distribution, for instance, it can be given by integration with respect to an absolutely continuous and presumably integrable f... |
How do you prove the following commutation relation for the lattice QFT
\begin{equation}
[\phi(X),\Pi(y)]=\text{i}a^{-d}\delta_{x,y}\mathbb{I}?
\end{equation}
|
does anyone know good books and/or other sources of information regarding black hole mathematics/physics? Currently I'm reading the black hole wars by Leonard Susskind; it seems to be a collection of general explanations rather than a mathematical resource.
|
Suppose a pendulum is allowed to rotate in a vertical plane(z-x) shown below:
What is the minimum velocity that it must start with such that it rotates an angle of $ \frac{\pi}{2}$ degrees?
In the proof where we find out minimum velocity such that it completes a rotation, we say that at the topmost point the centrip... |
I am looking for grad/undergrad level math and physics resources. In many topics, the most popular textbooks are not meant for either self-studying, or as an introductory text on the topic, which are, nonetheless recommended. It is often very difficult to find the desired resources which are self-contained. That is the... |
An electric bulb is designed to operate at 12 volts DC. If this bulb is connected to an AC source and gives same brightness , what would be the peak voltage of the source?
To this question answer is 12√2V
My doubt is that since this bulb can only operate upto 12V when maximum value of AC voltage will be 12√2 (peak valu... |
Consider continuum medium (no boundaries) and the electromagnetic wave Poynting vector
$$ \mathbf{S} = \mathbf{E}\times \mathbf{H}^*$$
with $^*$ the complex conjugate. When there is a phase difference between $E$ and $H$, then the Poynting vector becomes a complex value. The real part of the Poynting vector corresponds... |
Bare with me as I try to use my fishy understanding of relativity.
In the twin paradox, one body is able to know that it changed it's inertial frame of reference (from one moving away from the second observer to the one moving towards the second observer) because it knows that it accelerated. (I think that) The body (o... |
Let us suppose we have the operators $a(\omega)$ and $a^\dagger(\omega)$ with $[a(\omega),a^\dagger (\omega')] = \delta(\omega-\omega')$. Does a derivative of the Fock state $a^\dagger(\omega) |0\rangle$ with respect to $\omega$ exist, that is $\partial_{\omega} a^\dagger(\omega) |0\rangle $. Or more generally, do thes... |
I'm having a doubt with the following problem:
A uniform bowling ball of radius R and mass M is initially launched so
that it is sliding with speed V0 without rolling on an alley with a
coefficient of friction μ. How far does the ball go before it starts
rolling without slipping, and what is then its speed?
In the so... |
This answer to "How fast is fuel escaping a rocket for it to reach escape velocity 11km/s?" includes the following:
From Rocket and Spacecraft Propulsion: Principles, Practice and New Developments
It can be seen in Figure 1.6 that the rocket can travel faster than the speed of its exhaust. This seems counter-intuit... |
I am trying to understand crystallography and the space groups of crystals, but I have one major question bugging me. The book I am using adresses different lattice symmetries and applications of group theory. More specifically, the electron energy bands are characterised by the irreducible representations of the point... |
I wonder why ultrasound devices are using ultrasound. Is it a biological reason due to our human audible range? Or is there a physical reason for that?
The question mainly aims at understanding why ultrasound is used in medical applications, why not other frequencies e.g. lower or even higher?
|
The energy stored in a charged capacitor of capacitance $C$ with $V$ voltage across it is:
$$U= \frac 12 CV^2$$
Whereas the work done in charging the capacitor is:
$$W= CV^2$$
This means that $(1/2)CV^2$ amount of energy gets dissipated somewhere else.
I learnt somewhere that this is dissipated as heat. But an ideal ci... |
background
I read in the book Introduction to Electrodynamics by D. J, Griffiths the process of solving the four Maxwell equations in the most general form:
Firstly, the four equations were simplified using potentials as
$$\nabla ^2 \vec A-\mu_0 \varepsilon_0 \frac{\partial^2 \vec A} {\partial t^2} - \nabla \left({\nab... |
So I was wondering if you could use electromagnets to redirect the electric arcs created by a Tesla coil or the plasma arcs from a high powered plasma ball so you can control the direction it is going. I tried looking at lightning but lighting itself is too complicated and the forces of Nature won’t let me. Please hel... |
I was trying to prove the differential Bianchi identity by applying the covariant derivatives to each of the Riemann tensor terms
$R^{\lambda}_{\sigma\mu\nu;\rho}+R^{\lambda}_{\sigma\nu\rho;\mu}+R^{\lambda}_{\sigma\rho\mu;\nu}=0\space\space\space\space\space\space(1)$
and I got here:
$R^{\lambda}_{\sigma\mu\nu;\rho}=R^... |
In this stack-post, an equation relating the external work done and the change in potential and kinetic energy of the system was derived by the user Biophysicist. Given:
$$ W_{ext} = \Delta K + \Delta P$$
However, it is an equation often used in books and videos that :
$$ E= P + K$$
How was the above energy equation d... |
When trying to unificate $SU(2)_L$ and $U(1)_{em}$ one introduces and extended Gauge group with the direct product $SU(2)_L \times U(1)_Y$, where are introduced the concepts of hypercharge $Y(\psi)$, that should be determined for different particles, and a new coupling costant $g'$ to $U(1)_Y$ interaction.
The neutral... |
Somebody complained on a forum, that his microwave oven heats up the plate instead of the food. One explanation that the material of the plate is not suited to microwave ovens. Another explanation that the frequency of the emitted wave changed. Does the design of the emitter allow frequency change without going complet... |
As I understand the relevant popular sources (example), since the end of the Electroweak epoch, the Higgs field became fixed in the whole known Universe. Thus, we are somewhere on the deep blue part (which is really a 4-sphere) of the Mexican hat potential, and this is a constant value of the Higgs field everywhere. Of... |
If the universe wants to reach a state of entropy, how did it come to have such a large amount of concentrated energy in the first place?
|
Since the moment of inertia is defined as $\int r^2 dm$ where $r$ is the distance of the mass element from the axis, one can move a mass element parallel to the axis, without changing the moment of inertia.
For example, consider a thin rod of length $L$, inclined at an angle $\theta$ to the axis passing through its cen... |
If QED becomes nonlinear after the Schwinger limit, shouldn't QED no longer be unitary (above the limit) since linearity is a requirement of a unitary operator (and vice versa)?
Does this mean that superpositions cannot be used to fully describe physics above the limit?
|
Background: I would like to understand that gravitationally bound systems are not affected by the expansion of the universe. This statement is folklore, but I was not able to find a rigorous solution.
Question: Is there a proof or concrete example that in the presence of a cosmological constant $\Lambda > 0 $ the Einst... |
Say I have a rotating disk #1, that is connected via an axle to disk #2 with a person on it. Disk #1 has a torque about the axle from the person via the applied force at the edge and it rotates CCW. The person & Disk #2 would revolve around the axis with a CW direction.
But how does the person move or get any torque to... |
What does the phrase “Due to Lorentz invariance, only the Higgs particle can have a non-zero expected value in a vacuum” mean?
|
Why are there clear-cut states of matter instead of a gradual transition from gas to solid (let's set plasma aside for the purpose of this question)? If the main difference between them is the distance between molecules, then with temperature going down (let's neglect pressure for the purpose of this question), a gaseo... |
In page 296 and 297 of Kleppner and Kolenkow, The author goes over an example of a massless tilted rod rotating about the z-axis as shown in the figure having two point masses at each end:
Details: The perpendicular to rod's length makes an angle of $\alpha $ with the z-axis
Labelled diagram:
The author writes the $... |
When Hartle discusses the geodesics in his Gravity: An Introduction to Einstein's General Relativity book he uses the following definition for the Lagrangian:
$ L \Big(\frac{d x^\alpha}{d \sigma}, x^\alpha \Big)=\Big(-g_{\alpha\beta}(x) \frac{d x^\alpha}{d \sigma} \frac{d x^\beta}{d \sigma} \Big)^{1/2}$
where $\sigma$... |
I think I understand the idea of thinking about gravity not as a force pulling an object towards another object but instead a warping of space so that an object moving in a straight line ends up following a path that brings it closer to the object, like two people at the equator both heading North and ending up at the ... |
HCV Concepts(Physics) 17.26
Note that $\Delta$ means triangle
Consider a point source of light S, which sends two rays of light of wavelength $\lambda$ (order of magnitude $10^{-7}$ m) - one to point O (directly in front of it) and another to point P, which is at a distance $a$ (order of magnitude $10^{-4}$ m) from O. ... |
This is a bit a bit of a weird question. Simply put, if a body orbits something such as a black hole there is no internal issue (that I know of) that would cause it to eventually stop (by internal I mean that an external force can't be applied as an example). I'm assuming the reason this 'perpetual motion machine' fail... |
Consider the problem of determining the equations of motion in 2D for a point mass sliding down the quarter unit circle lying in the 3rd quadrant.
That is, at $t=0$, it is at position $(-1,0)$, and we wish to determine its position $x(t)$ for $t>0$, as it slides to $(0,-1)$.
Let $\alpha(t)$ denote the angle between the... |
An electromagnetic wave propagates in air toward a reflective plate and reflects off the plate. Is there any difference in the wave's reflection if the plate is charged versus uncharged?
Related: an electromagnetic wave propagates through a medium. Is there any difference in the propagation or any change in the wave if... |
For a plane electromagnetic wave, propagating in vacuum space, it's easy to prove that
$$\vec E=\vec B \times \vec c.$$
Does this relation holds for other types of waves other than plane waves?
|
What is meant by the following terms in QCD -
Dirac trace, trace in color space, trace in flavor space, etc. Could someone explain with an example (For eg. what's the diffrerence between something like $tr [A]$ and $tr_{Dirac} tr_{flavor} tr_{color} [A]$)?
|
Say I have some Hamiltonian $\mathcal{H}$ that describes a 1-D spin chain (i.e. Heisenberg model) which has a number of compatible symmetries $\{\mathcal{O}^i\}$ (i.e. total spin...etc). For all $\mathcal{O}^i$ we have $[\mathcal{H},\mathcal{O}^i]=0$ and thus for every $\mathcal{O}^i$ there exist a basis $\{o_j^i\}$ wh... |
Recently I was viewing this video which discusses Galileo's solution to Aristotle's wheel paradox and it got me thinking about when rolling turns into skidding. Why do geometric shapes with a finite number of edges skip and when an object has its several sides going to infinity, it skids.
Is there a precise number of s... |
I am looking for an intuitive explanation of the response of cold plasmas with refractive index $n=\sqrt{1-\frac{\omega_p^2}{\omega^2}}$ to electromagnetic waves.
All of the explanations I can find say that for $\omega<\omega_p$ the electrons react 'quickly enough' to cancel the incident wave so it is fully reflected, ... |
I am a private pilot and noticed something. Flying in the colder winter days seems way calmer and less turbulent to me than flying during the summer. Now because I do not have that much of experience this might just be coincidental. And of course I know that on any day there are so many factors that weigh in when it co... |
According my source, the Higgs field hamiltonian density is
$H(\phi )={\frac {1}{2}}\left|{\dot {\phi }}\right|^{2}+\left|\nabla \phi \right|^{2}+V(\left|\phi \right|)$
The first term is the kinetic energy of the field. The second term is the extra potential energy when the field varies from point to point. The third ... |
Paraphrasing an extract of the Feynman lectures on special relativity:
Newton's second law can be expressed by the equation:
\begin{equation}
F=\frac{ \mathrm{d} (mv)}{ \mathrm{d} t}
\end{equation}
It was stated with the assumption that $m$ is a constant.
However it turns out that the mass of a body increases with velo... |
I have a Condensed Matter Hamiltonian on some lattice (eg. square or triangular)
\begin{equation}
H = \sum_{i,j} :\hat{a}_j^\dagger \hat{a}_i \hat{a}_i^\dagger \hat{a}_j: = \sum_{i,j} \hat{a}_j^\dagger \hat{a}_i^\dagger \hat{a}_i \hat{a}_j = \sum_{i,j} :B_{ij}^\dagger B_{ij}: = \sum_{i,j} B_{ij}^\dagger B_{ij} - ... |
A lot of the description of vortices starts by saying a vortex in a Bose-Einstein condensate can be generated by imparting an angular momentum to the container. So as I understand it is described by a Hamiltonian of the form
$$ H= (p^2/2m + V_{ext} + g\lvert\psi\rvert^2)\psi - \Omega L_z\psi $$
But then when proceedin... |
I have consulted a book by Mark Fox on Optical Properties of Solids, and it states:
" The absorption of a photon by an inter-band transition in a semiconductor or insulator creates an electron in the conduction band and hole in the valence band. The oppositely charged particles are created at the same point in space an... |
I know that power/electricity generated (from conventional power plants or renewables) is generally instantaneously consumed, with grid operators constantly ramping generation to equal demand. My question is, what happens to the excess power, assuming insufficient storage? Regardless if it is a minor excess from an imp... |
There is an exercise in MTW that asks to prove that, given two vector fields u and v, there exists a coordinate system for which
$$
\textbf{u}=\frac{\partial}{\partial x^1} \mbox{ and }\textbf{v}=\frac{\partial}{\partial x^2}
$$
if and only if u and v are linearly independent and commute.
Now, I know that given those v... |
For example, in the following circuit:
The $2\Omega$ resistor is "floating" since it's not connected to anything in its right terminal. Hence, $i_1=0$. I've seen that one of the requirements for a current to flow around a path is to have a voltage difference, and since we don't have any voltage on the right terminal o... |
I am beginning to learn about special relativity, so I apologize for the (most likely) basic question.
I frequently see, for example, the Lorentz Factor given by the equation $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$, which makes sense to me. However, I also see it frequently written with a $u$ instead of $v$. (I... |
If I place a foil covered sheet of board in my window to reflect heat back into the room, will closing the shutters and pulling the curtains over it render it useless ? Will foil on the other side reflect cold back outside ?
|
I'm given the following problem:
A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the javelin 2.0 m above the ground traveling at an angle of 30 ∘ above the horizontal. Top-rated javelin throwers do throw at ... |
This is a sequel of this question, and assumes similar notation.
In the previous question I essentially asked if the process of entanglement is just a formal idealization, in which there's some sort of sudden change
$(\sum_i a_i \psi_i,\varphi_0) \mapsto \sum_i a_i \psi_i\otimes\varphi_i$
or if it's realized by unitary... |
I am currently gettting familiar with integrably systems and came the following statement in my literature:
$U=U(x,\lambda,t)$ some matrix (Lax component) we define
$$T(\lambda,t) = \mathcal{P} \exp \int_0^{2\pi} \mathrm{d}x U\tag{1}$$
then
$$\partial_t T(\lambda,t)=\int_0^{2\pi} \mathrm{d}x \mathcal{P} e^{\int_x^{2\pi... |
If I was interested in deriving an equation for the conservation of momentum for a fluid, I could write down an expression for the change in momentum density of a fluid point using the Reynolds transport theorem:
$$\frac{\partial \rho \vec{v}}{\partial t} + \nabla \cdot (\rho \vec{v} \otimes \vec{v}) = \vec{f}$$
I coul... |
I am stuck on this problem concerning the gravitational potential of a body. The body has a mass density $\rho(\mathbf x)$ and I have to calculate a contribution to the total gravitational potential defined by
$$f(\mathbf x) = \int_V d^3\!x' \, \rho(\mathbf x')\frac{ \mathbf x \cdot \mathbf x' }{|\mathbf x|^3} $$
wher... |
What is the density in g/cm3 of cane sugar, for example in the following product: https://www.amazon.com/gp/product/B01LYMXK56 ?
|
With my memory issues I can't be certain it was Sean Carroll, though I believe it was a video of him that explained that in an infinite Universe, we would inevitably see large scale patterns repeated, such as a whole solar system or galaxy. So, in theory, we could expect that somewhere in this infinite Universe another... |
There're several ways the Second Law of Thermodynamics can be stated. I'm thinking of these two:
Entropy never decreases spontaneously.
and
Heat does not spontaneously flow from cold to hot objects.
From the first statement, we know that the entropy of the object is given by $S = k \ln W$, where $W$ is the number o... |
Context: I am building a tennis ball machine and am having trouble interpreting the following formula for the flight path of the ball. I know all of the other values in the formula but the source I am using doesn't explicitly state what d is. I think it may be either distance or delta, any ideas?
If it helps the other... |
Warning, pop science coming.. please correct what I’m getting wrong. Einstein’s equations of relativity showed the potential for existence of wormholes that can connect different points in space time. I understand the mechanisms for their practical implementation are nothing near feasible. However, based on the equa... |
In Weinberg's QFT Page 109, he defines the "in" and "out" states as
the 'in' and 'out' states* $\Psi_{\alpha}^{+}$ and $\Psi_{x}^{-}$ will be found to contain the particles described by the label $\alpha$ if observations are made at $t \rightarrow-\infty$ or $t \rightarrow+\infty$, respectively.
And then he claims th... |
I'm doing something very wrong or It seems to me that I can't generate a finite Lorentz transformation using the exponential of the infinitesimal Lorentz boosts.
Let me define $L_{x;v}$ as the operator that produce a Lorentz boost in the $x$-direction with a speed of $v$. This operator acts on the components of the 4-p... |
According to the Kohn-Sham first theorem, the ground state energy of an electron system could be written as a function of the electron density
$$E = E[n]$$
And we know that according to the Kohn-Sham equation, the ground state energy can be expressed as
$$
E=-\frac{\hbar^{2}}{2 m} \sum_{i}^{N} \int \psi_{i}^{*} \nabla^... |
I am learning about various types of simple machines like levers, pulleys, ramps at the moment. And in researching about them I see that in all of them even though the work performed stays the same, the way they offer an advantage in performing work ( meaning reducing force applied) is that either distance of work perf... |
I recently saw a Walter Lewin lecture on YouTube, and he proved how solid cylinder rolls down faster due to a smaller moment of inertia.
In one of the steps we get,
my step:
$$ma=mg\sin\theta−\mu mg\cos\theta$$
his step:
$$ma=mg\sin\theta-Ia/R^2$$
He equates friction with moment of inertia and gets a dependence relatin... |
In EM Physics we were given the problem to show that
$$\vec a \times (\vec b \times \vec c) = \vec b (\vec a\cdot \vec c) - \vec c (\vec a \cdot \vec b).$$
I know first
$$ \vec a \times (\vec b \times \vec c) = \hat e_i \epsilon_{ijk} a_j (\epsilon_{kmn} b_m c_n )$$
but don't know where to go from here. I don’t want to... |
The classical Brachistochrone was actually counterintuitive wherein the time of descent is lesser (the least) for the cycloid than that of the corresponding straight inclined track.
Let an inclined and wavy track be given by $$y= 1-xe^{\epsilon \cos^2(7x\pi/2)}~~~(1)$$
for $\epsilon=0$ this is a simple inclined, strai... |
Coming from the NE Dirt Modified world, we are always looking to reduce the amount of friction that our tires need to withstand. This friction causes heat and wear in the tires. Our engines are longitudinally mounted, with the crankshaft lying parallel to the frame rails. The crankshaft rotates in a standard fashion, c... |
For Silicon at room temperature, Nc = 2.8x10^19 per unit volume. For 300K, m*/m = 1.81 for Silicon. Now Nc is proportional to 1.5th power of both temperature and m* (effective mass). So, at any other temperature, what should be the effective mass of electron to be taken? Or will it be same for all the temperature?
|
It is given in my book that the scientific definition of collision is that two or more bodies are said to collide when their motion is affected by the force they exert upon each other. For Eg. When two protons are moving towards each other, they change their direction of motion away from each other due to electrostatic... |
Most coaches in Indian trains are non-air-conditioned, i.e., the windows can be opened. Recently, the government has planned to convert all coaches in some trains to A.C., citing the fact 1 that for trains to achieve a certain speed (130 km/hr), the windows must remain closed.
Specifically, they have made the following... |
One question in a test I am going to take is: How does the form of the electromagnetic wave equations
$$ \Delta \phi - \frac{1}{c^2}\frac{\partial^2 \phi}{\partial t^2} = - 4\pi \rho $$
indicate relativistic invariance?
Is there a way to directly conclude this?
|
I am fine with part a, if I drop all the terms of the same and smaller magnitudes than $O(1/\eta)$ after expansion. For part b and c, although I don't understand why "only the second term is large" would imply "the two-level system must be in its ground state", I was hinted for the computation that I should treat $(\h... |
Learning about forces and frictions at the moment, one things I can't seem to grasp is what is the difference between the normal and reaction force? They both act perpendicular to a surface and away from it, but what is the difference between both of these forces? I have tried searching this up on the internet to no av... |
I have a question about a statement in Condensed Matter Field Theory (2nd edition) by Altland/Simons on p.124. In short, when we consider a motion in a double well we obtain a classical solution in Euclidean time - instantons. For example, for tunneling amplitude $$G(a,\pm a; t) = <a|e^{iHt}|\pm a>$$ we get a summatio... |
I'm reading these lecture notes on Anderson localization, and I cannot understand how the resonant regions contribute to the divergence of the resolvent expansion (sections 3.1 and 3.2). The relevant Hamiltonian is
$$ H=H_0+gT$$
where $$H_0=\sum_{i}\epsilon_i |i\rangle\langle i|,\quad T=-\sum_{\langle i,j\rangle}(|i\ra... |
Dirac equation is given by $$(i\gamma^\mu\partial_\mu-m)\psi=0.$$ The matrices $\gamma^\mu$ satisfy the relation $$\{\gamma^\mu,\gamma^\nu\}=\gamma^\mu\gamma^n+\gamma^\nu\gamma^\mu=2g^{\mu\nu},$$ where
$g^{\mu\nu}$ is the Minkowski metric.
I read from Ryder's QFT textbook (pg 43) that for a $4\times 4$ unitary matrix $... |
Consider an electromagnetic wave in a lossy medium. This medium has a complex permittivity $\varepsilon_r=\varepsilon_r' +j \varepsilon_r''$ and a wave impedance given by
$$Z=\frac{E}{H}=\sqrt{\frac{\mu_0}{\varepsilon_0 \varepsilon_r}}$$
where we assumed $\mu_r=1$. Hence, the complex permittivity results in a complex i... |
Far from major gravitational sources...
A man is standing throwing darts at a dartboard in a rocket ship. The thrust is upwards so he feels almost like he would on Earth but the G-force is slightly stronger. If he throws the dart straight at the bulls-eye without compensating for the thrust it will of course land below... |
For current loops the definition of magnetic moment is $\textbf{m}=I\int d\textbf{S}$.
But say I've a cube with a surface current, how can we define magnetic moment in this case?
|
Imagine a seesaw with blocks of mass m each placed on extreme end. The axis of rotation is in center. The length of seesaw is L.
If we are given a position of seesaw in which the seesaw is making 30 degree angle with horizontal. Will it be called equilibrium ?
Because when I see the equilibrium equations
Sum Forces in ... |
How would I calculate the force on an object (in Newtons) that is under the influence of an electromagnetic field produced from a solenoid? I know it would involve using the equation $B=(μNI)/L$ to find the strength of a magnetic field in Tesla, however I'm unsure where I'd go from there.
|
In a wikipedia article about rotating frames is written:
$$ \frac{d}{dt} \hat{u} = \Omega \times \hat{u}$$
What exactly is the intuition behind this equation? I seek a physical explanation of the above equation.
See under time derivatives in the two frames (here)
|
In the mathematical sense, a wave is
any function that moves. In that sense we can consider that any function that complies with the wave equation (let's consider in one dimension to simplify things) will be a wave. But is this kind of thinking physically valid? That is, any function that satisfies the differential equ... |
If nitrogen has 7 electrons, how come the ground state is $2s^2 2p^3$? This would mean that there are only 5 electrons in the nitrogen atom.
|
I am trying to derive Rutherford's scattering formula, with the coordinate system and polar coordinates chosen as in the picture below.
Angular momentum conservation yields $mvb = mr^2 \dot{\varphi}$. I then tried to make use of this in Newton's equation along the $x$-direction
\begin{equation}
m \frac{\mathrm{d}v_x}{... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.