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For clarity let me say that I am not asking for the general definition of time-ordered product in QFT, nor the definition of Wightman functions.
Precision:
In the first displayed equation on pg. 394 (section 2.5) of the book Quantum fields and strings: a course for mathematicians, volume 1, the author defines the time-... |
Supposedly, canonical transformations are used to provide a general procedure to transform a Hamiltonian such that all coordinates in the new frame are cyclic. I have done the proofs and derivations, but during my course I didn't actually get any practice on finding the right canonical transformations or the generating... |
I know, that gravity acts through time and space, as it propagates at the speed of light, through space.
I mean to discuss whether gravity has an effect in spacetime, along the time axis. Effects of gravity, that modify motion, are well known. The gravitational effect of "frame drag", for instance, as I understand it. ... |
Isotropy and homogeneity of space leads to the spacetime metric of the form
$$
ds^2=-dt^2+d\sigma_k^2,
$$
where $d\sigma_k^2$ is the metric on one of the standard manifolds (the 3-sphere, Euclidean 3-space, and the hyperbolic 3-space) depending on the curvature $k$. Here $k$ may depend on $t$, and there seem to be noth... |
Some Background:
I've been trying to understand electromagnetic waves, how they travel, and how they're produced. After some Googling and Wikipedia(ing?) I've learned that we use the EM Wave Equations to model how they propagate. However, every single derivation I've seen online does something like this:
$$\nabla\times... |
I am currently self-learning quantum mechanics with A Textbook of Quantum Mechanics Second Edition by P. M. Matthews and K. Venkatesan.
In Example 3.15 on p. 105, the author proved $\left<T\right>=\frac12\left<\textbf x\cdot\nabla V\right>$ in any stationary state, where $T$ is the kinetic energy operator, $\textbf x$ ... |
I have read somewhere (several times in different places, and can't find this now) that for a classical EM wave (or an approximation thereof) number of photons is not defined. I.e. if we have a state with definite number of photons $n$, then this state is not even close to a classical EM wave, however large $n$ could b... |
I have been studying RC circuits and noticed that even in a resistanceless circuit, when a capacitor is charged by a constant potential difference source, there is considerable heat generation, equal to the amount of energy stored in the capacitor, making the work done by the battery twice of the energy stored. Whereas... |
Peskin & Schroeder's expression of the Noether current If a (quasi-)symmetry is defined as a transformation that changes the action by a surface term i.e. $$S\to S'=S+\int d^4x \partial_\mu K^\mu(\phi_a),\tag{1}$$ or equivalently, the Lagrangian changes by a 4-divergence, $$\mathscr{L}\to\mathscr{L}'=\mathscr{L}+\parti... |
A charged particle in the presence of charges and currents experiences
a force due to electric (E) and magnetic (B) fields. Is
is described by the Lorentz force:
$$F = e (E + v × B )$$
where e is the charge of the particle and v is the instantaneous velocity of
the particle.
If we use the units of the International S... |
When a conductor is placed in some external electric field, why can't the free electrons just escape out of it? Is the positive charge distribution on the opposite side(surface) always strong enough to resist the electrons from escaping... and make they stay at the surface? Or is there much more to it?
Let me clear my ... |
Is it possible to define discrete (informational) Gibbs free energy
by analogy with Shannon entropy?
This is about cellular automata, in particular on a network.
We can easily calculate entropy of their states using Shannon's formula.
I'm interested is it possible to calculate somehow Gibbs free energy?
|
The curvature of a gaussian beam is usually given by
$$R(z)=z\left(1+\left(\frac{z_r}{z}\right)^2\right)$$
with $z_r$ the Rayleigh length. Is there a limitation for that curvature (similar to usual beam propagation methods such as the NLSE) depending on the focusing angle/NA of the lens which is focusing the gaussian b... |
By definition from Wikipedia, the beam splitter (BS) operation $U_{BS} = \begin{pmatrix} t & r \\ r & t \end{pmatrix} = \begin{pmatrix} \cos\theta & -i\sin\theta \\ -i\sin\theta & \cos\theta \end{pmatrix}$, and the rotation matrix $R=\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}$. N... |
I saw some videos on Youtube like this one from "Join the technicians" and this one from "Electroboom". The videos show an application of static electricity. In school, we were taught that we can generate static electricity with a triboelectric effect with a Van de Graaff generator. However, in those videos, they all u... |
The Heisenberg Uncertainty Principle is often written in two forms:
$$\Delta x \Delta p \geq \frac{\hbar}{2} $$
and
$$\sigma_x \sigma_p \geq \frac{\hbar}{2}. $$
Are these two equivalent? I've been told they are, but it doesn't make sense to me. For instance, in an infinite square well, $\Delta x = $ the width of the we... |
As the phase modulator, can electro-optic amplitude modulator generate sidebands?
I'm really confused now...
Please help me out.
|
Consider the commutator
$$\left[\hat{a},\sqrt{1-\hat{a}^\dagger\hat{a}}\right].$$
Because $\hat{a}^\dagger\hat{a}=\hat{n}$ is the familiar number operator, and $[\hat{a},\hat{n}]=\hat{a}$, I would expect that there is a simple expression for the commutator above. However, I don't see it, and writing out the square root... |
A generic $3\times 3$ Hamiltonian can be expressed in terms of eight Gell-Mann matrices ($\lambda$) as
\begin{align}
{\cal H} &= h_{0} I + H= h_{0} I + \sum_{\alpha=1}^{8} h_{\alpha} \lambda_{\alpha}, \\
{\cal H}|n \rangle &=( h_{0} + \epsilon_{n}) | n \rangle \qquad \text{For } n\in \{1,2,3 \},
\end{align}
where I... |
According to my physics book, one can use the following laws to identity the magnetic field:
div B = 0
rot B = μ0J
My book also states that, given a specific current density vector, many magnetic fields can satisfy the laws above, in corrispondente to the same current density vector. Esch field can be identified up to ... |
Imagine if we have a hollow bar magnet and we are trying to draw directions of magnetic field lines using a magnetic needle. The north of magnetic needle always points in the direction of the net magnetic field. Now, when we are inside the magnet, the north of the magnetic needle would point towards north and south tow... |
Let's consider the so-called Master formula, which expresses the cross-section of interaction between two protons, taking into account the parton density function and the intrinsic cross-sections between two partons, for example found here:
Where is the distance between the two particles that come in two opposite dire... |
What is physics behind counter-steering? When we drive bike, in order to achieve a sudden left turn, we turn the handlebars quickly to the right, and vice-versa. What is the physics behind it.
|
If relativity tells that from a moving charge's frame (observing current carrying wire) protons contract in length and its charge density increases making the charge experience a electrostatic force. In lab frame (observing current carrying wire and a stationary charged particle) the electrons are moving in wire, will ... |
I am studying the paper "Gravitational field of a particle falling in a Scharzschild geometry analyzed in tensor harmonics" by Zerilli. The author calculates the gravitational radiation emitted by a particle falling along a geodesic into a Schwarzschild black hole.
The stress energy tensor of the particle is:
$$T^{\mu\... |
One of the reasons why we can neglect electron-electron interactions in metals is the fact that their coulomb interaction is screened. I'm confused about the nature of this screening. In the literature the process is usually described like this:
If we bring an additional charge inside a neutral metal, the coulomb poten... |
I’ve read that short circuiting means that a huge amount of current flows through the conductor in an extremely small period of time.
Also, resistance increases with temperature for conductors, right?
So if temperature increases, resistance increases. Which would mean the current doesn’t have an easy path to flow throu... |
So assuming Einsteinian relativity is a bust, did any physicist thought through properly how a Galilean/Newtonian universe would work? Of course there are infinite ways of how it could, but one is already more than I have.
I search about this topic every once in a while, but Google never seems to turn up good results, ... |
The figure shows a light rod of length $l$ rigidly attached to a small heavy block at one end and a hook at the other end. The system is released from rest with the rod in a horizontal position. There is a fixed smooth ring at a depth $h$ below the initial position of the hook and the hook gets into the ring as it reac... |
We have seen CD drives that have slits. The CD gets drawn inside upon a gentle
push. how the CD gets drawn inside upon a gentle push? How it's mechanism works?
|
I think that the surface charge density is more appropriate as the cylinder, unlike a rod, does have a surface. However if I look at textbooks like Halliday or even stuff on the internet it seems everyone uses the linear charge density. Why is it so?
Example photos
|
Why is there no electric field in the hollow space of the dees of a cyclotron though it is open at one face?
Is electrostatic shielding applicable for space(hollow space) inside open conductors(like dees) also?
|
When they talk about the arms of LIGO or Virgo stretching by a thousandth of the width of a proton, they always emphasize that this is the wave's amplitude, not wavelength...
The wavelengths are apparently quite long, with correspondingly low frequencies... Articles usually explain what this means in terms of what is g... |
What will be the sensible extension of the 2D Ising to some curved surface - for instance, for a sphere or even something non-orientable?
For the flat space energy is given by well-known expression:
$$
E = \sum_{i, j} J s_i s_j + \sum_ih_i s_i
$$
What would make sense for the curved surface, should I imagine the spin a... |
How to derive the force between two parallel current carrying loops?(current flows in the same sense,say clockwise,in both the loops)
Radius of both the loops is R and each has a current I flowing through it.Both the loops are at a distance of 'd' from each other.
|
The most general form of the Noether's current (see here and here) is given by $$j^\mu(x)=\sum\limits_a\frac{\partial \mathscr{L}}{\partial(\partial_\mu\phi_a)}\delta\phi_a -\theta^{\mu\nu}\delta x_\nu-K^\mu\tag{1}$$ where $$\theta^{\mu\nu}=\frac{\partial\mathscr{L}}{\partial(\partial_\mu\phi)}\partial^\nu\phi-\eta^{\m... |
The conservation equations for the fluid mechanics of an ideal gas are \begin{align*}\dot{\rho}+\nabla \cdot (\rho u)=0 \;&\text{(mass conservation)} \\ \dot{(\rho u)}+\nabla \cdot (\rho u u) + \nabla p=0 \;&\text{(momentum conservation)} \\ \dot{(\rho e)} +\nabla \cdot (\rho ue+\rho p + \rho Q)=0 \;&\text{(energy cons... |
I want to find the moment of inertia for a cylindrical segment, show below:
On Wolfram MathWorld, I found a formula for the volume of a cylindrical segment. Let
$$h(r,\theta) = h_1 +\frac{1}{2}\left(1+\frac{r}{R}\cos(\theta) \right) (h_2-h_1)$$
Then
$$V =\int_0^R \int_0^{2\pi}\int_{0}^{h(r,\theta)}rdzd\theta dr$$
Note... |
I believe that the reason acceleration isn't measured as change in per unit distance but instead is measured as change in per unit time is because of the following reason :
Time is not geometrical. It either increases or decreases constantly and can be considered like a straight line. But whereas distance is similar to... |
My rudimentary understanding of dark energy as the cosmological constant is that the vacuum state of space has positive energy but negative/repulsive gravity/pressure.
Given a system dominated by "positive" gravity like a planet or solar system, "positive" gravity wins out and the system doesn't expand.
But in deep spa... |
Suppose we have 1D crystal of several types of atoms.
How many fundamentally different structures exist?
The obvious are the grid and the random distribution.
Substitution system A -> ABA, B -> BBB
produces approximations to fractal Cantor set.
According to Salvatore Torquato, distribution of non-trivial zeros of Riema... |
I'm hoping to get some clarification in the use of conservation of momentum in a 3D system. Say you have a rocket with some velocity $v_1$ and mass $m_1$. At time $t$, the rocket breaks into two separate pieces such that each piece has masses $m_2$ and $m_3$ (not necessarily equal) and at times $t+dt$ ($dt$ very small)... |
Let's say I have a system with two degrees of freedom and I can find two independent action variables. One action variable is total energy expression, such as is often used in classical mechanics.
$$E(p,q) = T(p,q) + V(p,q)$$
where $T$ is kinetic energy and $V$ is potential energy.
In $(p,q)$ coordinates, the Hamilton... |
When calculating the selection rules for electronic transition in the hydrogen atom in dipole approximation, we always focus on the angular integrals. But why the integral
$$
\int_{0}^{\infty}[rR_{nl}(r)]R_{n'l'}(r)r^{2}dr
$$
(where $n\neq n'$ and $l\neq l'$)
always gives a non-zero result, so we don't have any selecti... |
If a parabolic mirror is used to concentrate sunlight approximately to a focus point why can't an another smaller parabolic mirror be used to reparalelise the beams that are leaving the focal point and depending of the area cross-section finaly get all possible desired densities of the reparalelized beam? Although tha... |
Could we in theory change atoms on an atomic level (Think 5 protons, 5 neutrons -> 4 protons, 4 neutrons), and if so could we then use those protons, and neutrons to add to another atom? (3 protons, 3 neutrons -> 4 protons -> 4 neutrons)
|
Consider the simplest such system: a gas-filled chamber. I understand that, were all the gas particles concentrated in one corner, the entropy of the chamber will be lower than the entropy of the same chamber but homogenized. If so, the two states do not actually represent the same macro-state, hence we will never expe... |
I've read several times that if a discrete symmetry is spontaneously broken, then there exist domain walls that interpolate between the different vacua. However, Weinberg says that if the former happens, then we may have these domain walls.
Is there any case such that we have spontaneous breaking of a discrete symmetry... |
I know that voltage is the difference in electric potential energy between 2 points and that a higher voltage means more energy for a coloumb of charge (ie a 9V battery means 9 joules per coloumb). But how does increasing the voltage mean more current?
Why does increasing the potential difference mean more current?
|
I just started learning quantum physics and there is a particular notion confusing me.
While reading McIntyre book, he suggests I find the matrix representation of the $S_n$ operator, which is the operator for the spin component allong a general direction $\mathbf{\hat{n}}=\mathbf{\hat{i}}\sin\theta\cos\phi+\mathbf{\ha... |
The concept of relativistic mass is considered outdated and when people refer to mass now, it's the invariant or rest mass. If I understand the idea correctly, back in the day people tried to rewrite the relativistic momentum equation - $p=\gamma m v$ - as follows - $p = m_{relativistic} v = \gamma m v$ - to make it lo... |
I hope my question will be understandable. I wonder about the sinusoidal shape of an electromagnetic wave. I have the impression that something fundamental is behind this shape. To simplify things, let's put ourselves in the case of a single electromagnetic wave. Is the curve of an electromagnetic wave always sinusoida... |
According to me they don't reach their respective homes P and Q at the same time because the points at which they reach their home clearly don't coincide. Yet the solution given is that they reach their homes at the same time. How is this possible? It looks like A takes more time to reach than B.
I was able to solve t... |
This is a naive question about a shower thought, but perhaps someone could indulge me since I don't understand the physics at a sufficient level to know why it would not work.
Could the electromagnetic acceleration and deceleration of a rotating physical masses be used as a method of propulsion for a spacecraft? Since ... |
While taking my physics classes, I used to think that the formula mgh calculates the gravitational potential energy of a single object h distance off the ground.
Recently, I learned however that it is unreasonable to talk about the gravitational potential energy of a single object. So mgh actually calculates the gravit... |
A DM (dungeon master) is developing a game from the book "A Mote in God's Eye" and would really like to have a D3 die (left hand, right hand, gripping hand). One could use a six-sided die and just devote two sides to each choice, but the DM really wanted a die that had only three sides.
Then the DM realized that a coi... |
Usually in systems with ferromagnetic order, the spin $\mathrm{O}(3) = \mathrm{SO}(3) \times Z_2^t$ (where $Z_2^t$ represents time-reversal) symmetry is broken down to $\mathrm{SO}(2)$. Is it possible to have a spontaneous symmetry breaking phase where the residual symmetry group is $\mathrm{SO}(2) \times Z_2^t$ instea... |
I'm trying to understand what parameters uniquely define the state of a photon, and I can't seem to find a straightforward reference anywhere. Wikipedia is either unclear here, or over my head.
If you were to restrict yourself to parameters that are integer-valued or real-valued (if this is possible), how many paramete... |
I am totally stuck over this concept and google doesn't help.
First, We say that light's speed is constant for all colors in vacuum but different in all other media. Then which color's speed are we referring when we say that light's speed in that medium (like glass) is c divided by refractive index? Is it average of al... |
The formula for change in potential energy of a system made up of object A and B is:
change in potential energy of system = - (dot product of [conservative force vector of A on B] and the [displacement vector of B])
But what if we instead consider:
change in potential energy of system = - (dot product of [conservative ... |
We shipped a container of wet wipes packages by sea and when the container arrived to the port it was unloaded and the packages were verified to be ok.
Then, it was loaded to a truck and shipped to a 2,200 meters (7,200 feet) area in a 8 hours drive.
When the truck unpacked the packages in the final destination all the... |
Assuming that no-hair theorem is correct, can the position of a massive body under the black hole's event horizon be communicated through the change in the space-time curvature gradient surrounding the black hole?
If the answer is "yes", isn't this conflicting with the statement that no information from under the horiz... |
In section 15.1 of Peskin and Schroeder, expression (15.9) is given for the comparator $U(y,x)$ in an infinitesimal expansion to second order:
$$U(x+\epsilon n, x)=\exp \left[-i e \epsilon n^{\mu} A_{\mu}\left(x+\frac{\epsilon}{2} n\right)+\mathcal{O}\left(\epsilon^{3}\right)\right]$$
This uses the assumption that $U(y... |
First, I apologize for the long preface to my question. The actual question is in bold below.
In Kardar's Statistical Physics of Fields, on page 10, the author writes, "the free energy of the system is an analytical function in the $(P,T)$ plane, except for a branch cut along the phase boundary." While the above commen... |
Potential is defined as $\{\phi,\, 0,\, A,\, 0 \}$; fields are static and depend only on the axial coordinate $x$: $E_x=-\partial_x\phi$, $B_z=\partial_x A$. Charged particle moves in the $\{x,y\}$-plane, where $y$ is a direction of drift-motion.
There are two constants of motion:
$\frac{m}{2} \left(v_{x}^{2} + v_{y}^{... |
Can I make light dig a hole by increasing it's frequency? Can I relate force with wave using the equation $c=$ wavelength$\times$frequency?
|
This question refers to equation (11) in the latest preprint of the following paper:
X. Han, S. A. Hartnoll and J. Kruthoff, "Bootstrapping Matrix Quantum Mechanics", Phys. Rev. Lett. 125, 041601 (2020), arXiv:2004.10212.
The authors give an expression for the generator of the ${\rm SU}(N)$ symmetry:
$$G=i[X, P]+N I$... |
Shouldn't strangeness and charm be essentially the same quantum number, the eigenvalue of the family operator for family #2 of the quarks, and similarly for top and bottom, for family #3? It appears that the differing names are just a convenience in distinguishing them due to the widely differing masses between the tw... |
What is a naked singularity? Would a naked singularity be one that that the event horizon is so small that it is the same size as the singularity? what could make one that small?
|
Is dark matter bound by all the laws of regular physics?
i.e. laws of thermodynamics, speed of light, length contraction, mass-energy relation.
What about Newton's laws of motion (since all of Newton's laws assume an interaction between particles)?
|
All explanations of Terrell-Penrose effect seem imply that the effect makes some of the back-facing walls of a passing-by object visible. You can see some examples of those in many different references. However, from my understanding many of those sources assume that the light reflect or emitted from the surface travel... |
Does a star disappears from space time, if it spins faster than light?
|
I am trying to review my basic quantum and I somehow ended up with this expression:
$$
\frac{\langle m | \partial H | m \rangle}{\langle n | \partial H | n \rangle}
\frac{\langle m | \partial H | n \rangle}{\langle n | \partial H | m \rangle},
$$
where $|m\rangle$ and $|n\rangle$ are eigenstates of $H$, and $\partial$ ... |
In this question, the top answer gave a seemingly good description of the particle interaction, but what exactly the interaction is seemed to be left unstated.
I've only the most rudimentary comprehension of the fact that particles are not little billiard balls, but once that metaphor is removed, the notion of particle... |
I was wondering why $F=-\frac{dU}{dr}$ would give me a vector quantity when a scalar quantity is differentiated. There are similar pre-existing queries but I think this issue has yet to be properly addressed.
|
I am learning quantum field theory.
Now I am considering this case:
Suppose a spin-0 particle which obeys the Klein-Gordon field equation and its anti-particle obeying the same equation do not have the same solution to the equation. This means that the field should be a complex scalar field. Hence the field operator sh... |
So, in quantum field theory, how can one describe dynamics of a system of particles? According to what equation does this system evolve? Can one see how this system is moving through space? Is this described by equation of motion for a quantum field or by dynamics of many particle states? In QFT books there is much tal... |
Question:
Describe what will happen to two solenoids that are arranged next to each other as shown. The solenoids are the same length, and have the same number of turns and current flowing through them. Explain your reasoning.
Using the right hand grip rule for solenoid, that is, curled fingers represent the conventio... |
The adjacent figure shows a thin plano-convex lens of refractive index $μ_1$ and a thin plano-concave lens of refractive index $μ_2$, both having same radius of curvature $R$ of their curved surfaces. The thin lens of refractive index $μ_3$ has radius of curvature $R$ of both its surfaces. This lens is so placed in bet... |
As is proven, light can be bent by a heavy mass in the context of classical General Relativity. In a quantum theory of gravity, the gravity field around a heavy mass consists of a condensate of (virtual) gravitons, contrary to the GR case, where a static field is just a non-changing distortion of spacetime.
Because pho... |
When a process has no tree-level contribution to the amplitude but occurs e.g. at 1-loop level it is said to be loop-induced. One property of loop induced processes is when you calculate the amplitude there are no counter terms from renormalization. Therefore the amplitude is "inherently finite", why?
|
Now I am taking a quite a specific example here. Let's consider a circular race track banked at an angle of $\theta$. The coefficient of friction between the track and the tire is $\mu$. What's the maximum speed that the car can achieve without skidding out?
Now to solve this problem we draw the car's free body diagram... |
Let say we see a light source with apparent cross section area 1mm squared. If we position a flat slab with inductive high light sensibility at a very small angle to that source one dimension of the source is elongated on that slab so the 1mm of the source length is spread as let say 10cm on the slab. After that operat... |
In classical Mechanics it is possible to prove that the total Energy $E = T + V$ is conserved if the force is conservative. However, if you assume the mass is time-dependent this proof no longer holds:
\begin{align}
\frac{dE}{dt} = \frac{d}{dt}(\frac{1}{2}m\dot{\vec{r}}^2 + V) = \frac{\dot{m}}{2}\dot{\vec{r}}^2+m\do... |
Not sure if I worded the question properly, but my question is about an image shown in Your Daily Equation #17 by Brian Greene
He shows the following image:
Where
red is the case $v = v_c$ and
green is the case $v_c < v < v_e$
with $v_c$ meaning the velocity required for circular motion and $v_e$ the escape velocity.
... |
My understanding is that s and p polarisation of light will have a different angle when diffracted by diffraction gratings. In wikipedia it says that "According to the Huygens–Fresnel principle, each point on the wavefront of a propagating wave can be considered to act as a point source, and the wavefront at any subseq... |
The probability for a gas molecule to have any velocity $v$ is $0$ since there are infinite possibilities for the velocity for the gas molecule to have.
If that's so then how come the gas molecule has any velocity at all ,since according to probability there is $0$ probability for every velocity.
More confusion: How ca... |
I'm building an autonomous boat, to which I now add a keel below it with a weight at the bottom. I was wondering about the shape that weight should get. Most of the time aerodynamic shapes take some shape like this:
The usual explanation is that the long pointy tail prevents turbulence. I understand that, but I haven'... |
I was wondering if anyone knew of a reference which treat time-independent perturbation theory in a mathematical fashion. All of the mathematical textbooks in quantum mechanics that I know of do not treat this subject. I am hoping that such a reference would treat:
Perturbation theory of the pure point spectrum in a m... |
Is it possible for a hydrogen spectrum to show doublets and triplets?
My guess is that it is impossible as triplets and doublets are caused by the transition of electrons in having the same principal and azimuthal Quantum Numbers but different Magnetic Quantum Numbers (tell me I am right), but in the case of hydrogen s... |
My question refers to example theory introduced in the book "Supergravity" from D.Z.Freedman & A. van Proeyen p.80. Its Lagrangian is given by
$${\cal L}(Z,F) =-\frac{1}{4}(Im Z)F_{\mu\nu}F^{\mu\nu} -\frac{1}{8}(Re Z)\epsilon^{\mu\nu\rho\sigma} F_{\mu\nu}F_{\rho\sigma}=-\frac{1}{2}Im(Z F_{\mu\nu}^- F^{\mu\nu-})$$
where... |
What exactly is an oxygen defect in a semiconductor / crystal lattice structure?
Is an oxygen at a wrong place or is it missing somehow?
|
The following is the description for this figure provided by my textbook:
The paths of different types of radiation in a magnetic field. Using the right-hand slap rule, we see that positively charged particles are forced to the right. [...]
Why are the positively charged particles going to the right? I think there i... |
Equally spaced discrete harmonic oscillator levels, called Landau levels, are obtained for noninteracting electrons in 2D in presence of a magnetic field applied perpendicular to the plane. The Landau levels are highly degenerate and the energy eigenfunctions can also be obtained exactly.
In practice, however, the elec... |
Consider a hypothetical ball of mass -1kg .It is released from air .now will the ball go up or down towards earth?
my approach: since $\vec{F}=-\frac{GMm}{r^2}\hat{r}$ hence getting an extra minus sign should make the force repulsive, however it is said that gravitational force is always attractive in nature. Although... |
There are lots of questions here related to the spin-statistics theorem, though none of them answer this question directly.
I had the notion that one can only prove the theorem on relativistic grounds and for example the Wikipedia page on the subject list Lorentz invariance as one of the assumptions needed to prove the... |
The two point correlator of Quantum H.O. of natural frequency $\omega$, calculated using path integrals, is
$$C_{2}=D\left(t_{2}-t_{1}\right) \propto \int \frac{d w^{\prime}}{2 \pi} \frac{e^{-i w^{\prime}\left(t_{2}-t_{1}\right)}}{w^{\prime2}-w^{2}}\tag{1}$$
which evaluated using contour integral in complex plane, come... |
TL;DR: Why can't we write $\mathcal{L} = E - 2V$ where $E = T + V = $ Total Energy?
Let us consider the case of a particle in a gravitational field starting from rest.
Initially, Kinetic energy $T$ is $zero$ and Potential energy $V$ is $mgh$.
At any time $t$, Kinetic energy $T = \frac{m\dot x^2}{2}$ and Potential energ... |
While I can easily grasp the mechanism of energy absorption by the atom system resulting in a jump of the electron to a higher energy level, i.e. receiving energy from the outside in the form of a photon, I cannot really understand why would an electron be interested, or be compelled to go back to lowest energy level a... |
I'm trying to quantify some intuition I have about friction and rocket sled.
Suppose a rectangular sled with length $l$, weight $W$ on a surface with friction coefficient $\mu$. A rocket attached height $h$ from the ground on the middle of the sled exerts force $H$ causing the sled to accelerate, call the right pad Pa... |
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