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I am reading Quantum optics textbook of Peter Knight.
From the Eq 4.3
$
\hat{H} = \frac{1}{2m}[\hat{P}+e\hat{A}]^2-e\Phi + V(r)
$
Using
$
\hat{H}' = \hat{R}\hat{H}\hat{R}^{\dagger} + i\hbar\frac{\partial \hat{R} }{\partial t}\hat{R}^{\dagger}
$
where $\hat{R}$ = exp$(-ie\chi(\vec{r},t)/\hbar )$
The Hamiltonian is modif... |
I am reading A. Zee's book Einstein Gravity in a Nutshell and encountered this definition of a vector on page 43:
An array of two numbers $p = \begin{pmatrix}
p^1 \\
p^2
\end{pmatrix} $ is a vector if it transforms according to $p' = R(\theta)p$
and then he proceeds to give an example that $\begin{pmatrix}
ap^1 \\
bp... |
First a simple example to illustrate the essence of the question: If we have a spin half particle in the $S_z+$ state and if one wants to choose from either measuring $S_z$ or measuring $S_y$, which are incompatible, one could execute one of two complementary actions: ''Orient the magnets in the z direction'' or ''... |
Let's say I have an ideal gas in a cylinder with adiabatic walls. This cylinder has a piston (thermally insulating as well) in between dividing the volume in half. If I have a heating coil in one portion, causing the gas to expand, what happens to the pressure and temperature of this gas? I feel like this process could... |
Are there any textbooks, or good pedagogical review articles, on the subject of parton distributions? I'm looking for such sources that cover all the standard topics, such as:
Generalized parton correlation functions
distribution functions
distribution amplitudes
form factors
TMDs, and TMD factorization
On the lattice... |
The expression $\,\mathbf F_\mathrm G\boldsymbol{=}m\, \mathbf G\,$ and $\,\mathbf F_\mathrm E\boldsymbol{=}q\, \mathbf E\,$ make sense, but is there any derivation for $\,\mathbf F_\mathrm B\boldsymbol{=}q\,\left(\mathbf v\boldsymbol{\times}\mathbf B\right)$?
|
I had an argument with contributor @safesphere regarding this problem. He insists that an infinitely large plate with a finite surface density of $\sigma$ would eventually collapse into a black hole because the mass tends to infinity as well as the plate's spatial dimensions. He believes that an infinite plate that doe... |
In 2D (time + space) there is no notion of statistic. So particles can be described in terms of bosonic and fermionic fields.
Well-known example is Thirring/Sine-Gordon duality. There are also some examples: $\phi^4$ theory kinks as fermions?
Are some examples of application of bosonization in supersymmetry?
Is it po... |
Consider 2D motion of a particle,
For a particle to move in a circle there must be a force of constant magnitude acting on it always pointing towards the centre of the circle.
Similarly for an ellipse there must be a force acting on it with a magnitude inversely proportional to the square of the distance from one of it... |
I have just started learning about a topological Dirac semimetal. Then I'm wondering that the Dirac point always crosses the Fermi energy in a topological Dirac semimetal. If the Dirac point does not cross the Fermi energy, does the band structure indicate that the material is not a Dirac semimetal? And I want to know ... |
What i mean by the question is this:
If derive a formula using some simple observations and I receive a unit for that formula that I cannot intuitively understand it as I can for e.g. the speed of an object or its acceleration or even the force applied to and object, but I get such a unit which is a combination of SI u... |
I am trying to figure out the mass and/or volume of liquid inside a sealed plastic bag of about 150 litres (1x0.6x0.3m) without being able to use a weighing scale. Preferably, the measurement devices or method is placed on the exterior of the enclosed volume. Throughout the day, the bag fills up with water and when it ... |
In the lecture available here, at around 1:36:50, Susskind seems to argue that you can derive the fact that the gravitational field inside a spherical shell (of constant density) is 0 from the divergence theorem. I don't see how this argument works at all. All you get is that the divergence of the gravitational field i... |
From Newton's second law, a charged particle driven by a constant electric field should move with a constant acceleration. But electrons in a circuit acquire a steady average velocity which gives rise to a constant steady DC current. Of course, the electrons scatter with phonons and other defects leading to energy diss... |
The outgoing long wave IR spectral radiance graph by wavelength shows the spectral radiance of IR increasing as wavelength goes from 5 microns to 10 microns but the energy of oscillation goes down over the whole spectrum from gamma rays to radiowaves. What is the diff between energy of oscillation and spectral radiance... |
I'm searching for those values, but usually they are given at very low temperatures, usually 77K or 4K. I'm looking mostly for bulk values.
I was thinking of applying Vegard's law to AlAs and InAs... but I prefer more empirical data.
|
In TASI Lectures on Emergence of
Supersymmetry, Gauge Theory and String in
Condensed Matter Systems some continuous limit of lattice model with fermions considered. And on page 6 there is a statement:
The fermions are massless without any fine tuning, which is protected by
the time reversal symmetry and the inversion ... |
Given the time evolution operator $U(t, t_0)$, I don't understand why it is true that for a time-independent operator Q,
$$[Q, U(t, t_{0})] = 0 \Leftrightarrow [Q, H(t)] = 0 $$
where H is the Hamiltonian.
|
If an untouched (an object whose wavefunction has never collapsed) charged mass has a probability cloud of radius $3*10^8 m + \Delta x$ after one second of observing, shouldn't the mass associated with it also have a probability cloud of radius $3*10^8m+\Delta x$.(e.g electron)due to the combined effects of QM and GR... |
Thought experiments are very common in Special and General Relativity (SR,GR). Usually a thought experiment is structured as follows:
We present a setup in a frame of reference
We apply principles of SR or GR to derive what must happen
We then shift perspective to another frame of reference
We state that both observer... |
For full reference, refer to https://www.feynmanlectures.caltech.edu/I_20.html#Ch20-SUM
Here's the quote that I think is relevant to the question:
'Consider a wheel that is fastened onto a shaft in a lopsided fashion, but with the axis through the center of gravity, to be sure (Fig. 20–6). When we spin the wheel aroun... |
I have a question concerning the Fermi-surfaces of a square primitive cell with 2 and 4 valence electrons.
Consider these two plots, where the upper plot is for 2 valence electrons and the lower for 4:
The way I understand it is that in the upper plot, the white area in the middle circle is for 1st zone electrons. Ho... |
I understand that the accuracy of a reading/measurement is primarily dictated by systematic error and so the accuracy of your results can be improved by removing the source of the systematic error. However, I have heard mixed guidance on whether the accuracy of your readings/measurements can be improved by taking a mea... |
What is the tension required for a rope with a finite mass per unit length, hanging between two fixed equal altitude points under gravity, so that the rope is perfectly horizontal (without any "slack"). Assume other properties of rope such as elastic constant, total mass, length, mass per unit length to be finite. And ... |
I've wondered about that for a while but all I read is commonly just "Warm/hot air has a higher energy so when it hits the surface of a liquid, it has a higher probability to transfer energy, resulting in water molecules leaving the liquid".
Though it makes sense, I don't think that is actually a reason. It only decrib... |
I came across some analogous structure of diffusion and the quantum mechanical particle (Schrödinger eq.). I have seen that there have been similar questions asked, but the (probablitily flux and the mass/particle conservation was not adressed in those).
In diffusion the particle flux $\vec{j}(\vec{r},t)$ is related to... |
I am facing form this problem that why the electron flow in the opposite side of the electric field
|
I was reading the chapter about optical fibers of "Fiber - optic communication systems" and I have read this statement:
The fraction of the power contained in the core is given by the
confinement factor. Although nearly 75% of the mode power resides in
the core for V = 2, this percentage drops down to 20% for V = 1.
... |
The time evolution of a quantum mechanical operator $A$ (without explicit time dependence) is given by the Heisenberg equation
$$ \frac{d}{dt}A = \frac{i}{\hbar} \left[H,A\right] \tag{1}$$
where $H$ is the system's Hamiltonian. The time evolution of the corresponding expectation value is given by the Ehrenfest theorem
... |
I got dry ice, so I made a diffusion fog and tried to shoot the track. So I created a diffusion fog box with the following steps:
I prepared a circular plastic container with a radius of 6 cm.
Next, a sponge soaked with ethanol was attached to the top of the container.
I made a few mm hole in the container and put in ... |
We know the earth has both gravity and magnetism (which is very weak). Geomagnetism starts at the south pole and ends at the north pole. If I take a large sheet of superconducting material (very thin and several kilometers in area) and place it on the south pole will it levitate? I am not discussing antigravity.
|
If it CAN attract permanently then it can continuously give kinetic energy to magnetic objects by attracting them. I found answers about this stating that WE supply potential energy to the magnetic materials by pulling them apart from the magnet. But, where did they get the energy in the very starting? Suppose that if ... |
I have seen derivations of the the length scale, time scale and characteristic velocity of eddies in the inertial or large-scale range and in the diffusive or Kolmogorov scale range. I'm interested in the region in between, which Alistair Revell in his video titled “Advanced CFD Course: Turbulence Scaling” calls the T... |
Take a capillary tube (glass) of diameter $d_2$ dipped in water vertically. Now a glass rod with diameter $d_1$ is inserted in the tube. Find the height to which the water rises. Take contact angle to be 0.
Now, one approach to this problem is equating the force due to the surface tension to the weight of the liquid c... |
I would like to implement a model of the force/uplift the floor makes in a multicopter take-off, but I don't find any info of this exact dynamic.
Is there any paper that tackles this issue? Or any other similar approximation?
My final interest is to make a simple model, not so much as a full air particles simulation ty... |
In general relativity without matter, the equation of motion of the metric field is described by the Hilbert's action or the Einstein tensor $G$. It's natural to lead to this conclusion once one realizes how natural the Riemannian scalar curvature is. In short,
scalar curvature ==> Einstein tensor $G$
Enter the... |
I'm having trouble finding a simple answer to this question (maybe because there isn't one), but I'm just confused about how the Schrödinger Equation would look for two electrons. I understand that it would exist in 6 dimensional configuration space, but how does the potential look? It's confusing that the potential wo... |
From what I have read here, the concept of spin is attributed to a calculation based on a mathematical model using quantum mechanics. For example,
How can a particle with no size have angular momentum?
The experiment by Einstein and deHaas
https://www.dwc.knaw.nl/DL/publications/PU00012546.pdf
https://en.wikipedia.org/... |
Considering that the luminiferous ether exists around earth, if all electrodynamics experiments are done in earth frame how do we know that the speed of light $c$ we calculated from it is not $c$ with respect to the earth?
This Statement is from Griffith's book of Electrodynamics
If Maxwell’s equations are valid only ... |
I am following the following lecture notes: http://web.mit.edu/6.763/www/FT03/Lectures/Lecture9.pdf
In the last slide, we see how a gauge change for the EM field impact the phase of the wavefunction. I remind:
$$ \psi(x,t)=\sqrt{n(x,t)}e^{i \theta(x,t)}$$
$$ \mathbf{J}=qn(x,t) \left( \frac{\hbar}{m} \mathbf{\nabla}(\th... |
Consider the given arrangement of infinite uniform discs$A_1,A_2,A_3,...,A_n$, each of mass m and radius R. Each disc is kept on a stair. Height of each stair is R. Strings are wrapped around discs whose another end is attached to center of discs as shown. All surfaces are sufficiently rough, so that there is no slipp... |
So, one of my homework problems reads the following
Let $A$ and $B$ be commuting operators and $| \psi_i \rangle$ denote the eigenfunctions of $A$. Show that $\langle \psi_i |B| \psi_j \rangle=\delta_{ij}$
I have tried to approach the solution in the following way:
Since $A$ and $B$ commute, we have, for any vectors ... |
There are multiple ways I have found to map spin operators $S^+=S_x+iS_y,\quad S^-=S_x-iS_y,\quad S_z$ onto bosons.
most trivial: a spin-1/2 system is equivalent to bosons with hard-core interactions (as well as fermions), comprise also a two-level system. This mapping is often associated with a Jordan-Wigner transfor... |
To get straight to the question, skip to the 'This is what spherical symmetry really means' paragraph.
I recently inquired about the shell theorem but this is a different matter (link), so I hope it is ok to make a new post. There is an elegant way of deriving the shell theorem by taking advantage of the spherical symm... |
Is a qutrit considered to be in a state of tripartite entanglement?
|
Context:
I wish to know how to get the magnetic field strength (H) in a surface point of the condenser made by 2 circular plates separated by a dielectric which is a perfect insulator with a uniform field (D), assuming that it's an ideal condenser.
My work so far:
I think that I can use Maxwell's version of Ampere's l... |
Second the Gell-Mann and Low theorem, if a quantum system has a hamiltnian $H = H_{0} + V$, and $H_{0} | \Phi_{0} \rangle = E_{0} | \Phi_{0} \rangle$, then the following quantity
$$
| \Psi \rangle = \lim_{\epsilon \rightarrow 0} \frac{U_{\epsilon}(0,-\infty) | \Psi_{0} \rangle}{\langle \Phi_{0} | U_{\epsilon}(0, -\inft... |
I'm just trying to develop a picture in my head for what happens when two quanta interact with one another. Say we had two perfectly localized electrons some distance apart, how does the wavefunction for the system "look" as time progresses.
|
A block P of mass $m_{1}$ in on a frictionless horizontal plane and a block Q of mass $m_{2}$ is always on top of P. Initially P and Q are at rest. At time t=0, an initial speed $v_{0}$ is given to P in the rightward direction. Then Q also starts to move. When a time T is passed after P is given an
initial speed, the ... |
In our perceiveable world, an increment of speed typically results in needing less time to travel a given distance. When I go by car, it takes less time then going by bike. However, there is the timeparadoxon. It means, if someone could travel with a speed all close light speed, he would go to his destination and back ... |
If a permanent magnet is dropped down a vertical copper pipe, it eventually reaches a terminal velocity even if there is no air resistance. Why should this be?
|
If the energy of the light falling is not equal to the difference between any two orbitals of the atom then the electron absorb the light but re-emit it either through the object or reflect it backwards. Bit what determines that the re-emitted light would be transmitted or reflected?
|
Why is laser beam monochromatic and coherent?
My reasoning: Laser is monochromatic because there is equal energy difference between metastable and ground states.
Laser is coherent because there is no time and path differences between wave-fronts of any two directions (beams).
I am not sure if my reasoning is correct.... |
So my friend took a physics exam and one of the questions on it has me confused (It has been a long time since I have taken physics). The question was worded very badly (I had to translate from Spanish to English) and had incorrect formatting... but from what I can gather, the question asked:
There are 2 isolated south... |
My professor worked out this problem and I'm confused with the use of radius.
The hemisphere has a radius $a$. The charge density if a function where $\rho = Ar\cos^2(\theta)$ using spherical coordinates. You solve for $q$, with $dq = \rho\ dV$. You place this value into voltage from a point charge and solve? There is ... |
I am supposed to find the equivalent capacitance of the given arrangement of capacitors (between A and B) I have figured out that I get the correct answer if I assume that the middle row of capacitor is shorted i.e no charge accumulates on them . But I am unable to find an appropriate and rigorous explanation for this... |
Physicists will say that a certain system has $G$ symmetry, where $G$ is some group, such as $SU(2)$ or $S_3$ or whatever. To show that this is the case, they will conjure up an explicit representation $\rho_G$ of that group and show that the equations of motions—or the action, or whatever—are still the same. But a gro... |
I am looking at simple harmonic oscillators. The maximum potential energy is equal to the maximum kinetic energy:
$k {x_{max}}^2 = m {v_{max}}^2 \rightarrow x_{max}=v_{max}\sqrt{\frac{m}{k}} = \frac{v_{max}}{\omega}$
Also, the time to find the average speed, calculate the total distance traveled over one oscillation by... |
We know by no-ghost theorem (Polchinski I, section 4.4) that the physical Hilbert space have no longitudinal excitations ($X^0, X^1, b, c$). This is obvious by light-cone gauge quantization and in fact BRST cohomology is isomorphic to this space (no-ghost theorem). Witten (beginning of chap. 2) in "Non-commutative geom... |
The angular momentum of an object about an arbitrary point $O$ is given by,
$$ \mathbf{H_O}=[I_O]\mathbf{\omega}$$
where $[I_O]$ is the moment of inertia tensor about $O$. And for the center of mass $G$,
$$ \mathbf{H_G}=[I_G]\mathbf{\omega} $$
My book says that a new array of moments and products of inertia would
be ob... |
There's several concepts I don't have a clear understanding of:
Plots of the turbulent energy cascade have a wave frequency as the axis - yet I see definitions of this "frequency" as the inverse of the eddy size. How does one get Hertz from this if the dimensional unit is one of length. And what does this frequency ... |
Operator product expansion and perturbation theory both looked somewhat similar to Taylor/Laurent series expansion.
Quote: Conformal Field Theory, Philippe Di Francesco, Pierre Mathieu, David Senechal, Page 127 Eq. 5.72
"$$\displaystyle A(z)B(w)=\sum_{n=-\infty}^N \frac{\{AB\}_n (w)}{(z-w)^n}$$ where the composite fie... |
Assuming that we have a metamaterial that can slow down the velocity of propagation of changes in an EM field to around 15 000 m/s (without felling or applying any forces), can we build a propulsion system with two high frequency electromagnets with this material in between them?
Because when the field interacts with ... |
When a crystalline material breaks, it often does so along planes in its crystalline structure. As such this is a result of its microscopic structure.
When glass breaks however, the shapes along which it breaks are typically very smooth as well, rather than being very irregular or jagged. Being amorphous, one shouldn't... |
I apologize for my crude line of questioning, as I am not well versed in physics but there are concepts that interest me. I'm trying to understand the concept of imaginary-time, and I've read in multiple articles of questionable reliability that there is some special relationship between imaginary-time and heat? Or Ent... |
at first i thought time cannot be negative or zero but after going through the statement
"time taken by light to cross a distance of nuclear size is 10^-23" iam confused
|
I apologize for my crude line of questioning, as I'm not well-versed in physics at all but it fascinates me. I was researching the concept of "imaginary-time" and the shuttlecock model of the universe proposed by Hawking and Hartle, and the descriptions I've read explain that the universe started WITHOUT a dimension of... |
In many introductory textbooks on conformal field theories in two dimensions, the flat Euclidean manifold $\mathbb{R}^2$ is considered.
Later, when the global conformal transformation is derived, $\mathbb{R}^2$ is compactified to a Riemann sphere $S^2$ so that the infinity can be included by the compactification so tha... |
$F = MA$ is what I’d call an empirical truth, something we know to be true but can’t be demonstrated without presupposing it.
But I’m wondering if $Fr = Iα$ can be demonstrated from $F = MA$ and the conservation of angular momentum—- or whatever other physics principle.
The proofs I’ve seen so far of $Fr = Iα$ only con... |
I am currently studying Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Chapter 1.1.3 Boundary conditions at a surface of discontinuity says the following:
Let us replace the sharp discontinuity surface $T$ by a thin transition... |
Now, the iron nail becomes a magnet without rubbing or any other energy-consuming process. Now, if I take the magnetized iron nail near other iron pieces, it would attract them and give them kinetic energy. So, the magnetized iron nail must have got some energy. My question is that when we keep the nail near the origi... |
The standard method for synchronizing two clocks is to exchange light signals between the them and ensure the satisfy the relation $t_A' - t_B = t_B - t_A$. This method works because both clocks can agree on the one way speed of light.
When two clocks are synchronized, they will remain synchronized so long as they rema... |
Suppose I have a permanent magnet. It would attract any iron piece(or some other magnetic substance) on taking it to any part of the world or the universe. So, every magnetic object must have some magnetic potential for my magnet. If it is true, then can we trace this potential energy to the formation of the universe?... |
Consider a free particle in a rotating reference frame. Let us say the coordinates of the particle are given by $(x',y')$ in this frame. For an observer on this frame, (I suspect) the Lagrangian is just
$$ L' = \frac 1 2 m\left[(\dot x')^2 + (\dot y')^2\right] \tag{1}$$
However, for an observer on an inertial frame wit... |
Will there be any significant change (if any) in the formulas of electrostatics, if we use a negative test charge in the derivation. thanks for the help appreciate
|
Suppose a relation between distance of a particle $x$ and time $t$ as $x=t^2-2t-3$ where $x$ is in meters and $t$ is in seconds. We can differentiate $x$ w.r.t $t$ to get relation between velocity and time.
I think that how can the equation be dimensionally correct as its dimensions are like $[M^0L^1T^0]=[M^0L^0T^2]-[M... |
Suppose I have a positive charge and a negative charge at a distance on a rough table. The friction of the table overcomes the electrostatic force between them. So, they are stationary. Now, I push the negative charge a little more than the friction so that it moves towards the positive charge. In this process, I have ... |
Suppose that there is a rigid body, such as a satellite, which contains inside it a wheel that is spinning at a constant rate. This means that the satellite has a certain, constant, angular momentum vector $\vec L$. Now suppose that the internal wheel is slowed down by means of some brakes. My understanding is that no ... |
I was playing with bubbles and noticed that bubbles that shimmer due to thin film interference tend to lose their colour when touched by a wand. When once again released they do not regain their colour.Here is a video I took with my phone.
Why does this happen?
|
According to me, an object gains relativistic mass as it approaches the speed of light, and
$$\Delta x \Delta p \ge\frac {\hbar}{2}$$
So objects with speeds close to $c$, should show less uncertainty in position because an object with a small de broglie wavelength is less likely to spread.
$$\lambda = \frac{h}{m_0v}\sq... |
Let's say that we have a positive charge $Q$ and another positive test charge $q$ in the electric field of $Q$ placed at a distance of $R$ from it. A force is being applied on the charge equal to $\dfrac{K_eQq}{R^2}$ in the direction opposite to that of $F_e$ (the electrostatic force exerted on $q$ by $Q$). Now, we sud... |
I need to find the solution to the Poisson- Schrodinger equation in the newtonian approximation, which are basically coupled differential equations given by:
\begin{equation}
\nabla^2 V=8\pi G M^{2}\psi^{2}\\
\frac{1}{2M}\nabla^2 \psi+MV\psi=E\psi
\end{equation}
we are taking the case of stationary rotations, therefore... |
I'm familiar with how the mass of an object increases with the velocity, which makes it impossible to reach the speed of light. However does time dilation also add challenges to accelerating an object?
Ignoring how you get the spacecraft up to relativistic speeds, would time dilation make a rocket engine less effective... |
I am reading the book << Gauge theory of elementary particle physics >>. In chapter 15, it presents a model having finite-energy solution.
First, we have a $1+1D$ spacetime model
\begin{equation}
\mathcal{L}=\int dx [\frac{1}{2}(\partial_0 \phi)^2-\frac{1}{2}(\partial_x \phi)^2-V(\phi)]
\end{equation}
where
\begin{equa... |
If we have two coherent sources generating waves of the same amplitude, on the line joining the two sources, the waves are traveling in opposite directions. Will a standing wave form?
For example, two coherent sources are placed $3\lambda$ apart generating coherent waves.
Taking the source 1 as the origin.
$y_1=A\sin(... |
In article Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory there is statement (page 13):
Ordinary $1 + 1$-dimensional $U(1)$ gauge theory is effectively a quantum mechanical system of a single variable.
Such theory is defined as:
$$
L = -\frac{1}{4} F^{\mu\nu} F_{\mu\nu}
$$
In Lorentz... |
Suppose we have a mirror moving with some speed through space. Both the mirror's velocity and mass could potentially be very large. What would happen, if a laser beam would be fired at its front face (the face facing in the direction of its movement) perpendicular to it? I am not sure if this is right, but I think that... |
Question Statement:
Page's theorem in "Jerusalem Lectures on Black Holes and Quantum Information" is stated as (eq (5.12), page 51):
For any bipartite Hilbert space $\mathcal{H}_A\otimes\mathcal{H}_B$,
$$\int dU \|\rho_A(U)-\frac{I_A}{|A|}\|_1\leq \sqrt{\frac{|A|^2-1}{|A||B|+1}},$$
where $U$ is chosen from the group in... |
I am struggling to understand why we would predict the decay in correlation between the two measurements in a Bell Inequality experiment to be linear (see red line in this image from Wikipedia). I understand there is a max and min, that seems obvious. But why should we assume the function between those two points will ... |
My textbook lays out the following explanation of Force experienced by a current-carrying wire:
My question is where did the negative sign of the charge on electron go? How did Drift velocity go from vector to scalar and how did dl enter the vector form? I know that this formula can be derived using current density or ... |
Does physically pressure change the binding energy between the atoms in a molecule or is it always the same? I did not find anything about this in the internet? Maybe I was searching the wrong way.
Thanks for your answers!
|
Liouville's theorem states that phase space volume is conserved over time with respect to the dynamical system generated by the Hamiltonian and Hamilton's equations.
However, any given point in phase space will evolve within a submanifold characterized by certain values of the conserved quantities (energy, momentum,...... |
I'm trying to understand the symmetry of Wigner's 3$j$ symbols.
$3!=6$ permutations, as well as flipping the sign of all magnetic quantum numbers yields 12 operations, which are sometimes called the "12 classical ones".
Wikipedia lists two additional "Regge" symmetries, which would (to my understanding) both double the... |
I came across this basic exercise but I don't fully get the gist of it.
Consider two neutral particles in a 1D Box with the interval $0\leq x \leq L$. The interaction between the two particles is negligible.
We first compute the hamiltonian operator for the two non-interacting particles.
$$ \hat{H}=\frac{-\hbar}{2m_e}\... |
I just found out about symplectic geometry in the context about this question on volume preservation in phase space.
It seems somewhat complicated and I am not sure what to do with the notation $\omega = dx\land dy$, or what a 2-form is.
Could someone explain how the mathematical objects in symplectic geometry are mani... |
We are taught that in photoelectric effect if the frequency of light is lower than the threshold, then no matter how long a metal is exposed to it there won't be any ejection of electrons.
This made me consider a thought experiment. If we shoot two photons at an isolated atom, having energies equal to half of the ionis... |
The refractive indices of the core and cladding of a multimode optical fiber are 1.62 and
1.52 respectively. Calculate its numerical aperture if the optical fiber is placed in (a)
water (b) ice (c) placed in water with the core removed and cladding replaced with ice.
The refractive indices for water and ice are 1.33, 1... |
I just want to do a sanity check on my understanding of Hamiltonian mechanics:
My understanding is: For any number $n$, take the phase space $\mathbb R^{2n}$, and take any arbitrary differentiable function $H:\mathbb R^{2n}\to \mathbb R$ to be the Hamiltonian. Then all of the standard results about Hamiltonian mechanic... |
While reading one definition of torque, I saw its units are Newton-meter, which is the same as work. But sources usually make it a point to emphasize "even though both work and torque units are the same, they should not be confused, they are very different". One is like an object being pushed with force certain distan... |
I was reading about the tangent galvanometer online. I came across a youtube video : https://www.youtube.com/watch?v=wIuAnP9xfxw .
It said that the field produced by the circular coil of the galvanometer is always perpendicular to the horizontal component of Earth's magnetic field at that point. I know how the magneti... |
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