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What is the difference between potential energy of a spring and potential energy of the spring-mass system?
The reason I am asking this question is, is elastic potential energy a property of the spring alone? Or is it a property of the mass attached to the spring as well?
My textbook says that it is incorrect to say "... |
Typical metals have temperature coefficient of resistance with order of magnitude $\sim 0.001$, at $20$ degrees Celsius.
What kind of materials have TCR of order of magnitude $0.1$ at $40 - 160$ Kelvin?
I want to know what kind of material show behavior like the measurement results in the below picture.
I conjecture th... |
$C$ and $C_0$ are the capacitance of the capacitors. The wire marked with an arrowhead is to be switched from point 1 to 2. Resistance of wires is very very less (~0). Leaking of charge does not occur. Total capacitance of system in the two cases remains same hence no change in energy of conductors. This made me concl... |
A few years ago I taught a physics class for 6th graders at a school with an accelerated curriculum. These students are good at memorizing, and following procedures, so I was able to teach them the standard rules for deciding how many significant figures to include fairly easily, but I struggled to convey the underlyin... |
How can I calculate the amount of free electrons in a metal?
I search the forum but found nothing
What I want to know is how many electrons can I remove from a metal using photoelectric effect (consider a fully insulated metal)
|
I am confused about an aspect of coupling constant rescaling in the Wilsonian renormalization group procedure. (I'm following Kardar's "Statistical Physics of Fields, Ch5). I think I understand the basic idea of the renormalization group, but I'm in undergrad and haven't taken field theory or an advanced stat mech cour... |
If an image of an object formed by convex lens is simply meeting of the rays of the object due to refraction,then why do we require a screen to reflect these refracted rays?If we observe the image formation from the side the image is forming,shouldn't the rays of the image reach our eyes without a screen?
|
Classical Mechanics It is often said that the particles/atoms in classical mechanics are distinguishable because we can keep track of their trace. First how is this possible? If we have 3 atoms how can we know which is which? First we can close our eyes and then someone interchange their position. When opened them up w... |
To solve the Schrödinger equation we construct the Hamiltonian of the system that is:
$$\hat{H}=\hat{K}+V$$
So far so good. What bothers me is the conceptual approach. Do we assume that nothing else exists in the universe except 1 proton and 1 electron? That is as the electron and proton approach each other they wouldn... |
Is it possible to have a different estimated value of a parameter by Classical Fisher Information (CFI) compared to Quantum Fisher Information (QFI)?
Say, for example, I am plotting, $\mathcal{F_{\nu}} $, Fisher Information for parameter $\nu$ with respect to $\nu$. When estimating $\nu$ using CFI I get a peak in plot... |
In Scaling and renormalization in statistical physics by Cardy on page 44 he asserts that the free energy per lattice site defined by $f(\{K\})\equiv-N^{-1} \ln Z$ transforms as
$$f(\{K\})=g(\{K\})+b^{-d} f(\{K'\}) \tag{1}$$
under a renormalization group transformation.
Here the first term is non-singular and the seco... |
It's rather well known that the Apollo lunar landings installed retroreflectors on the Moon, and that these can be used to reflect laser beams back at Earth, to measure the Earth-Moon distance to exquisite accuracy.
However, the weaselly phrase, "can be used", in that common understanding, is rarely examined in practic... |
In this question: "Without the Michelson-Morley experiment, is there any other reason to think speed of light is the universal speed limit?", it is stated in Emilio Pisanty's answer that
From a purely mechanical perspective, the LHC routinely produces 7 $TeV$ protons, which would speed at about $120c$ in Newtonian mec... |
What are the conditions for the molar heat capacity equation viz.
$ΔQ=nCΔT$
to be true?
For example, if the process is isothermal, then change is temperature change is zero and so should be the change in heat i.e. $ΔQ=0$ (according to the equation). But that is not true. I think that the condition should be that work ... |
1/ I consider that the twin paradox is formulated as follows: "Two people in the universe cross each other, synchronize their clocks at this point in time, continue to travel in the universe and cross paths again. When they meet again, which one has aged faster?"
In that case, is it true to say that there is nothing in... |
Are there any physical qualities which have only one unit of measurement?
|
Here is an interpretation I came up with,
The friction, for a rolling body, converts the kinetic energy into rotational energy. Instead of dissipating it.
Questions:
1. Is my interpretation correct?
what happens to the motion once all the k.e is converted to rotational energy?
|
I recently read here (Hyperphysics page on Sun) since the Sun is a gaseous body and hence different latitudes can rotate at varying speeds. Naively, I was guessing that the poles would have faster rotation and hence smaller period of revolution than the equator. This intuition was rooted in the assumption that we start... |
How is the lift force is generated on a rocket? I've tried to find answer online but all efforts were in vain.
|
The quenched approximation of QCD (or other QCD-like theories) is when you basically ignore fermion loops, i.e. fermions are non-dynamical fields. For quantities that do not involve external fermion states, this is equivalent to setting $N_f=0$ (since fermion lines have to be connected/continuous).
But why is this appr... |
Still, I don't understand how come the satellites won't fall into earth. I know the general explanation to this question is that the satellite's horizontal velocity is too fast that makes the gravity impossible to pull it to the earth.
This, for me, sounds like the gravitational force need to take a few moments to sens... |
I have this problem:
Obtain Hamilton's equations of motion for a plane pendulum of length $l$ with mass point $m$ whose radius of suspension rotates uniformally on the circumference of a vertical circle of radius $a$.
This is my position vector:
\begin{equation}
\vec{r} = (a\cos{(\omega_0 t)} + l\sin{\theta})... |
Now since only two electrons (or any quantum object) can be maximally entangled due to the monogamy of entanglement how does the general $n$-qubit states which has more than two qubits make use of entangled states to increase the computational space to $2^n$?
so for example take this three qubit general state
$$a1|000... |
Say I have an oscillating sinusoidal current flowing on the z-axis (say $I_0\sin{\omega t}$), in a straight line conductor. This current produces an alternating magnetic field in the azimuthal direction, which produces an changing electric field in the z direction, which creates an EM wave in the radial direction. How ... |
I'm not very familiar with high-Tc and I have naive questions on cuprates materials (CuO2). It seems common that everyone treats it as a 2D material for good reasons: in undoped system, there are two outer-shell electrons bond with oxygen atoms, which is a Mott-insulator. And people have derived the effective hamiltoni... |
This question is somewhat related to (but not by any means the same as) the question I asked recently.
In his Lectures on Quantum Theory, Isham essentially says (reference given below) that if an operator $\hat{d}_x$ satisfies $[\hat{x}, \hat{d}_x] = i\hbar 1\!\!1$ (where $\hat{x}$ is the familiar operator correspondin... |
The inelastic mean free path (IMFP) is a quasi-universal curve which describes how far a beam of electrons will travel through a material before scattering inelastically. I have been searching for derivations of a functional form but have not been successful; however, this is not my main question.
I am curious: is ther... |
When reading about the Mott metal-insulator transition, it has not become clear to me if the transition from a metal to an insulator occurs with increasing or decreasing density of valence electrons.
For example, look at fig.3 in [1]. On the left, there is V203 doped with Ti (lower density of valence electrons) and on ... |
Assuming an ideal single frequency plane wave, we can determine the angle of retraction for the light beam.
But the more I make my pulse shorter, the less certain I am in the frequency and thus the angle of refraction, angle of total reflection and Brewsters angle.
Is this true?
If i target a pulsating laser on the gla... |
Every visualization of an electromagnetic wave is essentially some variation of this picture:
In every one of these graphs, both the electric and magnetic components are shown as being sine waves with the same phase angle. However, it is just as frequently stated that the amplitude of a magnetic field is related to th... |
I'm reading up about the geometry of flat spacetime in the context of special relativity, and I have a minor confusion about the following statement (in bold):
The figure shows timelike and spacelike unit vectors: each vector connects the origin with a unit hyperbola. These are not all unit vectors in the same frame; ... |
When doing some reading on particle physics, I came across the concept of a "multicharge nuclei". A Google search of this phrase returns a number of research papers, but no definition for what a "multicharge nuclei" is.
How does it make sense to say that a nuclei can have multiple charges (that is, a "multicharge nucl... |
I'm solving a problem where a ball rolls down a hill, but the friction between the ball and surface is 0. So it obviously slips, but does it only slip? As in does it not roll at all? Or does it slip and roll? Thanks.
|
I have already posted this problem here, closed for asking too many questions. I will reproduce the introduction and contextualization here, and try to ask a more specific one that I hope will be acceptable.
I have performed an analysis of the exclusion(discovery) perspectives for a BSM particle at the LHC.
The consi... |
I've been reading about how energy is actually transported in electric circuits (I first read about it here: http://amasci.com/miscon/ener1.html). The description in this article of why electrons don't move around the circuit carrying energy like buckets, picking up energy from the battery and dumping it at the load, i... |
I am told that, when a heavy charged particle passes through a substance, ionization occurs. I am then told that the most probable occurrence is collision with an atomic electron. Finally, I am told that, when this occurs, a relatively slow secondary electron, with kinetic energy not exceeding the ionization energy, is... |
I came across this quote today;
[Quantum computers] process information using quantum mechanical amplitudes. And probabilities are sort of the ghosts of amplitudes after they have been degraded to our mere classical world.
Michael Freedman on quantum computing research, circa 2015
Can someone explain what is meant ... |
Decomposing a function into a Fourier series is possible for periodic functions. Fourier transform, on the other hand, is used for aperiodic functions. How can we use Fourier series to analyse the initial configuration of a plucked string at $t=0$?
Edit The existing answer talks about periodic extension which I am awar... |
If there is a room filled with air and it had a door and a window, air only blows at a high speed through the window if the door is open. The wind stops if the door is closed. Does the air behave like a solid in this respect?
|
The famous $\Lambda_{\textrm{QCD}}$ parameter enters through the one-loop running of the QCD coupling, through a relation similar to the following:
$$\alpha_S(Q^2)=\frac{\alpha_S(Q^2_0)}{1+b\ln(Q^2/Q^2_0)}\equiv\frac{\alpha_S(Q^2_0)}{b\ln(Q^2/\Lambda^2_\textrm{QCD})}$$
My question is simple: how does this equation, and... |
Sometimes in the light-matter interaction described by the Jaynes-Cummingsa model, an additional coherent drive is included which drives the light in the cavity. I've encountered this so many times in various quantum optics papers, but I still don't clearly understand what this drive is.
$$ H=H_\text{r}+H_\text{a}+H_{... |
I have little knowledge of physics and have been unable to find a general mathematical analysis of this problem. I’ve tried to present it in a general way but the underlying principles are applicable to several practical situations.
A small spherical temperature-sensitive item is about the size of a ping-pong ball (an... |
I am told that, when a heavy charged particle passes through a substance, some (small number of the) collisions occur with electrons of relatively large energy. I am then told that the maximum energy of these secondary electrons is $4\dfrac{v}{M}E$, where $M$ and $E$ are the mass and energy of the incident particle, re... |
In Jackson (3rd edition p. 545) there are the following equations:
$$A = e^L \tag{11.87}$$
$$\det A = \det(e^L) = e^{Tr L}$$
$$g\widetilde{A}g = A^{-1} \tag{11.88}$$
$$ A = e^L , g\widetilde{A}g = e^{{g\widetilde{L}g}} , A^{-1} = e^{-L}$$
$$ g\widetilde{L}g = -L $$
$\widetilde{A} $ is the transpose of $A$. I have seve... |
I understand that the excitation of the Higgs field itself is the Higgs boson, and not the Higgs field itself, which does fit somewhat into the little String theory I've read (The excitations of the strings are the particles, not the strings themselves).
However, how does one actually get an excitation of the field? S... |
Its mentioned in several books that a satellite launched with a velocity less than the escape velocity and other than the critical velocity will follow an elliptical orbit. However I can't find a derivation of its equation of trajectory.
|
One of the larger puzzles (coincidences) of cosmology is that the cosmological constant $\Lambda$ has roughly the value given by the radius of the present universe.
At the same time, cosmological data states that dark energy obeys $w=-1$ with a high precision of only a few percent. This is usually interpreted as meanin... |
I have an acoustic resonator which is tube-shaped and open on both sides. The open ends of the tube open into a buffer volume. In the picture below I visualized my assumption.
Measuring the resonance frequency of my resonator with ambient pressure in the whole cell (buffers + resonator) I had a deviation from the theo... |
Compressing and cooling air in a Coolgardie Safe, then decompressing
I'm a 10th grader so it would help to explain how, in the answer to the link above, $$T_{cool}\left(\frac{V_{final}}{V}\right)\left(\frac{P_{ambient}}{P_{cool}}\right)$$ became... $$T_{cool}\left(\frac{P_{ambient}}{P_{cool}}\right)^{2/7}$$
Where did 2... |
I am currently reading Niklas Beisert's lecture notes on QFT, Chapter 10, on the scattering matrix $S$.$^1$ My main confusion lies in the construction of $\vert \rm in \rangle$ and $\vert \rm out \rangle$ states and in what picture these states are in.
Let $\phi(x)$ be the interacting field, that can be decomposed into... |
In the context of QCD (and more generally, any quantum gauge theory in even dimensions), the $\theta$-term is
$$
\frac{\theta}{8\pi^2}\langle F_A\wedge F_A\rangle = \frac{\theta}{32\pi^2}\langle F_A^{\mu\nu}, F_A^{\rho\sigma}\rangle\epsilon_{\mu\nu\rho\sigma}
$$
and its integral over spacetime is not exactly gauge inva... |
I'm confused about the state of a system after a measurement. Say we have a particle $v$ in the state: $ |\psi\rangle= \sqrt{1/4} \ |0\rangle + \sqrt{3/4} \ |1\rangle $.
From my understanding, if one were to measure the state of $v$, one would get the result $|0\rangle$ with probability $|\sqrt{1/4}|^2=1/4$, and simila... |
if gravity is just bending of spacetime according to general relativity why are we still considering it as one of the 4 fundamental forces. https://astronomy.stackexchange.com/q/12408/ this link provides that gravity is not force but just bending of spacetime so why it is the way it was?
|
Why do photoelectrons from a vacuum photocell move towards the collector plate if it is not charged? Has it been charged beforehand, or do they simply move forwards because of the kinetic energy they have gained?
The kinetic energy option sounds reasonable, because then it would give a measure of the electrons' energy ... |
The wave function (this is the wave function in mechanical waves. It is not the wave equation, which is derived from this wave function. Neither is this the wave function for quantum mechanics!) is given as:
\begin{align}
y(x,t)&=A\cos(kx \pm \omega t + \phi)
\end{align}
(where $k$ is the wavenumber, $x$ is the posit... |
I find it very difficult to visualize spacetime curvature in my mind. When I look at the depiction like the one below it doesn't make much sense to me, instead, it is making it more confusing for me to understand spacetime curvature. In the depiction, it looks like that if someone would be standing at the bottom of the... |
https://www.youtube.com/watch?v=UqBmdZ-BNig
why can't it be the other way around that the air flowing below the chamber moves faster than the air moving above the upper chamber?
|
What is the meaning behind multiplication in physics? Is multiplication in physics purely mathematical or there is a physical explanation to it? How do we explain the product for example, $s = v·t $? Is there any meaning behind this? For example, I can say that "Distance is defined as the product of velocity 'times' ti... |
I was recently reading about Hohmann transfer orbits from the MIT courseware
on orbital transfer (source).
I have two questions.
How did they arrive at the equations for $v_{\pi}$ and $v_{\alpha}$?
They have taken the potential at a radial distance of $r_1+r_2$ when the particle to be transferred never crosses $r_2$
... |
When we provide a potential difference in a circuit it does nothing more than provide an electric field to the conductor,When an electric field is provided in a conductor the free electrons move to the opposite direction of the field and hence there is an accumulation of charge on the ends of the conductor.Due to the a... |
What are dark matter and dark energy?
Do dark matter and dark energy have different physical laws from ordinary matter and energy?
Can string theory explain their mechanisms?
|
The question is the following:
A new state of matter is described with the following equation of state: $$ PV = AT^3 $$ Where $A$ is a constant. The internal energy $U$ is given by:
$$ U = BT^n \ln(\frac{V}{V_0}) + f(T) $$
Where $n$, $B$ and $V_0$ are constant.
Find $B$ in function of $A$, and find $n$.
I tried to m... |
We have a $D$ dimensional flat minkowskian spacetime, and a field theory with $T_{\mu \nu}$ symmetric, traceless ($T^{\mu}_{\mu} = 0 $) and conserved ($\partial^{\mu} T_{\mu \nu} = 0$). We also assume that the operator $E = \int d^{D-1} x \, T_{00}$ is well defined and semi-positive definite. Given a state $|{\Phi}\ran... |
I'm reading about the geometry of spacetime in special relativity (ref. Core Principles of Special and General Relativity by Luscombe). Here's the relevant section:
Minkowski space is a four-dimensional vector space (with points in one-to-one correspondence with those of $\mathbb{R}^4$) spanned by one timelike basis v... |
Is there any way of knowing which white objects or materials are white due to emission of most or all wavelengths, and which due to diffuse reflection?
If there is one type of material I would like to know about especially, it is white textiles/fibers.....
Also white paint (titanium dioxide, e.g.)
|
I watched the video which says that electric and magnetic forces are one and the same thing it is just that when electric Field when viewed from different frame of reference becomes electric field the link for the video is given below .
My confusion is that if the two forces are same and differ only in frame of refer... |
How far the gravitational waves can travel? Does it depend on the mass which is converted to energy in a black hole/neutron star merger? If there is a finite distance, were we lucky to be in the range to detect these in 2015 for the first time?
|
I am studying through the photon self-energy
$$
i\Pi_{\mu\nu}(q) = \int\frac{d^4 k}{(2\pi)^4}Tr\left[(-ie\gamma_\mu)\frac{i(\require{cancel}\cancel k+m)}{k^2-m^2+i\epsilon}(-ie\gamma_\nu)\frac{i(\cancel p-\cancel k+m)}{(p-k)^2-m^2+i\epsilon}\right].
$$
I don't know to expand this trace, some textbooks give direct res... |
On RC circuit, capacitor discharges when the voltage supply is removed.
But I've learned that the net electric field outside a charged capacitor is zero by gaussian surface and gauss law.
I don't understand the mechanism. Shouldn't be there an electric field in order to make charge flow when discharging happens?
Is the... |
In Goldstein's Classical Mechanics, he wrote
If a particle is constrained to move on a surface, the force of constraint is perpendicular to the surface.
Why must the force of constraint be perpendicular to the surface?
Intuitively I think that to keep a small bead moving on the surface of the sphere, I would have t... |
Suppose I have a ferromagnetic material. It is known that the magnetization $\textbf{M}$ can be determined from a magnetic field $\textbf{H}$ using hysteresis curves as exemplified in the figure below.
Here, $\textbf{M} = [M_x ~ M_y~ M_z]^{T}$ and $\textbf{H} = [H_x~ H_y~ H_z]^{T}$.
P.S.: The curves are not necessari... |
I have been studying a bit of GR and am still a bit confused as how it works with perturbations of the metric or even in what norm the perturbation is meant to be understood.
For example, what happens to the Einstein field equations if we take the metric to be a small perturbation away from the Scwarzchild metric?
|
While I was listening to my teacher present the basic idea's of Schrodinger's famous thought experiment, he said that because we can not SEE the cat, the cat exists in some sort of position in which it is both dead and alive.
I was wondering if "see" encompasses all the other senses? Surely if we can hear the cat meow... |
I'm stuck trying to solve analytically the transparency current of a laser, Itr.
I've calculated the transparency carrier density N, and I know the area of the active region A, but simply going Itr=NA gives a value that's unreasonably large.
Are there any other methods to get the transparency current?
Thanks
|
My understanding is that to obtain a finite vacuum energy density prediction from QFT, one must choose a cut-off point for the maximum allowed energy of a photon. Two seemingly natural choices are the Planck energy, which gives the oft-cited $10^{112}$ ergs/cubic cm figure, and the electroweak energy, which I recall re... |
So I watched this video
It is a fairly popular one by veritasium, and one that confused me. I was wondering if someone can cover the physics behind this in a intutitive and easy to understand manner. I understand torque and angular momentum come into play here, but what I don't get is the vector pointing away from the ... |
In the ADM formalism of general relativity, one obtains a $3+1$ split of spacetime by setting $$\mathrm d s^2=(-N^2+N_a N^a) \,\mathrm d t^2 + 2N_a\,\mathrm d t\,\mathrm d x^a + q_{ab} \,\mathrm d x^a\,\mathrm d x^b \text{.}$$ The Einstein-Hilbert action $$S[N,N^a,q_{ab}]=\int\sqrt{\mathrm{det}(g)}\,R\,\mathrm d^4x$$ i... |
Given a Killing Horizon $\mathcal{N}$ of Killing vector field $\xi$, one can prove that the surface gravity $\kappa$ is constant on orbits of $\xi$, i.e $$\xi\cdot\partial\kappa^2 = 0.$$
What is the meaning of orbit of Killing vector field? Do they cover all of the Killing Horizon? (this second question, is because $\x... |
I understand why a released object moves as it does once it has started moving, and why all objects fall at the same speed, removing other effects. But I don't see why the curvature of space would make it start to move in the first place, thank you.
|
Let's forget about the quantum knowledge here.
Lets say that we just want to know what speed an electron can get,
when falling straight on to a nucleus.
It does not miss the nucleus and start spinning around.
It goes straight at the nucleus.
Just think of charge and radius of proton and alpha particle and mass.
At wha... |
I am currently working on a tilt rotor aircraft, for that I need to size a motor the applies the torque to swivel the propellers from a down facing position into a rear facing position. We are using counter rotating propellers. H
I have troubles understanding how to calculate the torque required to rotate a spinning ma... |
I just don't understand this. I have read about the right hand rule, but I am finding it hard to take it on faith, and would like to have some proof.
Also, try not to make your explanation too mathematical. I would prefer something intuitive and conceptual.
|
The elastic dynamics of an isotropic continuum (solid or fluid) can be described in terms of the bulk modulus ($\kappa$), shear modulus ($\mu$, zero in a fluid) and density. (The two elastic moduli are sometimes expressed in terms of other variables such as Young's modulus [$E$], Lamé's first parameter [$\lambda$], or ... |
So the most general local superspace transformation generator I can write is:
$$\hat{L} = A^\mu(x,\theta)\frac{\partial}{\partial x^\mu} + B^\alpha(x,\theta)\frac{\partial}{\partial \theta^\alpha}$$
With $x$ normal variables and $\theta$ grassman variables. What additional conditions on the functions $A$ and $B$ must w... |
This could be extremely trivial but I am having problems figuring it out.
I think I understand properly the difference between waves and fields.
A field is a function valued on space or spacetime which takes values that can be scalars, vectors, tensors and so on. While waves can be understood as a consequence of fiel... |
What happens if I place myself in the center of one of the Earth's poles?
Could I see how the earth revolves around me?
|
Here is a thought experiment for which I cannot find a good answer or explanation. Let us imagine that in the void and on a (very long) line there are two lights switched off in points A and C. Two observers are waiting in point B, at the same distance of A and C.
The experiment is such as at 12 PM in the reference fra... |
Looking at the Dirac equation of the form
$$\Big(i\gamma^{\mu}(\partial_{\mu}-iA_{\mu})-m\Big)\psi=0$$
There is a simple solution to this equation, which is
$$\psi=\exp\Big(i\int^xA_{\mu}dx^{\mu}\Big)\psi_0$$
Where $\psi_0$ solves the Dirac equation in the absence of the gauge field.
My question is, are there any oth... |
In the reference $[1]$ I saw a very neat formula, given by:
$$ \mathcal{E} =: \int_{\Sigma} d^{3}x T_{00} = \frac{1}{8\pi G}\int_{\Sigma} d^{3}x G_{00}. \tag{1}$$
The author stated that this is the "energy in a space-time". At first glance nothing is bothering me at all, though it seems a little bit hand-waving notat... |
In Bjorken & Drell vol. 1 "Relativistic quantum mechanics", the parity operator acting on solutions of the Dirac equation is represented as $P=e^{i\phi}\gamma^{0}$, where $\phi$ is a phase. Let's apply this operator to a solution of the equation with definite energy, momentum and spin $\psi$. At page 71 it is said tha... |
When deriving the governing equations, we consider conservation of mass, momentum and energy.
Why don't we consider angular momentum too? Granted it seems difficult to me how to go about writing the statement and I know that vorticity is considered, but why not a separate equation for angular momentum?
It would certain... |
This is probably a newbie question (but I guess is what I am right now) but I can't understand de difference between Galilean Boost and Galilean Translation.
I thought a boost was something like an S' frame of reference with constant velocity in relation to an S frame of reference. Mathematically:
$$ x' = x - vt; y' =... |
Is there any special reason why Pauli matrices are:
$\sigma _1=\left(
\begin{array}{cc}
0 & 1 \\
1 & 0 \\
\end{array}
\right)$, $\sigma _2=\left(
\begin{array}{cc}
0 & -i \\
i & 0 \\
\end{array}
\right)$, $\sigma _3=\left(
\begin{array}{cc}
1 & 0 \\
0 & -1 \\
\end{array}
\right)$
and not for example
$\sigma _1=\... |
If we consider a canonical transformation from $(q,p)$ to $(Q,P)$, it is stated in several sources that by Jacobian rules,
$$ \frac{\partial(Q,P)}{\partial(q,p)} = \frac{\partial(Q,P)/\partial(q,P)}{\partial(q,p)/\partial(q,P)}. \tag{1}
$$
By taking books such as Riley's Mathematical Methods for physics and enginee... |
Under normal atmospheric pressures, liquid helium does not freeze even when cooled very close to absolute zero. This is attributed to the uncertainty principle or due to zero-point energy.
But the quantum uncertainty or zero-point energy is not an exclusive feature of liquid helium only. Then, why should it stop the f... |
Classical mechanics says that if I throw a ball with velocity perpendicular to the wall and it collides elastically with the wall with a velocity $v_0$, then it bounces back with the same velocity $v_0$.
However, if I shoot a beam of water perpendicular to the wall, in most cases it will not deflect back perpendicular... |
When an object moves in a circle it experiences centripetal force directed towards centre, But when we place an object on a disk which is rotating why does the object moves away from centre instead of moving towards the centre.
|
In the book Methods of Contemporary Gauge Theory by Yuri Makeenko, the loop equation in the large-$N$ limit is given by
$$\partial^x_\mu \frac{\delta}{\delta \sigma_{\mu \nu}} W(C) = \lambda \oint_C dy_\nu \; \delta^{(d)}(x-y)W(C_{yx})W(C_{xy}). \tag{12.59}$$
Equation (12.59) in the book, page 264. Where $\frac{\delta}... |
I was recently instructed by my instructor that say if a person is standing on a disc(stationary and hinged) and decides to jump off it then linear momentum of system is not conserved as a hinge force acts on the body thus preventing conservation of momentum Can somebody please explain how the hinge force acts in this ... |
If a charge $q$ is placed at rest at a point $P$ near a wire carrying current $I$, with some distance $x$, it experiences almost no force.
However, if the charge $q$ is projected from the point $P$ in the direction of the current, it deflects towards the wire.
Now my question begins. Let us consider this event in fron... |
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