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Explicit expansion of the term $\overline{\psi}(i \gamma_\mu \partial^\mu-m) \psi$
In QED, one finds the first part of the Lagrangian density to be $\mathcal{L}=\overline{\psi}(i \gamma_\mu \partial^\mu-m) \psi
+\dots$
I am interested in expanding the term.
Am I correct to define $\psi$ as:
$$
\psi=\pmatrix{R_0+i C_0... |
Would there be any specific change in the physical/chemical laws if one day we changed the convention that electrons are negatively charged to the one that electrons are positively charged and vice versa for the holes?
|
To calculate electrostatic pressure, force on an area of the conductor is required. So we calculate the electric field due to charges other than those on the small area on the conductor. Consider a charged conductor. The electric field due to charge on a small area S is E1 and due to rest of the charge is E2 (at points... |
This problem is from one of my practice papers for the JEE , the situation of a freely falling rotating ball which collides with the ground twice.
Question asks for the horizontal distance covered between the first two collisions .
Coefficient of restitution , coefficient of friction , mass and moment of inertia of a b... |
Fluid is a substance that continually deforms (flows) under an applied shear stress, or external force. Fluids are a phase of matter and include liquids, gases & plasmas. My question: Does plasma have viscosity like a real fluid & why or why not?
|
I am in need of an optics expert on imaging, and in particular a fresnel lens is being used as for an imaging device. From my understanding a condenser lens can be considered equivalent to a plano-convex lens.
Setup:
-A condenser fresnel lens is used, for which both the fresnel and plano conjugates are finite. Meaning ... |
I'm looking to write down a second quantized Hamiltonian to include the intrinsic spin-orbit coupling term in addition to the hopping spin-orbit coupling Rashba effect.
How would I construct the term in the Hamiltonian that expressed hopping between orbitals instead of lattice sites, say for the $p$ orbitals with $ l =... |
From my, probably flawed, understanding of Hawking Radiation, virtual particles get turned into non-virtual particles. I'd imagine since both Gravity and Electromagnetism both follow the inverse square law, they'd have some similar properties.
So, could a powerful enough magnetic force, i.e a Magnetar, produce similar ... |
I know that the uncertainty principle says that we can't measure the position and momentum at the same time but I still can't relate it to the electron diffraction experiment. Isn't that the electron diffraction experiment is used to explain the duality of the nature of electron only?
|
I understand the proper velocity is the velocity as measured by the traveler, and relative velocity as measured by the observer.
Relative velocity is limited to $c$, but is that also true of proper velocity? Theoretically, of course, assuming a sufficient energy source was available. And what would be the effects on t... |
Reading this acticle www.mirror.co.uk/news/weird-news/huge-asteroid-could-cause-earthquakes-7019482 I was surprised at the claim that a 2.4km wide asteroid could cause earthquakes on earth by way of a near-miss. Of course, I have no questions regarding what would happen if it was actually a hit ...
The first line state... |
Im studying charged particle and i recently came up with a question that stated that a charge was released from a position in which had no electric potential but however accelerated due to a electric field, this puzzles me as the question later said that the after the particle accelerated it came to a stop infinity far... |
I was reading some lectures on quantum information theory and it came with the idea of "
mutually unbiased bases" that I never heard about. But the definition is very simple: two basis $ B = \{|b_0> , |b_1> \} $ and $ C = \{|c_0> , |c_1> \} $ are said to be mutually unbiased if $ <b_i|c_j>$ is independent of i and j... |
The most common explanation to this phenomenon which I have read is that the pressure disturbance signal cannot propagate upstream, as the medium in which it travels itself flows downstream, so signals can no longer reach the upstream part, hence flow is choked.
How I look at is, that there are a lot of particles conne... |
I know that laser wavelength depends on four important properties:
Bandgap of its material
Gain spectrum
Length of cavity
Size of a quantum well, if we talk about the quantum well laser
But it's a bit hard to wrap my head around the the interplay of those four factors. Is there some final formula for that?
For exampl... |
I'm trying to prove the following equation which is recieved by the energy momentum tensor:
$$\partial_{\mu} T^{\mu \nu}=\frac{1}{c}j_{\mu}F^{\mu \nu}. $$
The energy momentum tensor is defined by
$$ T^{\mu \nu}= \frac{1}{4\pi}(F^{\mu \rho}F_{\rho}^{\nu}+\frac{1}{4}\eta^{\mu\nu}F_{\rho \kappa}F^{\rho \kappa}).$$
Now i... |
Consider the Kohn-Sham equation
\begin{align}
\left(
- \frac{\hbar^2}{2m} \nabla^2
+ \nu_\mathrm{eff}(\mathbf{r})
\right) \varphi_j(\mathbf{r})
&= \varepsilon_j\varphi_j(\mathbf{r})
\end{align}
The external potential will be considered the interaction potential of electrons and nuclei.
Then \begin{alig... |
I heard this in a lecture. I was hoping someone can provide a reference that I can cite.
To deflect a proton, the proton must be able to complete its larmor orbit. But if we have a fluctuating field lines (complex), the proton would require a smaller overall distance to be deflected when compared to a laminar field of ... |
Let there be a particle in a plane at any general time instant $t$. Let the coordinates of the particle are $x\mathbf{\hat i} + y\mathbf{\hat j}$, where $x$ and $y$ are functions of time $t$. Then we calculate velocity as $v_x=dx/dt$ and $v_y=dy/dt$. Then we write velocity as
$$\mathbf v= (dx/dt)\mathbf{\hat i} + (dy/d... |
I have seen to calculate $\int dA$ for a sphere, $dA$ is equal to:
$$d\vec{A}=d\theta d\varphi r^2\sin\theta(\cos(\varphi)\sin(\theta),\sin(\varphi)\sin(\theta),\cos(\theta)).$$
I don't understand the meaning of the: $\cos(\varphi)\sin(\theta),\sin(\varphi)\sin(\theta),\cos(\theta)$.
Link to original post:
https://phys... |
My problem is all about this previous question. I'm trying to understand the reasoning behind the definition of the momentum operator in quantum mechanics. Sakurai tells me that for the infinitesimal translation of the previously cited question:
$$X=x+dx$$
$$P=p$$
I have the following generating function for this trans... |
Given is a vector potential
$$A(\vec{x},t)= \frac{\mu_0}{4\pi}\frac{\vec{m}\times\vec{x}}{|\vec{x}|^3}$$
Now I want to calculate the magnetic induction $\vec B$:
$$\vec{B} = \nabla\times{\vec{A}} = \frac{\mu_0}{4\pi}\left(\nabla\times (\vec{m}\times\vec{x})\frac{1}{|\vec{x}|^3}+\nabla\left(\frac{1}{|\vec{x}|^3}\right)\... |
I have a question which may be very naive yet I have no answer. I studied undergraduate quantum mechanics 4 years ago now and even if I studied more advanced stuff like QFT I feel like I don't understand the basics yet, so feel free to answer me with "take a QM book and study it" and close the question.
My problem is a... |
I came across this question: https://www.quora.com/How-do-you-prove-that-Newtons-2nd-law-non-relativistic-takes-the-same-form-in-all-inertial-frames-under-Galilean-transformations
Proving that Newton's 2nd Law is form invariant under Galiliean transformations - and I've noticed the approach described in the answer to t... |
My question:
If I have the Ampére-Maxwell law
$$\oint_\gamma \mathbf{B}\cdot d\mathbf{l}=\mu_0\left(I_{\text{enc.}}+\epsilon_0\frac{d\Phi_S(\mathbf{E})}{dt}\right) \tag 1$$
where $I_{\text{enc.}}$ is the current due to a difference in potential $\Delta V$ and the $$\epsilon_0\frac{d\Phi_S(\mathbf{E})}{dt} \tag 2$$
is t... |
I've recently read that ventilators make sweat or water in your skin to be more likely to evaporate. How can that be the case? If the temperature does not increase, how can it provoke such an effect?
|
I'm reading through Dodelson chapter on BBN. I'm trying to follow the examples, but having trouble with the basics. First, the proton to neutron ratio is quoted as:
$$\frac{n_p}{n_n}=e^{\frac{Q}{T}}$$
Where Q = 1.293 MeV and T is the temperature of the soup. Then they go on to say that at $T_{FO}$ (The freeze-out te... |
I am currently studying Clssical Mechanics, fifth edition, by Kibble and Berkshire. Problem 1 of chapter 1 is as follows:
An object $A$ moving with velocity $\mathbf{v}$ collides with a stationary object $B$. After the collision, $A$ is moving with velocity $\dfrac{1}{2}\mathbf{v}$ and $B$ with velocity $\dfrac{3}{2}\... |
We know that Ohm's laws are experimental laws. Ohm's first law for ohmic materials follows a linear approximate progression of the kind:
$$\frac{\Delta V}{I}=R$$
What are the functions of type $$\Delta V(I)=f(I)$$ that are characteristics of non-ohmic materials?
Are there any known functions for non-ohmic materials an... |
I am designing an algorithm. The problem statement is relatively straightforward. You are given some initial state (initial velocity and initial acceleration) as well as a target acceleration and a displacement over which this target acceleration must be reached.
I need to know how long it would take to linearly ramp a... |
I see this mechanical problem here.
I want to solve this problem with the variational method. The Lagrangian of this system is obtained by subtracting potential energy from kinetic energy.
m = 1;
g = 9.8;
R = 1;
EulerEquations[
m*g*R (1 - Cos[θ[t]]) - m*g*R*Cos[θ[t]], θ[
t], t](*L=T-V or L=kinetic energy - potentia... |
Does the magnetic field exert a force on the magnetization current inside the ferromagnet?
In this case, does the following formula also apply?
$$
\pmb {d \hat F = I_{m} \ d \hat{L} \times \hat{B}} \tag{1}
$$
where $\mathbf{I}_{m}$ is the magnetization current inside the ferromagnet.
I am a little confused about the ca... |
In this question, I'm referring to a specific step in https://arxiv.org/abs/hep-th/9306153. I want to reproduce equation (2.4) on page 15. I think I lack the experience required for dealing with saddle-point approximations to multi-variable integrals such as the one appearing in (2.3). I'm approaching this having an un... |
I am asking in the context of a paper of Witten on instability of Kaluza-Klein spacetimes (https://www.sciencedirect.com/science/article/pii/0550321382900074).
The discussion involves applying Witten's positive energy theorem to the space $\mathbb{R}^{3,1}\times S^1$. The proof involves (zero-mass) solutions to the Dir... |
If the Universal Wave Function definitely existed, would that mean the Many-Worlds Interpretation was automatically true or would it only imply that?
|
Two identical bottles with different straw length are filled with identical liquids (obviously up to the same height as depicted in the picture). Bottle with long straw is emptied first.What can be it's possible reason?
|
I understand that waterfalls conserve energy, given the fact that the top of a waterfall possesses gravitational potential energy, and as the water is falling from top to bottom, this potential energy is converted into kinetic energy, which, in turn, has high velocity.
How, if in fact, can waterfalls be applied to the ... |
Is it necessary for a motion to execute simple harmonic motion to be periodic? Can't simple harmonic be non-periodic?
|
With ref. to "Introduction to Special Relativity by Robert Resnick (1968)"
In the book, while explaining the Michelson Morley experiment there's a statement on pg. 21 that says
"If $M_1$ and $M_2$ are very nearly (but not quite) at right angles, we shall observe a fringe system in the telescope..."
$M_1$ and $M_2$ ar... |
Going from position to velocity to acceleration makes sense. But suddenly acceleration to jerk is hard to grasp. Why is that?
|
Well before a liquid reaches boiling point, it gradually looses molecules with exceptionally high kinetic energies to its surroundings, which is called evaporation. Does this phenomenon occur to some solids as well, where before their melting points, the lose some of their mass into liquid forms? Why don't ice cubes ... |
Can the statement "the sun is $1000$ times hotter than the Earth" make sense without a scale system. I often hear such statements but does it only make sense when using a system with $0$ as absolute zero such as kelvin? For example, $\mathrm{20^\circ C}$ is twice as hot as $10$ degrees but the equivalent $68$ Fahrenhei... |
I was curious as to why in all the diagrams I have seen that the diamond-graphite phase diagram does not display a critical point, do all substances eventually reach a critical point?
|
In quantum mechanics, I read that when operators corresponding to observable commute, then they form a complete set that can define the state of the system.
But in the case of $1$ dimension, we say that, since $\hat{x}$ (position) and $\hat{p}$ (momentum) don't commute, so to define the state of a system, we only need ... |
The other day I created an optical cavity with a first surface mirror and a beam splitter. Here’s a pic of the interference. Has anyone seen something like this. Is it common?
|
Nobody hass seen cold dark matter. Are ultra-cold (non-relativistic) neutrinos, below 1 fK (femtokelvin), an option for dark matter?
This is a question about normal neutrinos - electron neutrinos and muon neutrinos and tau neutrinos - and not any additional, invented neutrino types.
This is a question about neutrinos t... |
Can someone explain Silk-damping in a conceptual way?
I understand that it is the effect causing the power spectrum to decrease in amplitude at smaller angular sizes because the effect is apparently more significant for small diffusion length(small regions), but I do not understand why that is so. How does silk-damping... |
STATEMENT#1:
A vector field can be considered as conservative if the field can have its scalar potential.
STATEMENT#2
If we can have non-zero line integral of any vector field along with a single loop then the field can be considered as non-conservative.
STATEMENT#3
If a static vector field F is defined everywhere, the... |
As one know, according to the ideas of theoretical physics, the equations of motion of particles and the laws of motion of fields (field equations) can be obtained from the principle of least action:
\begin{equation}
S = \int \underbrace{-mcds + \frac{e}{c}A_{\mu}dx^{\mu}}_{\substack{\delta S_{m+mf} = 0 \\ \text{given ... |
This is from MIT OpenCourseWare, 2.003SC Engineering Dynamics, problem set #1, concept question #6. The situation is: given a fixed reference frame $O$, there are two cars having mass $m_1 = 1000 kg$ and $m_2 = 2000 kg$ moving with velocity $v_{1/O} = 25\hat i$ and $v_{2/O} = -25\hat i$ respectively. The two cars then ... |
I'd like to understand the limits to which effective field theory works to sweep microscopic details under the rug in quantum many body problems.
In standard many body text, we start with the picture of second quantization. We start with a many body hamiltonian:
$$ H = {\sum_i} {{p_i}^2 \over 2 m_i} + V(x_i) + \sum_{i... |
When a small droplet is dropped on a extremely hot surface (at around $220^\circ C$), it shows a dancing behavior by moving around fast on the surface. What is the concept behind this bizarre behavior of droplet on a hot surface?
|
In elastic collisions of spheres, there are two approximations that can be made: Either they are perfectly smooth, and you ignore the rotation component, or they are perfectly rough and the rotation is such that there is no slipping.
Consider the situation of hitting a wall with a ball at a $60^\circ$ angle, not rotati... |
Consider the vector field $\vec{u}=(xy^2,x^2y,xyz^2)$
The curl of the vector field is $$\nabla \times\vec{u}=(xz^2,-yz^2,0)$$
Consider the line integral of $\vec{u}$ around the ellipse $C$ $x^2+4y^2=1, z=-1$.
With $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a=1, b=\frac{1}{2}$, the parameterisation gives $$\vec{r}=(x,y,z)=(c... |
I know how to solve these kind of questions but here since it is an inelastic collision I have some doubts. I checked the solution where they conserved linear momentum as: $(M+m)v=mu$ [$v$ is final, $u$ is initial]. My doubt is that shouldn't it be $Mv+m(v+rw)=mu$, where $w$ is the angular velocity of the system and $r... |
The fringe width produced on a screen remains constant as the two double slits get narrower, but you are able to see more fringes on screen.
I don't understand why the fringe width would remain at the same width when the slits get narrower.
In the single slit experiment, fringe width is directly proportional to wavelen... |
I try to get my sound program right, and hoped to find some help here with the understanding of frequency modulation by a square wave.
My modulation looks like this: (please excuse if my formula naming and writing is not standard, glad to learn it)
$$y_m=A \cdot sin( 2 \pi f_c x + \\I \cdot \color{green}{( \frac4 \pi \... |
I know that inner product between 4-velocity is invariant under Lorentz transformation and I know that inner product between any 2 vectors under general coordinate transformation is invariant. Therefore, the inner product between two 4-velocities $u^{i}=\left(d x^{i} / d \tau\right)$ should also be invariant under arbi... |
In photoelectric cells, a current is detected when photoelectrons reach the electrode on the opposite side of the tube after being emitted. But shouldn't current be detected when photoelectrons leave the first electrode and not just when they reach the second electrode? Because this would create a positive charge on t... |
Relative change (or fractional change) in a quantity is defined as the difference between its final and initial values divided by its initial value.
But, what would be the relative change in a quantity whose value starts oscillating? Would it be equal to the difference between its maximum and minimum values divided by ... |
I recently read a question which even I am having a doubt in. So here it is
Suppose there are two isolated conductors both the condcutors are brought in contact now the charges will flow through the conductors so that they both have equal charges and of the same sign. Now they are again taken apart. In this configurati... |
This may very well be a very basic question, but I am somewhat confused by a version of the Schrodinger equation I have encountered studying quantum scattering.
Let us assume we have some potential that is sharply peaked around the origin, and vanishes otherwise. Intuitively this problem was introduced as contact scatt... |
I have a bosonic harmonic oscillator with annihilation and creation operators $a$ and $a^\dagger$. These operators are defined with the position and momentum operators $\hat{X}$ and $\hat{P}$ and verify the usual commutation rules
$$ a = \hat{X} + i\hat{P}\text{ ,} \quad a^\dagger = \hat{X} - i\hat{P}$$
$$ [a,a^\dagger... |
For example a simple complex scalar field theory has a global $ U(1) $ symmetry where the field $ \psi $ can be replaced by $ e^{ i \alpha } \psi $, where $ \alpha $ is just some real constant, without changing the value of the Lagrangian.
Turning this global symmetry into a local one, where $ \alpha $ depends on the... |
The following passage comes from a high school physics textbook, in a chapter about special relativity and length contraction. Specifically, an example was given about a train travelling at relativistic speeds passing a stationary observer, and the fact that a stationary observer would measure the train to be shorter t... |
In the original Brown-York paper on quasi-local charges, they start with this action
$$S = \frac{1}{16 \pi} \int_{D} \mathrm{d}^4x \sqrt{-g} R - \frac{1}{8 \pi} \int_{^3B} \mathrm{d}^3x \sqrt{-h} K + \frac{1}{8 \pi} \int_{\Sigma_{t_1}}^{\Sigma_{t_2}} \mathrm{d}^3x \sqrt{-\gamma} \Theta ,$$
And say that its variation le... |
In cosmology, studying the evolution of the matter perturbations for structure formation, one frequently mentions "horizon entry", meaning that a perturbation of (fixed) wavelength is super-horizon at first, but since the particle horizon evolves with time, it eventually becomes sub-horizon and causal connections are a... |
(1)
On Peskin&Schroeder's book (P&S), page 105, it is written that
Assuming that we are not interested in the trivial case of forward scattering where no interaction take place, we can drop the $\mathbf{1}$ in Eq.(4.72)
, hence they evaluate the amplitude with only non-trivial part, T-matrix, of S-matrix:
\begin{alig... |
Why do physicists dislike naked singularities?
Why do physicists consider the potential existence of Naked singularities as a serious problem?
|
I stumbled on the question I can't quite grasp:
What is the meaning of poles for transmission probability $T(E)$?
$$
T(E) = \left( 1+\frac{1}{4}\frac{V_0^2}{E (E+V_0)} \sin^2 \left(\frac{2 a}{\hbar }\sqrt{2m (E + V_0)}\right) \right)^{-1}
$$
$V(x)$ is a potential, $V(x) = -V_0$ for $-a<x<a$.
First of all, why this func... |
If mosquito and train each travelling in a straight line towards each other with the same velocity, collide with each other head-on, then which object would under the exercion of a greater force?
Now since,
$\mathit {m_{mosquito}} \lt \mathit {m_{train}}$ and
$\therefore$
$\dot p_{mosquito} \gt \dot p_{train}$
Now her... |
According to the definition of the dielectric constant(k) for a dielectric, the electric field in the dielectric is defined as the corresponding electric field in vacuum divided by k.
We are also aware that the cyclic line integral of a electrostatic conservative field is 0 in a closed-loop. Keeping this in mind, let ... |
For an assignment on Quantum Mechanics, we have been given an expression for the quadrupole moment of the deuteron
$$\langle Q\rangle = \langle(2z^2-x^2-y^2)\rangle$$
It is known that the quadrupole moment is a rank 2 tensor, but how come it appears to be a scalar from this definition? Is it actually not the quadrupole... |
How does the expansion postulate allow predictions to be made about measurement outcomes?
I understand the postulate as:
$$
ψ =\sum_{n} a_n φ_n
$$
with coefficients calculated by:
$$
a_n =\int φ_n^*ψdτ.
$$
I think that:
$$
|a_n|^2
$$
is the probability of the system being in state φ, but I do not think that is the ans... |
In the quantum mechanics, the dynamics of quantum system are described in terms of probability amplitude. However, we want to calculate the probability in the end which can be measured. Why don't we develop quantum mechanics directly describing the probability instead of probability amplitude? Wouldn't this make the qu... |
I'm trying to figure out what the driving term in the Hamiltonian is when you drive an emitter (say a transmon qubit) through a coupled cavity (such as a CPW resonator).
For this I am considering a typical Jaynes-Cummings Hamiltonian of the type
\begin{equation}
H = \omega_r a^\dagger a + \omega_q \sigma^\dagger\sigma ... |
Bosons have integral spins and so the total wave-function of a Bosonic system should fundamentally be symmetric under particle exchange. Fermions have half-integral spins and so the total wave-function of a Fermionic system should fundamentally be anti-symmetric under particle exchange. How is this conclusion about the... |
When studying a potential well, the energy is defined as that: $E=\frac{\pi h^2 n^2}{2ma^2}$ and then some books say $E=\frac{p^2}{2m}$. Why energy is just kinetic energy and we aren't considering relativistic energy? Is that because we are talking about non-relativistic quantum mechanic?
|
I want to arrive to Hamilton-Jacobi equation using the Riemannian geometry.
So let $\textbf{X}\in \mathfrak{X}(M)$, where $M$ is Riemannian manifold whose metric is $g:\textbf{T}M \times \textbf{T}M \longrightarrow \mathbb{R}$. On the other hand, let suppose that $\textbf{X}=grad f$.
So $$g(\textbf{X},\textbf{X})=g(g^... |
Heisenberg’s uncertainty principle states that we cannot determine the position and momentum of a particle at a time. I think I have an idea to prove it wrong ( although I believe I must be wrong here) :
Taking two electrons,, $e_1$ and $e_2$ in motion, we can determine the precise position of $e_1$ and the precise mom... |
When I studied about superfludity, everyone just mentioned that He4 and He3 do not crystalline into solid even at absolute zero because the masses of those atoms are very light and then the quantum flutuation prevents them to solidify. However, we all know we very well that Hydrogen atom is even ligher than Helium atom... |
I have a problem understanding the solution of an exercise that deals with a gas in the framework of the canonical ensemble. Because I'm not a native english speaker some sentences might sound a bit weird.
The exercise:
A cylinder with infinite height is filled with an ideal classical gas. A homogenous gravitational fi... |
I know that the density and potential (in spherycals) of a charged ring is, respectively,:
$$
\rho(\textbf{r})
=
\frac{\lambda}{a}
\delta(r-a)\delta(\theta-\tfrac{\pi}{2})
$$
$$
\varphi(\textbf{r})=
\frac{2\pi a \lambda}{r_>}
\left[
1+ \sum_{n=1}^\infty (-1)^n \frac{(2n-1)!!}{(2n)!!}\left(\frac{r_<}{r_>}\right)^{2n... |
I was thinking about orbital velocities, and came across this question (Velocity of satellites greater than required velocity). Does the answer to this question imply that for planets going round the sun, or satellites going round a planet, the eccentricity of the orbit depends on the initial velocity of the orbiting ... |
Recently we had an exercise about the precession of Mercurys perihelion. It went like this:
Using the Schwarzschild-solution of Einsteins field-equations, we can derive the Lagrangian for a test particle (Mercury) in the gravity-field of a much more massive object (Sun):
$$
L=\frac{GM}{2}[(1-\frac{2 GM}{r c^2}) c^2 t^2... |
I know the question sounds a bit broad, but I will specify it a bit more. I also don't think there is a right answer necessarily, I am just interested in the scales of different processes happening out there.
So under the requirement of being able to observe such process today, with our current state of technology, wha... |
This is a direct observation, which many readers can repeat themselves. If you're a nearsighted person, then without glasses or contact lenses, look at a distant light (a solar powered white LED garden light in this instance) through a large black window screen.
When your eyes are very close to the window screen, the ... |
With gravity being so weak I know we need a fairly macroscopic amount of matter to test the value of the gravitational constant, this is hard to come by when we start looking at matter other than that which is comprised of up and down quarks. Have we been able to test gravity on other types of matter without "backing i... |
In Sakurai's Quantum Mechanics the concept of a Hilbert space underlying classical quantum wave mechanics (Schrödinger equation) is extensively developed.
But when dealing with the Dirac equation this concept is dropped and one only works in the position basis (wave mechanics). Why is it that we never use the abstract ... |
Is it true that an ideal capacitor will take no time to discharge? How can it be possible? In discharging, the excess electrons from negative plate leaves the plate and the postive plate acquires some electrons (not the ones from other plate). The motion of charges has to happen in definite time. How can it (time taken... |
Exterior Schwarzschild metric
$$
ds^2=\Big(1-\frac{2M}{r}\Big)dt^2- \Big(1-\frac{2M}{r}\Big)^{-1}dr^2-r^2 d\theta^2-r^2\sin^2\theta d\phi^2
$$
I knew that there are two Killing vectors associated with the Schwarzschild metric, $K^{(1)}=(1, 0, 0, 0)$ and $K^{(2)}=(0, 0, 0, 1)$.
But, in an article written that there are... |
I understand that the gradient $\partial_i$ is covariant.
Let f be a function of 3 variables
So I can write the total differential as
$$
df=\partial_1fdx^1+\partial_2fdx^2+\partial_3fdx^3 = \partial_kfdx^k,
$$
summing correctly over the same lower and upper index.
But when I write
$
\displaystyle\partial_i=\frac{\parti... |
I have just found out that proteins (at least in some cases) are folded into their functional conformation (i.e. their functional folding), through thermal fluctuations, and that this conformation minimizes free energy. i.e. that the reason that a protein has a certain conformation, is because this conformation minimiz... |
I am confused about a given solution for the following exercise:
A thermodynamic system consists of N atoms in the Volume V. Every atom has a magnetic moment. The hamiltonian can be written as a sum of two parts, where H0 describes the system in the absence of a magnetic field, and H1 describes the influence of the hom... |
What are the longest and shortest wavelengths of the cosmic microwave background?
Since it is 'black-body' radiation, does this correspond to max. and min. temperatures?
|
I read the claim that the total weight of the air above my (or rather: the average adult human's) body equals that of two elephants.
Now I am pretty sure that if two elephants would stand atop of me, I would get crushed. But does the above mean that this crushing is due to the combined weight of air and elephants (net ... |
The properties of a system in thermodynamical equilibrium are described by a partition function:
$$
\mathcal{Z} = \text{Tr} \ e^{-\beta E} = \sum_n e^{-\beta E_n}
$$
This defines so called canonical ensemble. When we have several conserved quantities - particle number $N$, angular momentum $J$, ... , one can define gr... |
I am trying to calculate EM-energy store in a Gaussian beam as
$U_{EM} = \epsilon_0 \int_V d^3r \vec{E} \cdot \vec{E}^{\dagger}$
What I get is $U_{EM} \propto (\pi A^2/2)*\infty$ because of integration over $z$. What is the consistent way of defining the EM-energy stored in an optical beam?
Thanks in advance for help!
... |
In this paper (Four-Dimensional Asymptotically AdS Black Holes with Scalar Hair by Gonzalez et. al.), the following standard metric is taken as an ansatz for the hairy black hole:
$$ds^2=-f(r)dt^2+f^{-1}(r)dr^2+a^2(r)d\sigma^2$$
where $d\sigma^2$ is the metric of the spatial 2-section, which contains the curvature. Thr... |
I found a recursive scheme to solve the Kohn-Sham equation.
However, I have a misunderstanding: how to choose the electron density for the initial step?
There are two ways to calculate the electron density:
\begin{equation}
\begin{gathered}
n (\mathbf{r_1})=N \int |\Psi(\mathbf{r_1}, \sigma_1,..., \mathbf{r_N}, \... |
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