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I'm currently struggling with understanding how to find the momentum-representation of a wave function and I could need some help with understanding this. I know from varying sources that the Fourier-transform is an important key of understanding and computing this.
I have one proposed way of finding the momentum repre... |
In CFT, one ususally begins quantization by defining radial ordering on the complex plane, with the notion of radial ordering being the equivalence of time ordering. This is often "motivated" by making a conformal map from the (assuming Euclidena signautre ) cylinder $\mathbf{r}=(t,x)$ to the complex plane via $z\equiv... |
I know to carry out an NAA analysis, the specimen is placed into a suitable irradiation facility and bombarded with neutrons. This creates artificial radioisotopes of the elements present. Following irradiation, the artificial radioisotopes decay with emission of particles or, more importantly gamma rays, which are cha... |
A White object reflects all the visible colored light but so does a flat silver object (mirror) so what makes them look so different?
This has been answered here but that shouldn't be true because white objects can be highly polished too. Also if we make a silver object irregular/rough it doesn't turn white
EDIT:
(1s... |
I am working on a thermodynamics problem involving a pressure cooker and have come across two different approaches to solve it. Surprisingly, both methods yield the same result. I am looking for some guidance and clarification on why this is the case, and if one of the methods is more appropriate than the other. Here's... |
Say the dispersion is isotropic:
$$E=E_0+\frac{\hbar^2k^2}{2m}$$
Then the density of states in the valence bands are given by
$$g_{lh}(E)=\frac{\sqrt{2}}{\pi^2\hbar^3}m_{lh}^{3/2}\sqrt{E_v-E}$$
$$g_{hh}(E)=\frac{\sqrt{2}}{\pi^2\hbar^3}m_{hh}^{3/2}\sqrt{E_v-E}$$
If I want to calculate the total number density of holes w... |
According to Maxwell's equations, electric and magnetic fields (EF and MF) should have the same phase for EM waves.
Also, they must be perpendicular and perpendicular to the propagation direction.
If we consider a planar wave spreading in the +x direction with an EF in the y axis, the MF would be in the z axes. At any... |
So, in many papers, I found this intuitive illustration and I have a problem with understanding it.
So, as I understand in the insulating state, we consider a system and there are electrons that move in a circular orbit around some atom (red in the picture). And below, in the quantum Hall state, there are similar circu... |
In R.Wald's book on "General Relativity" appears on p.61 (section 4.2) a rather peculiar definition of the energy of a massive particle:
$$ E = -p_a v^a \tag{4.2.8}$$
I guess the minus sign comes from the use of the east-coast metric in Wald's book
$\eta=diag(-1,1,1,1)$.
Right before he first defines the momentum 4-vec... |
How does Stirling engine work exactly? What I am really curious about is how one side is hot and the other cold at the same time all the time shouldn't the heat source heat one side then the heat move to the other side and they become both hot
and another thing I don't understand is after one side is heated the piston ... |
Suppose that there is an isotropic, homogenous space which is non-stationary in time (expanding/collapsing).
Let say that some package of electromagnetic radiation flows in portion of space far from gravitating bodies for large period of time.
According to Noether theorems, energy conservation stops to be applicable in... |
I'm simulating simple 1D superconductors gap using the BdG method, considering hopping terms just with the nearest neighbors, with periodic boundary conditions, using the following Hamiltonian:
$$H = \sum_{<i,j>} t_{ij} c^{\dagger}_{i} c_{j} + \sum_{<i, j>} \Delta_{ij}c^{\dagger}_{i} c^{\dagger}_{j} + \sum_{<i, j>} \D... |
I calculated a Feynman diagram once the standard way, and once I used Cutkosky rules to get the imaginary part and then an unsubtracted dispersion relation to get the real part. The imaginary part from both methods agrees, but the real part does not agree. Can this be correct, or does the real part also have to agree s... |
I was solving '200 Puzzling Problems in Physics' as a recreational activity and I encountered this beautiful question which surprised me as I understood a basic flaw in my conceptual understanding.
The problem is the following (but my doubt is on the conceptual side)
A long, thin, pliable carpet is laid on the floor. ... |
The generalised Fermi-Dirac integrals can be written as
$$F_n(\eta,\theta)=\int_0^\infty \frac{x^n \sqrt{1+(x\theta/2)}dx}{e^{x-\eta}+1} \ .$$
Is there any possibility of rewriting the following integral
$$\int_0^\infty dpp^2\frac{1}{\exp\left(\frac{E(p)-\mu}{kT}\right)+1}\ln\left(\frac{(k+p)^2}{(k-p)^2}\right) \ ,$$
w... |
Let $C^{\rho}_{~\alpha \beta \gamma}$ be the Weyl tensor of a spacetime $(M,g)$, that is a solution to Einstein's equation. Let $X^\alpha, Y^\alpha, Z^\alpha$ be null vector fields, i.e. $X_\alpha X^\alpha = Y_\alpha Y^\alpha = Z_\alpha Z^\alpha = 0$.
Are there conditions on $(M,g)$ s.th.
\begin{equation}
k^\rho := C^\... |
I try to answer the question whether spacetime of Schwarzschild vacuum solution is geodesically complete by analyzing its null geodesics. The infinitesimal length element is $$ds^2=(1-\frac{r_s}{r})~c^2 dt^2-(1-\frac{r_s}{r})^{-1} dr^2-r^2 d\Omega^{2}. \tag{1}$$
The solving of corresponding differential equation for $d... |
i wanted to verify the measured data with calculations. So i got two totally different answers when calculating average acceleration.
V0 = 0 km/h
Vf = 30 km/h = 8.33 m/s
t = 9.32 s
S = 55.59 m
So "S" is measured distance when i reached 30 km/h and i wanted to verify that by calculating it from average acceleration. So ... |
Lets say I am in a circular orbit around the sun. From the suns perspective, Im 'rolling' circles in its gravitational well.
But from my perspective I'm just being stationary. Spacetime is flat for me but I can calculate that the sun should bend/accelerate towards me (or I towards the sun).
But because, from my perspec... |
I'm looking at the chiral anomaly in QFT and the term
$$d_{abc}=Tr_R(T_a\{T_b,T_c\})$$
shows up where $Tr_R$ means the trace in the representation $R$, $\overline{R}$ is the conjugate representation and $T_a$ are the lie algebra generators.
I've seen it stated in a number of sources that for real and pseudoreal represe... |
I’m an undergrad currently writing a report on a lab we’ve done using X-ray diffraction to look into the structure of crystals. We’ve been told that the structure factor of an element relates to the amplitude of diffraction, but not much more than ‘if it’s zero, you get no diffraction’.
I found a formula that seems to ... |
What is the orbital velocity formula in Schwarzschild metric assuming that the orbit is circular? this formula should also work for relativistic velocities.
|
In Fermi liquid theory, the quasi-particle is well-defined only near the Fermi surface. However, in calculating specific heat and compressibility, we also assume that the quasi-particle obeys the Fermi-Dirac distribution
$$
n_{k\sigma} = 1/(e^{\beta \epsilon_k}+1),
$$
where $\epsilon_k$ is the renormalized energy of ex... |
can i just turn electricity into light and back¿?
light is a wave so i can send light from point to point
the idea would be applied to have wireless electricity in the world, turning electricity into light
at the point A and then sending the light wirelessly from point A to B and turn back light into
electricity at the... |
Imagine an ideal pendulum who's length can change arbitrarily throughout its motion. Does the length of the curve described by the bob during the descent phase of the pendulum's oscillation always equal the length of the curve described by the bob during the corresponding ascent phase?
Assume that the bob never swings ... |
In the chiral model $SU(N)_R × SU(N)_L$ with gauged Left-handed $SU(N)$, we take as the field the $SU(N)_L$-valued $\Sigma (x)$, defined as
$$\Sigma(x) = \exp\big( \frac{2i}{v} \chi^a(x)T^a\big).$$
What is the reason for which, in the chiral lagrangian, we take the exponential field $\Sigma (x)$ defined this way, inste... |
The solutions of the Klein-Gordon equation for free particles are $e^{-iE_p t+i\vec{p}.\vec{x}}$ and $e^{iE_p t+i\vec{p}.\vec{x}}$ for energy eigenvalues of $E=E_p$ and $E=-E_p$ respectively. The charge denstiy $\rho=\frac{ie}{2m}[\psi^*\partial_t\psi-\psi\partial _t\psi^*]$ is postive for positive energy and negative ... |
I am working on a problem in which I need to numerically solve the continuity equation in an axisymmetric coordinate system (i.e. cylindrical with no $\phi$ dependence). For concreteness, I will use my problem, which deals with an electron number density function $n_e$ and electron velocity function $\vec{u_e}$, but of... |
At the equator at sea level you are about 17 miles higher up than at the poles ie 17 miles further from the center of the earth. Yet the air is not the same as it would be 17 miles up at a higher latitude. It seems to average the same as at sea level anywhere else on the earth. Is there one reason for this or is it ... |
Suppose a CFT hilbert space contains a unique state $|0\rangle$ satisfying $D|0\rangle = 0$, where $D$ is the dilation generator.
By assuming $D\geq 0$, one can prove $K_\mu|0\rangle = 0$ (since $K_\mu$ is a lowering operator, if $K_\mu|0\rangle$ were nonzero it would have negative dilation eigenvalue, a contradiction)... |
I know that the cosmological principle states that the universe is both isotropic and homogeneous, but I was wondering if these both had to exist at the same time? Is there a way that the universe could be isotropic, but not homogenous or the other way around and what would that look like?
|
I have heard that gravity as described by General Relativity (GR) is non-renormalizable, so it is not possible to quantize GR. What about Newtonian gravity? Is it renormalizable? Is a quantum version of Newtonian gravity possible?
|
I have read these
What are quantum fluctuations, really?
Quantum fluctuation
https://www.physicsforums.com/insights/vacuum-fluctuations-experimental-practice/
and found out that quantum fluctuations (or virtual particles) are just tools of QFT theories in the perturbative context. Nothing more than mathematical tools... |
What are all the fields that we know so far that can be associated to charges of the kind "+" and "-" (not necessarily the electric +/- charges). I already know the EM field. Are there other examples? Will the disturbances in such a field propagate slower than the speed of light? (like for the EM field)
Example: not g... |
I understand that in an inelastic collision, mechanical energy is lost to heat, sound, deformation, etc. However, if there is no friction between the two objects that collide or the two objects with the ground, then is mechanical energy still lost in a collision where the two objects stick together afterward?
|
I've been doing some reading on the free-electron laser and its practical applications, one of which seems to be in the (relatively) quick and uniform production of single-wall carbon nanotubes via laser ablation.
I understand that, in what is likely a very hand-wavy sense, laser ablation forms carbon nanotubes by heat... |
If the Moon became suddenly gained 20% of its mass, would it come crashing down to the Earth, or would it just stabilize at a lower orbit? Similarly, if it suddenly lost 20% of its mass, would it fly off into space, or just stabilize at a higher orbit?
Assume that the mass just spontaneously appears/disappears without ... |
I am trying to fit data (muon decays) to find the decay rate. The detection technique introduces a background rate of false decays uniformly distributed throughout the range of data (0 to 20 µsec). So, in other words, the data theoretically should fit the function
\begin{align}
N(\Delta T) = N_0 \exp(-\Delta T/\tau) ... |
I am trying to calculate the cross sectional area of the impingement zone created by two equal, two-dimensional streams impinging upon one another. The attached diagram shows Stream 1 impinging with equal stream, Stream 2, at an angle of $2\beta$. All quantities on the diagram except $y$ are known. I need to calcul... |
When I try to understand magnetic reconnection, I have a fundamental conflict with my intuition of magnetic fields.
I think it is literally a case of cognitive dissonance, my intuition and any kind of disconnection of magnetic field lines, even temporary, can not coexist.
In my intuition, a magnetic field line is a clo... |
Given two round bars with uniformly tapering radii, one from a smaller to a larger radius and one from a larger to a smaller radius, the former bar experiences greater maximum stress.
Since stress depends solely on the weight and area of a bar, I don't understand how this occurs. The force while taking cross-sections o... |
I'll start with the common setup where a free charge is placed near a wire through which current does not flow. The wire is neutral so the free charge does not feel any force upon it. When the a current is generated through the wire (meaning that electrons start moving and the atoms remain in their places, ignoring sma... |
I am working with deterministic Ising model in this form
$$
p(\sigma; W_\beta, h) \propto \exp(-E(\sigma; W_\beta, h))
$$
where
$$
E(\sigma; W_\beta, h) = - \frac{\beta}{2} \langle \sigma, W\sigma \rangle - \langle h, \sigma \rangle
$$
and it is defined over $\{ -1, 1 \}^N$.
I want to find the expectation $\langle ... |
While studying about Hawking radiation, I read that the last evaporation phase of a black hole is a gigantic explosion. This webpage says
... The more massive the back hole, the
more energy would be released. Over time, the black hole would
eventually lose so much mass that it would become small and
unstable ...
So, ... |
I have been asked to find the equivalent resistance in the following circuit. However, is the circuit valid, as a zero resistance wire is connected between 2 different potentials?
Also, how to calculate the net resistance here?
|
Liouville theorem states that the phase space distribution function of a system remains unchanged with the system evolution,
$$
\frac{\text{d}\rho}{\text{d}t}=\frac{\partial \rho}{\partial t}+\sum_{i=1}^N\left(\frac{\partial \rho}{\partial q_i}\dot{q}_i+\frac{\partial \rho}{\partial p_i}\dot{p}_i\right)=0.
$$
A consequ... |
If a (varying) force was applied to a charged particle such that it moved towards the (point) source of a static electric field at constant velocity, would that particle in its reference frame experience an EM wave?
The particle would be experiencing time varying electric field, which suggests to me it would experience... |
I want to obtain the diffraction pattern in the focal plane produced by an input Gaussian with waist $\omega$ and a phase disk with radius R and offset $\pi$, i.e. of an input field
$$E_i(\rho) = A_0 e^{-(\rho^2/\omega^2)}\times e^{i\phi(\rho)}$$
with $$
\phi(\rho) =
\begin{cases}
\pi , & \rho \leq R \\
0, & \text{el... |
I am processing the experimental data of wave pulses. The amplitude of these pulses is a piece of important information to acquire.
In my data acquisition, we acquire the sample data and some reference data (to compare the sample's data to).
When analysing the data I was told to instead of analysing the total amplitude... |
In many text books on general relativity it is shown that you can compute the gravitational wave metric in the TT-gauge by projections with the Lambda tensor.
$$
\bar{h}^{\mu \nu} = -\frac{4G}{c^4} \int_\mathcal{V} \frac{T^{\mu \nu}(t-\frac{|x-x'|}{c}, x')}{|x-x'|} d^3x'
$$
$$
h_{i j}^{TT} = \Lambda (\hat{n})_{ij,k... |
I am reading the calculation of charge conductivity by Non-Equilibrium Green Function (NEGF) method in this following paper.
Van-Nam Do, Non-equilibirum Green function method: theory and application in simulation of nanometer electronic devices, Adv. Nat. Sci.: Nanosci. Nanotechnol. 5 (2014) 033001 (21pp)
According to ... |
I am working on an experiment to learn about rotation motion and find the correlation behind the between the spheres’ diameters and the time taken for them to make their way down an track at constant length, L, held at a height h. Different diameters, d, of spheres were used. They sit on the rail with inner width, w.
I... |
Say I have an ellipsoidal dispersion:
$$E(k) = \frac{\hbar^2}{2}\left[\frac{k_x^2}{m_x}+\frac{k_y^2}{m_y}+\frac{k_z^2}{m_z}\right]$$
If I want to talk about the conductivity in the x-direction, I need to use $m_x$.
But what if I want to talk about the conductivity along the unit vector $(1,1,1)$? More generally, what i... |
I am reading a paper on creating ponderomotive traps for neutral atoms.
The setting is that we consider the far-field (Fraunhofer) diffraction pattern of the input field
$$E_i(\rho) = A_0 e^{-(\rho^2/\omega^2)}\times e^{i\phi(\rho)}$$
with $$
\phi(\rho) =
\begin{cases}
\pi , & \rho \leq R \\
0, & \text{else}
\end{cas... |
I am currently working on a signal vs. background study for some particle physics detector.
I am having a hard time understanding how I should normalize the signal/background histograms such that my analysis makes sense.
The idea of the study is to apply selections on the data in order to reduce the background while sa... |
In the top-down approach, e.g., Fermi interaction obtained from EW Lagrangian, the loop corrections (using dimensional regularization) and renormalization of $G_F$ are done using the full EW Lagrangian. What happens when we don't have a UV complete theory (which we will never have anyway, in Wilsonian picture, since al... |
Consider the operators
\begin{equation*}
\mathbf{J}^{2} = J_{x}J_{x}+J_{y}J_{y}+J_{z}J_{z}
\end{equation*}
where the $J_{i}$ are the generators of infinitesimal rotations. Choosing $\mathbf{J}^{2}$ to be simultaneously diagonalizable with $J_{z}$, we have
\begin{equation*}
\mathbf{J}^{2}|a,b\rangle = a |a,b\rangle
\end... |
It was previously my understanding that the reason blackbodies only emit light was because light was the only massless particle, so there exist excitations of the electromagnetic field of arbitrarily low energy. And that if a blackbody somehow had a temperature near $500\text{ keV}$ it would also emit electrons and pos... |
I'm puzzled by the fact that the CoP (Coefficient of Perfomance) of residential heat pumps is usually stated to be between 4 and 5, meaning that for every kWh of electricity used by the pump one gets between 4 to 5 kWh of heat transferred into the house. How's that even possible?
Here's my reasoning: the gaseous fluid ... |
Assume that the Dirac string is lying along the negative $z$-axis, and is subject to a magnetic field $B$. Assume throughout this question that we are considering a static situation. The force on the Dirac string is given by
$$F=g\int_{-\infty}^0 dz'\nabla '(e_z\cdot B)$$
Assuming a) $B$ vanishes at infinity i need to ... |
What is the highest frequency of AC that we can possibly produce?
is there only one method of inducing AC?
for dipole antennas that can produce frequencies up to GHz, it must need an AC current, or is it?
for configurations of generators that I know, it would break into pieces if spinning up to such high RPM.
|
For my physics research course I am supposed to get the equation of motion from a given action $S$:
$$
S = \frac{-1}{2} \int d^4x \sqrt{-g} (g^{\mu\nu} \frac{\partial \phi}{\partial x^\mu} \frac{\partial \phi}{\partial x^\nu} - m^2\phi^2).\tag{1}
$$
I take the variations according to the following rules:
$$
\phi \right... |
I have proved this statement in multiple ways. Yet my intuitive proof goes against the mathematical proof: one must be wrong!
Statement
In a projectile motion with no drag, the magnitude of the projectile speed at height $h\leq h_{max}$ of its trajectory depends on $v_i$, $g$, $h$ but not on $\theta$
Intuitive Proof... |
I have an implementation of over-damped Brownian dynamics, with particles that follow the version of the Newtons law where the inertia is absent. This is a common thing to do at micrometer scale.
$m x''(t) = \Sigma F(t) - \gamma x'(t) + \xi (t)$
with no inertia, the equation is reduced to
$ x'(t) = (\Sigma F(t) + \xi (... |
Why does raising the sample under a FD OCT machine cause the image to flip at the top? I know that FD OCT is looking at the time delays of backscattered light at every tissue layer which interferes with the reference beam. Then a fourier transform of this interference yields the frequencies which correspond to specific... |
As we can see bellow TE01 and TE11 mode taken from the manual bellow.
The fiirence between the two in the first index,but the shape is totally changed.
Is there a logic regarding the shape of the mode with respect to the indexes?
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Book%3A_Applications_of_... |
Consider a situation like this
There is a rope of uniform mass $M$ whose one end is attached to a wall.
Obviously, the gravitational force $mg$ and normal force are acting on it in vertical direction (that's not our concern).
My real concern is:
When I "push" on the rope, I basically apply a force on the end of the ro... |
As we are able to see the egg, is this diffraction? Is light bending here somehow?
https://www.instagram.com/reel/CrXyD-NLbNl/?igshid=YmMyMTA2M2Y=
|
In this Wikipedia post the $r_p$ Fresnel reflection coefficient is given by:
$$r_p = \frac{\tan{(\theta_i - \theta_t)}}{\tan{(\theta_i + \theta_t)}}.$$
How can this be derived from the previous expression, given below?
$$r_p = \frac{n_1 \cos\theta_i - n_2 \cos\theta_t}{n_1\cos\theta_i + n_2\cos\theta_t}$$
The article s... |
I would like to get the differential equation (Which solution is v the speed of the electron and using Newton's second law) for an electron where the only force applied on it is the electric part of electromagnetic force (we neglect the magnetic part).
In this situation I know the electric field :
$$\vec{E} = E_0 cos(\... |
The question is quite straightforward. A $K^+$ meson can decay weakly as follows:
$$
K^+ \longrightarrow \mu^+ \nu_{\mu},
$$
with a decay time of ~12 ns, whereas the weak decay of an anti muon,
$$
\mu^+ \longrightarrow e \ \bar{\nu}_{e} \ \nu_{\mu}
$$
has a decay time of ~2 $\mu$s. Why is there such a difference betwe... |
I'm looking at this wikipedia derivation
(link) for the threshold energy of a reaction of the form
$$
1+2 \rightarrow a + b + c
$$
but I get to a different result because wikipedia says
$$
E_1 = \frac{E_{CM}^2-(m_1+m_2)^2}{2m_2}
$$
but I get
$$
E_1 = \frac{E_{CM}^2-(m_1^2+m_2^2)}{2m_2}
$$
who's right and who's wron... |
The theorem:
Let $F$ and $C$ be two finite geometric figures (those defined by two continuous functions in a given region $D$), where $F$ belongs to an $n$-dimensional Euclidean space and $C$ is the result of applying a transformation $T$ to $F$ that introduces curvature on its surface, placing it in a non-Euclidean s... |
The crucial step in the typical (see e.g. Sakurai Chapter 3.5.1) proof of the eigenvalues of the angular momentum operators $J^2$ and $J_z$ is (after defining the ladder operators $J_\pm :+ J_x \pm iJ_y$ and showing that they map an angular momentum eigenstate $|j,m \rangle$ into the $m+1$ eigenspace but not out of the... |
I have read (https://academic.oup.com/book/25938) &(https://link.springer.com/chapter/10.1007/978-3-642-05169-2_3) that initial state radiation can be used to make a determination of the Z boson's invisible width, but I'm a bit confused as to the details of how exactly. Taking LEP as an example, a photon could be emitt... |
This is a long post, but only because I have explained the scenario very very clearly,90 percent of this post is explaining you a simple situation,my doubt is only 5-6 lines at the very end of this post,so please bear the patience and please help me
Imagine a scenario where 2 people are pulling with equal forces of 100... |
I'm not a physicist so all my understanding comes from educational content online.
I think I understand how transformations for switching perspectives between moving frames of reference work, and if this understanding is correct, it should imply that each object must exist at all times, forming a sort of "stack of fram... |
In the electroweak lagrangian, after symmetry breaking we get $W^1_\mu,W^2\mu,W^3\mu$ and $B_\mu$ bosons. These fields don't however diagonalise the mass matrix $\frac{\partial^2V}{\partial\phi_i\partial\phi_j}$ (where the $\phi_i$ are one of the fields, in this case $W$ or $B$).
As I understand it, the mass matrix is ... |
Is it possible to have a hypothetical temperature scale that does not follow a linear relationship with another temperature scale? For example, the graph formed between the readings taken by a thermometer in Fahrenheit and Celsius is a straight line.
|
In David Pine's Theory Of Quantum Liquids: Normal Fermi Liquids, it's said that we can find charged Fermi liquid has plasmon modes easily from Eq. (3.40), replicated as follows:
$$
(\boldsymbol{q} \cdot \boldsymbol{v}_p - \omega) \delta n_{\boldsymbol{p}} + \boldsymbol{q} \cdot \boldsymbol{v}_p \delta(\varepsilon_p - \... |
Let us imagine a rough horizontal surface with static frictional coefficient $u$ and an object of mass $m$ sitting on that surface. The maximum static frictional force that can be applied is $uN$ where $N$ is the normal reaction. So,if we apply a force $F<uN$,then the object won't move. However,as soon as we apply a fo... |
I am currently on a small individual research project researching the evaporation rate of miscible liquids and have some questions about the data that I have received and how to interpret it. The following graph shows the data gathered over 5 repeats for each concentration of a mixture of ethanol and water by % volume ... |
When 2 bodies collide with each other, they deform for a while. The contact force rises, reaches a maximum, then falls. It is easy to find the average force during this time if we know the duration of collision and the change in momentum. But how should we find out the maximum force that is exerted between the 2 object... |
the density operator can be written as
$$
\rho=\sum^N _{i=1} w_i |i\rangle\langle i|
$$
Now I am not sure if the following is true
$$
\langle k|\rho|k\rangle=\langle k|\bigg(\sum^N _{i=1} w_i |i\rangle\langle i|\bigg)|k\rangle=\sum^N _{i=1} w_i |\langle i|k \rangle|^2
$$
I know that $ |i \rangle \langle i| |k\rangle = ... |
by definition magnetic wall is PMC where magnetic field perpendicular to the wall and electric field is parralel to the wall .PEC in the opposite.
In the top photo shown bellow taken from the link bellow the electric field is horizntal.
so there could be magnetc wall in parralel to the electric field.
In the buttom pho... |
(This is a classical-mechanics question)
Sorry for the trivial question. A force $\vec{f}$ doesn't depend on the frame of reference; however, the work $W$ done by $\vec{f}$ is, in general, a quantity that changes if we choose a different frame. A simple example: a body $P$ falls from an height $h$ to the ground because... |
So I recently learned about bomb calorimeter and it said that we stirred it to have temperature constant all over, but we also need it to be accurate so doesn't stirring also generate heat, so do they account for it or just neglect it.
|
In order to work out the angular dependence of the differential cross section of an interaction, we can use the Wigner rotation matrix elements, which quantify the probability of rotating through some angle in the CM frame. I understand how this works in the case of a system in which the total spin is 1. For example in... |
Suppose I have a family of effective field theories, parametrized by a cut-off $\Lambda$ and a coupling constant $g$ and specified in terms of generating functionals $Z_{\Lambda,g}(J)$. Asymptotic freedom means that there is a renormalized trajectory $g(\Lambda)$ such that $\lim\limits_{\Lambda\to\infty} g(\Lambda) = 0... |
One of the problems in making a coil gun shoot high-velocity projectiles is that after the projectile passes the mid-point of the coil, it experiences suck-back: a force that slows the projectile and tries to bring it back to the center. You can get around this to some extent by shutting off the coil at the right time,... |
I have been trying to wrap my mind around how the resolving power (in terms of the modulation transfer function, or MTF) of individual elements in an optical system affect the overall resolving power of the system, and I've come across the following formula (which I believe is an approximation) in a few places, namely ... |
I could use some help understanding the initial conditions described in
Omar, Yasser & Paunkovic, N. & Sheridan, L. & Bose, Somesuvra. (2004). Quantum Walk on a Line with Two Entangled Particles. Physical Review A. 74. 10.1103/PHYSREVA.74.042304.
https://www.researchgate.net/publication/2194149_Quantum_Walk_on_a_Line_w... |
I am trying to design a heatsink as part of a broader system and deturmine two things:
Given the size constraints of the system, commercially available fans, and heat dissipation requirements, is it even possible to design a heat sink to meet the requirements?
If it is possible, what is the optimal number and size of... |
I had a brief question regarding 2 fermions (with spin) in a 1D infinite potential well (going from $-L/2$ to $+L/2$, where $L$ is the width of the well).
To start off with the question, "what would be the wave function (both space and spin) for the 2 fermions in the ground state?"
Here's what I've got so far:
From the... |
We take a horizontal cylinder of length $L$ and fill it with incompressible water of mass $m$ and close the two ends with lids. If we start rotating the cylinder with respect to one of the ends,the other end will feel a force due to the centrifugal force. Since water is a continuous body,we can assume it to be concentr... |
I was reading the Wikipedia page on fine structure, and it had the following expression for the fine structure of Hydrogen:
To recap the image, Wikipedia includes the spin-orbit interaction, the first relativistic kinetic energy correction, and the Darwin term.
The expression of the perturbation to the energies matche... |
As we can see below, they say that for $TE_{01\delta}$ if a wave hits the border between dielectric constants then it will reflect back so why exactly is this property is PMC (as they say below)
PMC is perfect electric conductor, what does it have to do with reflecting a wave?
I see PMC only as a boundary that allows m... |
I've been looking into black holes and Hawking radiation recently (just on the surface level) and was reading "A Brief History in Time" by Stephen Hawking to understand the basics of Hawking radiation. Then I came across a website online which stated that Hawking's explanation (in the book) was not entirely accurate. ... |
I am taking a first course in statistical mechanics. Consider a one-particle system $S$ connected to a heat bath $R$. The total energy of $R + S$ is $U$, which stays fixed, and the total number of particles is $N$ so that the reservoir has $N-1$ particles, and this stays fixed throughout, too. We want to find the most ... |
A snippet out of the lecture notes from my first course in statistical mechanics:
For a simple example, consider a single spin-half particle with spin down in system 1
coming into thermal contact with system 2 containing nine spin-half particle all
spin up. After thermal contact, the particle in system one is most lik... |
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