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If we assume the many-worlds interpretation of quantum physics is true, what exactly happens during decoherence, that makes it impossible for the different worlds to create interference with each other afterwards?
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I'm curious about how entropy is defined within chaos theory. Are there analogous laws similar to the second law of thermodynamics? How do we define steady-state or equilibrium within the state space of a system governed by chaos theory? Is the dynamics considered reversible in principle? These questions highlight my l... |
If 2 objects connected by a massless rod or wire, rotate around the center of mass, do they experience time dilation ? I'm thinking that the smaller one will move faster so time will pass slowly, but the bigger one being bigger time will also pass slowly. Do the 2 effects cancel out and they both experience time at the... |
In the diffraction phenomenon, when I search for layman examples in youtube, I see an image of an obstacle with a tiny hole (aperture) in it, so that light goes through the aperture and scatter around on the other side.
What kind of object does this obstacle need to be? Does it need to have low electrical resistivity? ... |
I am told that the azimuthal coordinate operator $\hat{\phi}$ is not self-adjoint. I am told this by people who I am sure know much more about this stuff than I do. To my unsophisticated mind, "non self-adjoint" means "not Hermitian". So I think I will demonstrate this to myself by calculating some matrix elements. ... |
I wondered about that question and regardless of the obvious answer (If $k$ increases, the Electrostatic force increases), What can we conclude from $||\vec{F}_e||$?
|
As it now widely dicussed and accepted that Earth is not a 'perfectly round sphere/ball but more a 'oblate spheroid' why then do NASA have 'photographs' of a ROUND Earth?
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Similar questions have been asked before in the forum regarding the sign problems when integrating the electric field, but they do not fully clarify the problem for me, so I just want to ask for some further clarification.
Suppose we have a positively infinite line charged ($\lambda$ is the linear charge density), whic... |
I am attending an advanced QFT course, and trying to verify the instructor's claim that the retarded Green's function
$$ G_{\text{ret}}^{(4D)}(t,\mathbf{x}) = \theta(t) \left[ \frac{1}{2\pi}\delta(\tau^2) - \theta(\tau^2) \frac{m}{4\pi\tau} J_1(m\tau) \right] \\
(\tau^2 = -t^2+\mathbf{x}^2, \text{ mostly positive signa... |
To preface, I've little experience with optics. This is a very use-case specific project I'm undertaking. So, if there are any improvements in my method, I'd appreciate it!
I'm working with the vector Rayleigh-Sommerfeld integral to propagate polarized light incident on an aperture as dictated by diffraction theory. Th... |
Why don't we divide each by $B$ in equation(2) in the following:
We start of by defining a method to plot field lines. For this we will be using the general differential field line
equation. If the magnetic field $\vec{B}=(B_{x},B{y},B{z})$ is known than the field lines of the magnetic field will be defined
by;
$\frac... |
Solutions to the Schrödinger equation can take the form $ \psi(r,t)=\psi(r)f(t) $, where $f(t) = e^{\frac{-iEt}{\hbar}}$,
$$ H \psi(r) = E \psi(r) ,$$ where $\psi(r)$ is the eigenstate of a Hamiltonian.
If I consider the general function $\Psi(r)$, for example taking $\Psi(r)$ as a Gaussian wave packet, does $\Psi(r)$ ... |
In the very beginning of the book "Fundamentals of Optical Waveguides" by Okamoto, there is a description of light ray propagation in the waveguide. I provided an updated Figure from it:
According to Okamoto, the distance RQ between points Q and R is defined as $2a/tan(\phi) - 2a*tan(\phi)$, which is MQ - MR, accordin... |
I'm studying the concept of grounding of neutral wire in AC. I have done an extensive research on the internet to answer the question "Why the neutral wire has 0 potential ?". The answer is because it is connected to the Earth. But I don't get it.
In general, why should something connected to Earth has 0 potential ? In... |
As far as I understand it, in the context of large structure formation, the interplay between gravity and cosmic expansion can cause certain anisotropies in voids that can make them collapse (https://arxiv.org/abs/astro-ph/9601026)
Can something similar happen to superclusters as well?
|
I am confused about some principle relations. We look at an atom interferometer which consists of a beam splitter and recombination.
We are given a wavelength $\lambda$ and a paths length difference of $d$. We want to calculate the de Broglie wavelength.
Here is what I am confused about:
What's the difference between ... |
If we are going uphill using Tesla car, it uses energy from the battery however when we come downhill it charges the battery, I am not sure if the charge produced while driving downhill will be equal to the charge used when going uphill but if hypothetically we consider it to be equal, will still be work done zero?
|
I know torque due to Fg is zero on a level rod. However if the rod is tilted like below, is the torque still zero? The pivot point is on the center of mass.
|
The equation for a travelling wave is usually taken in the form of,
$$y = A\mathrm{e}^{i(kx - \omega t)}$$
When a standing wave is formed by the interference of two counter-propagating waves, then it implies that the equation of the reflected wave is in the form of,
$$y = A\mathrm{e}^{i(-kx - \omega t)}$$
Now, given a ... |
In my book it says:
We can choose a convenient reference by noting that the coulomb force at infinite distance is zero. It makes sense for this case, then, to choose $r=\inf$ as the vacuum level $E_v$:
$E_p(r=\inf)=E_v$
(In here, p means potential)
When the nuclei are allowed to approach each other, an electron woul... |
I can't comment to ask for circuit clarification on some of the other questions addressing this, insufficient reputation, so I am asking as a new question. Looking at answers to the other questions a capacitor can be used to charge a battery if it acquires a voltage higher than the battery. Would it be correct to say... |
Some time ago in my QM class, we were working with an infinite well potential, and my professor told us we could know beforehand the bound states we were going to obtain for said potential would have a well-defined parity (that is to say, would be either even or odd in all of the domain). Nonetheless, he never told us ... |
In terms of special relativity. An astronaut marks a spot a at the ceiling and shoots a light beam at a in a spaceship. The spaceship, astronaut and light source are stationary in an inertial frame A. For an observer outside the spaceship, stationary in an inertial frame B, B and A having a relative speed v, will she s... |
In the context of compactifying the open string with Chan-Paton factors, Polchinski (Volume I Section 8.6) considers a toy example with a point particle of charge $q$ which has the action
$$ S = \int d \tau \left( \frac{1}{2} \dot{X}^M \dot{X}_M + \frac{m^2}{2} - i q A_M \dot{X}^M \right) \tag{8.6.3}$$
where $M=0,...,2... |
I'm new to quantum mechanics, and I am beginning to study Dirac notation, but I do not understand the significance or meaning of the following equation:
$$\sum_n\left|e_n\right\rangle\left\langle e_n\right|=1$$
or for that matter, this equation as well:
$$\int\left|e_z\right\rangle\left\langle e_z\right| d z=1$$
But I ... |
While going through the calculus approach to accelerate, we have,
$$a = dv/dt, $$
I think, here, v and a should be in the same axis,
is my process correct?
in a planar motion in two dimensions, it will become,
a net = dv net/ dt, but I think it will not work,
pl clarify this confusion,
thanks.
|
Quantum field theory describes forces as being mediated by a field (e.g. gluon field for strong force, electromagnetic field for electromagnetic force). These are often modeled as a mediating boson particle (gluon, photon). However, in the case of the strong nuclear force, because of color confinement, gluons do not di... |
I'm a mathematician slowly trying to learn quantum field theory and I have a small question about renormalization, which I still have a shaky understanding of.
One common way to explain what's happening in renormalization is to pick some scheme for regularizing the apparently-infinite quantities that show up in the "na... |
CONTEXT (skip to "my question is"):
As I understand it, and correct me if I'm wrong, an orbit trades momentum between the X and Y directions. But spacetime can have negative and even null directions.
Relativistic length contraction is rotation into a direction that has negative magnitude in the metric: time. Relativist... |
I am new to quantum field theory and I am trying to understand how to work with quantum field operators and the notations that are used here.
Context:
Assume a hamiltonian with operator: $\hat{W} = t\hat{a}^\dagger\hat{a}(\hat{b}^\dagger + \hat{b})$ , where $t$ is a constant, $\hat{b}^\dagger$ and $\hat{b}$ correspond ... |
Let's first take an example. I understand that if a car has $v=20 \,\text{m/s}$ this means that every second it moves $20 \,\text{m}$. But how should I interpret units that are multiplied like $\text{N m}$? Or even $\text{kg m/s}^2$ which is a multiplication divided by seconds squared? This makes no physical sense to m... |
I have been trying to understand the concept behind this for days now and am seemingly puzzled by a variety of methods.
The Problem : A rod of mass $M$ and length $L$ is attached to a hinge at one end while the other end is kept free. Initially the rod is kept horizontally and then left to drop. What will be the final... |
While reading The Theoretical Minimum for Classical Mechanics the author said that the derivative of the potential energy is equals the force and showed this equation describing the potential energy of a single particle in a one dimensional space:
$$F(x)=-\frac{dV(x)}{dx}$$
He said that the force here depends on the lo... |
I understand that the reason why we construct the theta vacua is because instantons allow tunnelling between different vacuum states, $\left|n\right>$. This means that we have to consider a real vacuum state
$$
\left|\Omega\right> = \sum_n a_n \left|n\right>.
$$
Now, my question is why do we have $a_n = \frac{1}{\sqrt{... |
I am very confused by the following situation.
In the classic kinetic theory of gas, one calculates the pressure of an ideal gas in a $L*L*L$ space. Suppose we have a molecule start with a velocity $-v_x$, it hits the wall with rate $\frac{2L}{v_x}(*)$, so one calculates the average force $F = \frac{m{v_x}^{2}}{L}$, an... |
In Appendix "Some Useful Definite Integrals" of Feynman & Hibbs "Quantum Mechanics and Path Integrals" they use some integral formulas that I'm struggling to derive. The integral is:
I've seen a question to solve an almost similar integral, but the guy just gave a hint, and I still can't solve it. I know that is possi... |
im working on an experiment on the photoelectric effect in which i try to calculate the saturation current of different wave-lengths.
i do so by calculating the photoelectric Voltage on a resistor and then calculating the current. my light source is a mercury lamp which is flickering as expected from this kind of light... |
What is the formula for equilibrium charge on a non-rotating black hole with spherically symmetric hydrogen-1 inflow at the Eddington limit of luminosity based on photon scattering acceleration of electrons vs that of protons?
To the best of my knowledge no one has bothered to publish this.
It seems this would be an in... |
I'm reading An Introduction to Mechanics by Kleppner and Kolenkow. In the chapter on angular momentum, a (beautiful!) example is given by discussing Kepler's second law of planetary motion.
The law states that the when a planet is orbiting the sun, the area swept by its radius to the sun for a given time length is cons... |
I came across a question which says:
"A force $F$ acts tangentially at the highest point of a sphere of mass
m kept on a rough horizontal plane. If the rolls without slipping ,
find the acceleration of the centre of mass of the sphere."
The equations in the solution are:
For translational motion,
$F+f=ma$
For rotatio... |
We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why macroscopic objects mostly obey laws of classical mechanics and that quantum effects are only seen at small scales.
So let's say ... |
I am trying to understand the different combinations of quarks in a hadron. I have seen that the positive pion is written as $\pi^{+}=u\bar{d}$, but I have not seen it written in the opposite order. Can we write it as $\pi^{+}=\bar{d}u$?
Further, all the quarks are fermions. So, they can be represented by a four compon... |
I'm trying to learn quantum mechanics and this is a question that came to mind. I tried searching for it online, but I couldn't find a good answer (or at least one I could understand). From what I understand, you should theoretically be able to determine the position of a quantum object by observing the spacetime-curva... |
I've heard this kind of shark fin on the roof reduces drag by breaking the wave that forms behind, where the roof bends into rear window.
image source
The story goes that it's similar to these fins on fan blades, that are claimed to reduce fan noise.
Noctua fan. source
Is there any paper or simulation images that sho... |
Given a surface emitting radiation according to some radiance function $L\left(\theta,\phi\right)$, what is the radiant intensity of the source?
This question came after reading Robert Boyd's book "Radiometry and the Detection of Optical Radiation".
Boyd defines the radiant intensity as
The radiant intensity, $I$, is... |
I am reading An Introduction to Quantum Field Theory by Peskin & Schroeder, and I am confused about what is the square $T^2$ of time reversal operator $T$.
My guess is that for $P^2$, $C^2$ and $T^2$ they assume they are the identity, though they don't say it explicitly.
As an example on page 69 they calculate the time... |
Following up this question I am trying to calculate the dynamical friction of a black hole passing through solid matter
$$\frac{d\mathbf{v}_M}{dt} = -16 \pi^2 (\ln \Lambda) G^2 m (M+m) \frac{1}{v_M^3}\int_0^{v_M}v^2 f(v) d v \mathbf{v}_M$$
G is the gravitational constant
M is the mass under consideration
m is the ma... |
The (Italian) book that I am currently reading introduces the topic of symmetries in quantum mechanics in the following way:
Let O and O' be two distinct observers and let $A$ and $B$ be two quantities that result from certain possible operations of measurement performed by O and let $A'$ and $B'$ be the quantities re... |
I am trying to model the shape of the tidal bulge caused by the moon.
I asked GPT for a formula and it gave me equilibrium tidal bulge height as
$$\frac{2 R_{earth} G M_{moon}}{3 r^3 \Delta g}$$
and attributed this to George Howard Darwin. I tried to verify this formula but Googling it gave me different formulae for di... |
The stress-energy tensor has 16 components, but this question is only about the 9 components $T^{ij}$ with $i,j=1,2,3$. According to Wikipedia, these components are defined as follows:
The components $T^{kl}$ represent flux of kth component of linear momentum across the $x^l$ surface.
I find it hard to see how this u... |
I've come across RMS in a variety of fields. I've come across dB units in a variety of fields.
Right now I'm looking at an algorithm for determining the perceived loudness of an audio track (EBU R128's referenced ITU-R BS.1770 for anyone who might be interested).
But they measure in this weird way.. First they take th... |
Gregory L. Naber's book introduces the Lorentz transformation like this:
Now let $L :M→M$ be an orthogonal transformation of $M$ and
${e_1, e_2, e_3, e_4}$ an orthonormal basis for M. By Lemma 1.2.3, $\hat{e}_1 = Le_1$, $\hat{e}_2 = Le_2$, $\hat{e}_3 = Le_3$ and $\hat{e}_4 = Le_4$ also form an orthonormal basis for $M... |
I am trying to calculate the stress–energy tensor of an electromagnetic wave in curved spacetime, characterized by the diagonal metric
$$
g_{\mu\nu} =
\begin{pmatrix}
-g_{zz} & 0 & 0 & 0 \\
0 & g_{xx} & 0 & 0 \\
0 & 0 & g_{yy} & 0 \\
0 & 0 & 0 & g_{zz} \\
\end{pmatrix}
$$
with signature (−, +, +, +), where $g_{xx},g_{y... |
Imagine a charged ball with surface charges. Let it travel with a constant velocity $v$.
Imagine a point outside the ball. Since the charge is moving, there is a electric displacement displacement current $\frac {\delta E}{\delta t} > 0$
There is no current $j$ at this point.
By maxwells law:
$$\nabla \times B = \mu_o ... |
I'm confused about the Israel Junction Conditions. I've seen them written several different ways so far, but here I'll use: $$K^-_{ij}-K^+_{ij}=8\pi(S_{ij}-\frac{1}{2}g_{ij}S).$$
My understanding is that $K^-_{ij}$ and $K^+_{ij}$ are the extrinsic curvatures of the shell measured from the inside and outside respectivel... |
A quantum channel $\Phi$ acting on an $n$-mode bosonic space is called phase-covariant if it commutes with the phase-shift operator, i.e. if $U_{\phi}\Phi(\rho)U_{\phi}^\dagger=\Phi(\rho)$ for any $\phi\in[0,2\pi)^{n}$ and $U_\phi=\bigoplus_{j=1}^n e^{-i\phi_j\hat N_j}$ where $\hat N_j$ is the number operator for the $... |
Sometimes it is known to happen. For example, neutron star mergers might result in unstable neutronium droplets which lose the enormous pressure that makes them stable. A "nucleon" of $10^{30}$ neutrons can not remain together, neither by its gravity nor by the strong force.
For example, in the case of other nuclear fi... |
Now this is my suggestion so please guide me. Take a plane mirror. We know that light reflects from it. This is a case of regular reflection meaning the surface is smooth. But we experience friction on a plane mirror. This means there are asperities on the plane mirror. This means that light reflects on a surface with ... |
I was solving a mechanics problem from a book called Problems in Physics for IIT-JEE , the solution for a question is something I'm not convinced with. It goes like-
In the arrangement shown in the figure the coefficient of friction between the blocks C and
D is $\mu_1$ = 0.7 and that between block D and the
horizonta... |
Consider A particle performing Uniform Circular Motion.
We know that its projection on diameter performs SHM.
Then, if that projection starts SHM on the y axis from mean position, then $y=A\text{sin}(ωt)$
if that projection starts SHM on the y axis from extreme position, then $y=A\text{cos}(ωt)$
if that projection star... |
I have equations such as
$\frac{dx}{dt} = y \\
\frac{dy}{dt} = \mu y + x - x^{2} + xy$
This system is known to be homoclinic bifurcation at the origin. To find the critical value of $\mu_{c}$, one found $\mu_{c}$ by the numerical calculation. In this case, how can I find critical value of $\mu_{c}$ where the bifurcatio... |
In classical mechanics, the action may not be the minimum value, but the maximum or extreme value. (For example, imagine a particle on the surface of a smooth celestial body.)
Will a similar situation occur in electrodynamics and general relativity? (Consider only electromagnetic or gravitational effects, without other... |
This is my understanding (please tell me if i am going wrong anywhere):
During phase change (i.e. ice melting into water) the molecules absorb heat, gain more random kinetic energy, and spread apart (leading to weaker intermolecular bonds). When all the molecules are separated enough to become fluid, they turn into wat... |
During my nuclear physics class, we talked about the multipolarity of gamma radiations but without going too much into the details, and I was wondering about the meaning of that, how can the radiation be electric or magnetic ?
|
I am dealing with the dynamics of a two-bands lattice system. The idea is that you have a lattice model of free fermions, with some hopping amplitudes and on-site energies.The lattice have two fermion species per site, and therefore the model has two energy bands. In this problem, each band is the negative of the other... |
Consider swinging a ball around a center via uniform circular motion. The centripetal acceleration is provided by the tension of a rope. Now, is this force a constraint force? If it is, since it is the only force, the applied force must be zero. Then, the following equation must apply:
$$Q_j = \frac{d}{dt}\left(\frac{\... |
I was solving this question and I faced a problem :
See the problem is I know the conventional way of impulse momentum and energy conservation to solve this question but ,
I do not know why applying energy conservation from starting to end that is when the ball is released from rest to the time the the ball is at its ... |
I struggle with understandinng the Gibbs free energy $G$ for a very long time now. I still managed to pass the thermodynamic courses, but this lack of understanding haunts me till today.
So finally I want to understand it. My problem is based on two different treatments of $G$ I always encounter, which look like they c... |
This is a basic question but I struggle to grasp it really. In the Wikipedia page for Ground state, it's written
According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. [...] It is also possib... |
As a theorist, I’d guess that in Newtonian gravity we can check for proportionality to mass, and inverse square proportionality to distance, by measuring the ratios of gravitational forces.
Is there similar, fundamental constant independent, test for general relativity?
|
In general relativity one has the Hilbert stress-energy tensor defined as
$$T^{\rm matter}_{ab} = -\frac{2}{\sqrt{-g}}\frac{\delta S_{\rm matter}}{\delta g^{ab}}~,$$
which is covariantly conserved i.e $$\nabla_a T^{ab}_{\rm matter} = 0~.$$ In deriving this one assumes that the total action functional (matter action an... |
Very brief question. Assume a string that is made half out of a thin rope and half out of a thick rope (the thick rope is heavier of course). A transverse mechanical pulse is applied at one end (assume it is very sharp, with all Fourier frequencies in similar amounts). How to calculate how much energy arrives at the ot... |
I just don't get how Energy is measured in $\frac{1}{m^2}$. Wasn't it measured in Joules? (source is https://en.wikipedia.org/wiki/Cosmological_constant#Equation)
|
I am trying to ask my doubt by converting it into a example problem but i am really not able to do so properly- heres my best attempt at it:-
The pressure at a certain depth(~ 1km) in a ocean ,a gigantic one (total depth~100 km), i think is created from 2 different forces
1. The downward force due to weight of ocea... |
There is a problem I'm trying to solve for some time now and is about the standard (?) approximation that it is made when one tries to solve the Helmholtz equation in inhomogeneous media, that is
\begin{align} \nabla^2\vec{E} + k^2\vec{E}=-\nabla(\vec{E}\cdot\frac{\nabla\epsilon}{\epsilon})\approx0 \end{align}
where \b... |
I'm studying the work of Giddings-Kachru-Polchinski (GKP) for hierarchies in string theory and I came across the five-form flux defined in eq. 2.9.
Now, if one calculates the Ricci tensor for the given ansatz (eq. 2.6) and compare it with the action 2.1, one should get eq. 2.45 here. My question is how to get from 2.45... |
Let's consider the unitary group $\hat{S_{\tau}^†}$ such that :$$\hat{S^†_{\tau}}|\psi(t)\rangle=|\psi(t-\tau)\rangle$$
Since we know that:
$$\hat{U}(t,t_0)|\psi(t_0)\rangle=|\psi(t)\rangle$$
Where ${U}(t,t_0)$ is the time evolution operator, we can conclude that:
$$\hat{S^†_{\tau}}=U(t-\tau,t).$$
Now we also know that... |
This must be fairly basic I fail to understand. According to Weinberg, QFT Vol2, Ch.18 (The preamble)
When we replace bare couplings and fields with renormalized couplings and fields defined in terms of matrix elements evaluated at a characteristic energy scale $\mu$, the integrals over virtual momenta will be effecti... |
Is there a graph somewhere showing how the electron mass changes with energy due to renormalization up to around the Planck scale - assuming that the pure standard model is always valid (thus no GUT, no Susy)?
Note: The question is about the running of the mass due to renormalization.
|
A perfectly circular orbit of a constant height (distance from the center of mass of the orbited planet) around a perfectly spherical planet with smooth surface and no gravitational anomalies will have a certain constant orbital velocity, specific for the given height and planet (specifically, its mass, I presume).
Con... |
Consider the lagrangian of a system of classical coupled harmonic oscillators of mass $M$, connected with springs with elastic constant $\chi$ and connected to the background with springs of elastic constant $\Psi$. The Lagrangian for a one dimensional system then reads
\begin{equation}\label{eq:CSHOLagrangian}
L=\... |
When looking at an object, the highlights are usually on the corners and edges. Highlights can occur anywhere on an object, but it seems like the brightest parts are where it is the most sharp.
|
This is the moment of inertia tensor about the COM.
$$I_{ij}'=\sum_{k=1}^Nm_k\left[\vert\mathbf{r}'^{(k)}\vert^2\delta_{ij}-r_i'^{(k)}r_j'^{(k)}\right]\neq I_{ij}$$
I don't understand how to compute the last term $r_{i}r_{j}$
I understand that $i$ and $j$ refer to the indices of the $r$ vector, I know that the $r_{j}$ ... |
In this answer my2cts says "The electromagnetic field is to photons what the Schrödinger or Klein-Gordon wave function is to electrons." Could someone expand on this further? Is this just a descriptive analogy, or is there some kind of mathematical equivalence between the field description of e.g. photons and the vecto... |
Non-relativistic no-magnetic-field many electron hamiltonian contains no spin operators. How would spin polarization happen in many electron ground state (modeled by LSDA DFT for instance)?
I often heard Spin polarization in solid state system ground state is due to exchange interaction. I think it is mostly due to ele... |
Please consider a pulley with a taut rope over it and two objects (with different masses m1 and m2) hanging on each side. The pulley is not negligible - it has a mass Mp.
In the solution to a problem I'm working on (from An Introduction To Mechanics by Kleppner and Kolenkow), the free body diagram seems to show the fol... |
I am following section 6.3 of Weinberg's Lectures on Quantum Mechanics 2nd ed. to understand how time-dependent perturbation theory can be used to calculate the ionization rate of hydrogen. For monochromatic polarized light, Weinberg gives the differential ionization rate as follows:
$$
d\Gamma(1s \to \vec{k_e}) = \fra... |
I am studying the non-relativistic scattering theory. I know when the incident particle is in the bound state the scattering amplitude diverges. Then does it mean the cross section also diverge? If so, what does this divergence mean?
I think the cross section should be zero because the incident particle is in the bound... |
I work in finance, and studied math in college. I'm trying to use QFT statistics to model some aspects of the market. (I've already made some progress by deriving the Black-Karasinski Hamiltonian for spot interest rates.) To this end, I am reviewing classical field theory, and I don't understand variational principles ... |
consider the following variational principle:
when we vary $p$ and $q$ independently to find the equations of motion, why aren't we explicitly varying the Coeff $u$ which are clearly functions of $p$ and $q$? the authors also either didn't vary $u$ and got the EOM (or) varied $u$ but neglected it since $\phi_m$ are ul... |
I took electromagnetism a while ago, but now that I took Lagrangian and Hamiltonian mechanics, this question came up to me when I imagined an electric dipole in the presence of a uniform electric field. Do I have to consider the potential energy generated by the potential of the dipole? Also, due to the external electr... |
If we consider a $D=0$ theory with the Lagrangian:
$$\mathcal{L}[\phi]=g\phi^n+J\phi$$
And its Green functions:
$$G_n=\langle\phi^n\rangle_{J=0}=\frac{1}{Z[0]}\frac{\delta^nZ[J]}{\delta J^n}|_{J\rightarrow0}.$$
An infinite change of the integration variable $\phi$ leads to the equation of motion:
$$\langle d\mathcal{L}... |
Let us consider our Universe at its heat death state, and the rogue wave phenomenon that is due to improbable superposition of small waves. Is it possible that a rogue wave-like quantum fluctuation can transfer the state of maximum entropy of Universe into a state of very low entropy, i.e., a new Big Bang?
The Universe... |
In Griffiths Introduction to Quantum Mechanics (3ed.) problem 2.1, we are asked to prove that the normalizable solutions to the time-independent Schrödinger equation can always be chosen to be real, in a simple 1-dimensional position-space setup. The question instructs the reader to do this by first showing the complex... |
It's probably straightforward, but I would like to see the proof of the identity:
$$g_{\mu\nu}g^{\nu\alpha}=\delta^\alpha_\mu.$$
In the book 'Spacetime and Geometry' by Carroll, this identity is the motivation for calling $g^{\mu\nu}$ the 'inverse' of the metric.
|
In non-interacting quantum field theories, the particle number is conserved so we can restrict to a given subspace of fixed particle number. On the single-particle subspace, the state will evolve according to the equations of motion and I was wondering what these would be. In order to investigate this, I thought I'd lo... |
From my understanding helicopter blades work similar to a planes wings, ie the air going over is faster due to the shape. So my question is why then are the blades rectangular? ie they are the same width the whole length of the blade? I feel like it would make more sense to have it thinner towards the base since the bl... |
For this question the answer key says it is A. However I think it should be B. At T=0 the particles will be headed towards the node. Given that the equillibrium points happen when T=T/4 it would make sense that the particles at T=0 to be farther apart then move inwards.
I even tried to look at a simulation which seems... |
There is a well known solution to Navier-Stokes equations for atmospheric boundary layer according to Ekman (see for instance PalArya's book "Introduction to Micrometeorology" or Holton's "Introduction to dynamic Meteorology"): https://glossary.ametsoc.org/wiki/Ekman_spiral
However, by calculating the second derivative... |
Let's take the Gordon solution of the central field Dirac equation for the Hydrogen atom and look at the wave functions.
There is bounded functions inside the spinor, which represents here the full eigenstate of the electron (4 parts), like the electron bounded to the nucleus, perfectly logical. Then we can define an e... |
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