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Consider a ring with string wound upon it, on a rough surface with $\mu$ enough for pure rolling. If we pull the string tangentially with force $F$, in which direction would the frictional force be?
Let $f$ be the frictional force taken along the positive $x$ direction. Let the mass be $m$, and the inertia around it... |
I am struggling to work out correct Lorentz transformation for a boost in the 3-direction on a Dirac spinor, $u(p)$. According to Peskin & Schroeder pg. 46, I need to use the equations:
$$S^{0i} = -\frac{i}{2}\pmatrix{\sigma ^i &0 \\ 0 & -\sigma ^i} \hspace{10mm} (3.26)$$
$$\Lambda _{\frac{1}{2}} = exp\left(-\frac{i}{... |
Consider a Ring (radius $r$) rolling without slipping with angular speed $\omega$ on the surface. We want to find the radius of curvature of the top most point.
1.The radius of curvature(R): Regardless of the actual path that the particle travels, a particle at every instant can be thought of as tracing a circle, of ra... |
My QM text defines the position operator as follows:
The position operator $X= (X_1,X_2,X_3)$ is such that for $j=1,2,3: \ X_j \psi(x,y,z)= x_j \psi(x,y,z)$.
To me this can mean two things.
1) $X$ is a vector and acts as $X \psi(x,y,z)= (x \psi(x,y,z), y \psi(x,y,z), z \psi(x,y,z))$. But this doesn't make sense as ... |
I am reading David Tong's excellent lecture notes on kinetic theory, but I am confused in the derivation of the hard-sphere scattering cross-sectional area
He uses figure 5 to discuss the scattering angle of the incident hard-sphere. Both spheres are identical.
I have two things I am confused about.
Firstly, doesn't... |
Does the color of the refractive medium affect its index of refraction? I want to determine the refractive index of different colors of jello. By keeping as many controlled variables as possible (brand, concentration, volume) and by using a monochromatic light (like a Green or red laser) to measure the angles of incide... |
Let's assume that we have delta potential well with $V = -\lambda\delta(x)$, where $\lambda >0$. Now if we solve Schrodinger equation, we get one eigenvalue $E_b=-\frac{m\lambda^2}{\hbar^2}$ with only one eigenfunction $\psi(x) = \sqrt{\frac{m\lambda}{\hbar^2}}\exp(-\frac{m\lambda}{\hbar^2}|x|)$. What does that even me... |
The motion of particles is governed by Schrödinger's equation,
$$\dfrac{-\hbar^2}{2m} \nabla^2 \Psi + V \Psi = i \hbar \dfrac{\partial{\Psi}}{\partial{t}},$$
where $m$ is the particle's mass, $V$ is the potential energy operator, and $(-\hbar^2/2m) \nabla^2$ is the kinetic energy operator ($= p^2/2m$).
The state funct... |
If I have a gas that starts in a corner of a box it will have low entropy. I have a detector on the corner that measures "1" if all the particles are at the corner and "0" otherwise. If I let the system evolve (starting at the corner) its entropy will increase (proportional to $1/V^n$), but in one of the Poincaré recur... |
I have a little mess with the conditions required in thermodynamics for a certain process to be quasistatic, non-quasistatic, reversible or irreversible.
Let's start with the classification of the processes. As I understand it, every reversible process is quasi-static. Therefore, non-quasi-static processes can only be ... |
Maybe it is impossible to break an iron nucleus but let pressume we have 10 inert iron atoms and somehow fission them in lighter elements. Will the electrostatic force cause to accelerate these lighter elements so they gain kinetic energy and become very fast so causing an explosion?
|
In the papers I’ve seen with GR solutions in (asymptotically) AdS$_5$ spacetimes, when Boyer-Linquist-like coordinates $(t,r,\theta,\phi,\psi)$ are used, the ranges of the angular coordinates is as follows
$$\theta \in [0,\, \pi/2], \quad \phi \in [0,\, 2\pi], \quad \psi \in [0,\, 2\pi].$$
Could someone explain to me w... |
I have the following task and I have no idea how to start.
To do: The angular momentum of the radiation field is given by $$ J = \int x \wedge (E \wedge B) d^3x $$
Define the corresponding operator.
I have no idea what a corresponding operator is or what I have to do. Hopefully you can help me, thanks :)
|
So I was thinking about a demonstration our teacher gave us in physics class. He had a spool of thread where the thread was on the downside of the spool, so he asked us questions before pulling on the thread horizontally, he asked us to guess which direction the spool would go. My thought was, since he is pulling on th... |
Given the following Feynman Amplitude:
$$\mathscr{M}=\bar{u_s} (\vec p') \Gamma u_r (\vec p) \tag 1$$
Where:
$\bar u_s, u_r$ are Dirac spinors ($1\times 4$ and $4 \times 1$ matrices respectively)
$\Gamma$ is a $4\times4$ matrix containing Dirac-$\gamma$-matrices (which are of course $4\times4$ matrices)
We're also gi... |
I have a system I would like to describe with a Lagrangian formalism. I model friction on my system with a torque ($\tau$). Having non conservative forces and torques, I use equation:
$$ \frac{d}{dt}\left(\frac{\partial T}{\partial \dot{q}}\right) - \frac{\partial T}{\partial q} = F_q \label{a}\tag{1} $$
Where $F_{q}$ ... |
I was reading about Mathison–Papapetrou–Dixon (MPD) equations which describe the motion of massive spinning particles. I am wondering if these sets of equations are just a quantum version of the classical Thomas precession or not?
The reason why I believe so is that Thomas precession gives us evolution of spin 4-vector... |
You strap a super powerful speaker on your back, blast it on max volume. Would it propel you forward?
|
Suppose we have some charged particle above the ionosphere. Then in a simplified model, it will experience a curvature and gradient drift. Assume further that a particle is in the equatorial plane. Since the particle is in the equatorial plane, using spherical coordinates, the magnetic field will yield the form:
$$
\ve... |
I'm trying to solve a problem about rotation dynamics, but can't arrive at an answer. Any help would be much appreciated.
Consider the following system:
the two rigid bars with masses at their tips are perpendicular and connected with the fixed horizontally bar by an articulation (the three bars are in the same plane)... |
I never really understood why we can neglect rapidly oscillating terms in favor for slowly ones. As an example, in my quantum-mechanics studies I ran into this ODE:
$$i\frac{d}{dt}\gamma_a = Ae^{i(\omega-\omega_0)t}\gamma_b+A^{*}e^{-i(\omega+\omega_0)t}\gamma_b$$
The author of the book says that if $\omega \approx \ome... |
I'm trying to find the amplitude for:
$$\gamma(p_1) + \gamma (p_2) \to e^- (p_3) + e^+ (p_4)\tag{1}$$
(My questions are stated in the end)
The possible answers are:
My take on it:
and so
$$\tag{2} \require{cancel} \mathcal{M}= e^2\{ \epsilon_1 \gamma \bar{u}_3 \frac{(\cancel{p_3}-\cancel{p_1})}{t} \nu_3 \gamma\epsilo... |
I am trying to show gauge invarince of the Yang-Mills lagrangian
$$\mathcal{L}=
-\frac{1}{4}F_{\mu \nu }^{a}F^{\mu \nu ,a}+\sum_{i,j}^{N}\overline{\psi}_{i} (\delta _{ij}i\partial_{\alpha}\gamma^{\alpha } -\delta _{ij}m+gA_{\alpha }^{a}\gamma^{ \alpha } T^{a}_{ij})\psi_{j},$$ by rewriting it in terms of the covariant d... |
Consider the process
$$e^+(p_1)+e^−(p_2) \to S(p_3)S^∗(p_4)\tag{1}$$
$S/S^*$ is scalar particle/antiparticle described by
the complex scalar field $\phi$ coupled to QED through the Lagrangian:
$$\mathcal{L}= \mathcal{L}_{QED}+ (D_\mu \phi)^* (D^\mu \phi)-m^2 | \phi|^2$$
and $D$ is the covariant derivative $D=\partial +... |
Why is the maximum entropy of $n$ qubits (in $\log_2$ units) equal to $n$? How does one calculate $\operatorname{Tr}(\rho \operatorname{log} \rho)$ (since $\log \rho$ must be expanded). What is even the density matrix of this state?
|
I just watched a video of cubes of various metals being crushed by a hydraulic press (on the hydraulic press channel). Two of the cubes (made of somewhat stronger materials) deformed into an interesting shape that looked like the silhouette of a circle and square super-imposed on each other.
You can see the shape I'm d... |
Why is heat the resulting form of energy when molecules are in motion? Is this just an intrinsic property or is there a deeper explanation as to what causes this?
|
This question is about topological string theory and it was also posted in MathOverflow.
The existence of a new brane called "an NS-2 brane" is predicted in (the second paragraph in the page 14 of) the paper N=2 strings and the twistorial Calabi-Yau and confirmed to exist in S-duality and Topological Strings.
The argum... |
A free scalar QFT can be understood as a wavefunctional that maps classical field configurations to complex numbers representing amplitudes. An eigenstate of this basis is a classical field configuration that assigns a specific real number to each point in spacetime $n$. Each of these points can then be thought of as... |
I am asking if there is any case in classical i.e., non-quantum, mechanics in which one cannot use Newton's second law $$\sum \mathbf{F}=\frac{\mathrm{d} \mathbf{p}}{\mathrm{d} t},$$ to find the equations of motion of a system in classical mechanics (relativistic or not), and more general equations of motion are needed... |
This is very similar to this question:
How can momentum but not energy be conserved in an inelastic collision?
However, I feel as though an important caveat was not resolved for me which is why I am asking it here.
We have that in a collision (namely, an inelastic one) energy is not necessarily conserved among the obj... |
The Pauli Exclusion principles states that no two identical fermions can have the same quantum state. In my lecture notes, it is mentioned that this principle helps us explain the fact that metals are very hard to compress. Why does this principle explain the incompressibity of metals?
|
This may seem more math related but this question crossed my mind as I was reading the derivation of the Euler-Lagrange Equation.
In math, we were introduced to the Lagrange notation of the derivative chain rule with a demonstration as to why it's true.
In physics, it is more practical to use the Leibniz notation, whic... |
Is it possible that if I have a current creat by magnetic field inductance, I will get that the average power that consume to heat on a resistor is zero?
and if yes what does it mean?
|
Is it possible to accelerate the air electrically?
There are other techniques such as, for example, compressors where the air can reach supersonic speeds. But is it possible to accelerate air to supersonic speeds using electric fields?
|
I began to study the literature on superconductivity and discovered a very strange fact that I could not explain for myself:
1) The BCS theory establishes the fact that the energy gap is proportional to the critical temperature:
$2\Delta(0)=3.53 k_BT_c $
(In some experimental articles, there were $5-7$ instead of $3.5... |
Fluorescent materials convert some visible or invisible electromagnetic radiations from a certain range of frequencies to another one, usually from higher to lower frequencies, rarely, the other way around ("anti-Stokes"). Is there any equivalent mechanism in acoustics? Are there any structures that are able to vibrate... |
If I have a gas in a box and bring the box to temperature $T = 1K$ for example, so that $E = kT = 8*10^-5 eV$, from the Boltzmann distribution I have a non-zero probability for excited states even if the difference in energy between the G.S. and the first excited level is much greater than $E$. How is this possible?
|
Already more than a year ago, scientists claimed to have reversed the direction of time. What they actually did (see this article) to have reversed the direction of time. Which was hugely exaggerated. The process was simulated on a quantum computer, of which none of its constituents went back in time for the tiniest fr... |
I'm confused about the valence bond solid (VBS) in condensed matter literature. The idea is a lattice is covered by spin singlets and thus spin rotational invariant. It seems that it's commonly accepted there are four ground states by rotating the whole lattice by $\frac{\pi}{2}$. I have roughly two questions:
1) how d... |
Say we have a concave mirror which is converging light rays from you at a distance $v$ from the mirror where $v>u$. ($u$ is the distance of you from the mirror). So if the light is converging behind us, can we still see an image?
Thanks.
|
My textbook says,
When applying equilibrium conditions for a rigid body, we are free to choose any point as the origin of the reference frame.
(source)
I am trying to understand this by looking at the following picture (from an exercise problem), in which the ball is in static equilibrium because of the applied horiz... |
In the attached problem, i'm curious what effect, if any, the incline would have on the torque generated by the 50 kips force (shown below). Would it lead to a smaller/larger torque and, if so, why? I think the incline wouldn't influence torque necessarily, since the angle between the applied force and the lever arm i... |
Don't mistake me for asking why Faraday's law of induction works fundamentally. (I know there exists duplicates if that was my question). Firstly, I can explain why when a straight infinite wire moved in a magnetic field with a velocity, an E.M.F is generated or basically current is generated with the help of Lorentz f... |
In the physics book I am reading, Mecánica elemental by Juan Roederer, the concept of gravitational mass is introduced by a series of ideal experiments:
Body $O$ is fixed at the origin and body $1$ is put at different distances $r, r', r''$ from it. The gravitational force acting upon body $1$ is measured at each posi... |
Is there a limit to gauge fixing conditions we can impose in gravity ? I have seen two gauge fixing conditions. The DeDonder gauge $\partial_\mu g^{\mu\nu}$ and then in 3+1 formalism the gauge fixing condition $\nabla^2 t = 0$ is imposed where $t$ is the time coordinate. What if I imposed $\nabla^2 x_i = 0$ where $x_i$... |
I am looking for a generic treatment or a concrete example where canonical quantization is performed without using free fields. For a scalar field
$$\phi(x,t) \sim \sum_k \phi_k{(t)} \, u_k(x) + \text{h.c.}$$
$$\pi(x,t) \sim \sum_k \pi_k(t) \, u_k(x) + \text{h.c.}$$
$$[\phi_k, \pi_l] = -i\delta_{k,l}.$$
This means tha... |
We all know that the asymmetry between matter and antimatter is a big puzzle in physics. But I don't know why one expects matter-antimatter symmetry in the first place? As in, is there a fundamental principle which suggests that matter and antimatter should have been produced in the same number at the beginning of the ... |
A plane sound wave is travelling in a medium. In reference to a frame A, its equation is
$$y=A \cos (\omega t - k x)$$
In reference to a frame B, moving with a constant velocity $\vec{v}$ in the direction of propagation of the wave, the equation of the wave will be:
$$y=A \cos \bigl[(\omega-k\cdot v) t-k x\bigr]$$
but... |
In the middle of the day of early spring, the snow is wet everywhere due to high temperature, while in the afternoon the snow becomes icy and hard on the road and in the forest it is still soft.
Why does this happen?
|
Assume we have a projectile which we want to shoot straight up into the air, such that we are only working with the y-component, what formula can be used to determine the impulse required for this projectile to reach a certain height?
I was able to derive the following formula assuming no initial velocity:
$$F\Delta t ... |
Is there is any difference between electrons from different elements?
|
I am trying to determine whether the ground exerts a horizontal frictional force On the ladder (in addition to the normal contact force) when the surface is not frictionless and came up with the above thought experiment. If there exists such a force, then in its absence, the ladder should also slide in addition to fall... |
Traditionnal definition of speed in space-time
If I understood it correctly (relative to the General Relativity context)
a speed is defined relatively to space-time, i.e. we can talk of the speed of anything moving or propagating “inside” space-time. This speed is measured in m / s. The space-time has a structural “spe... |
I understand that it is possible for 4D objects to exist in a 3-D space. I also speculate that 5D objects cannot exist in a 3D space? Is there a reason to this limitation (assuming there is a limitation)? And I don't understand how it is possible for a higher dimension object (4D) to exist in a lower dimension space (3... |
The Wigner function is given by
$$W(\alpha)=\frac{1}{\pi^2}\int \text{e}^{\alpha \beta^*-\alpha^*\beta}\text{Tr}\left(\hat \rho \hat D(\beta) \right) \text{d}^2\beta,$$
where $\hat D(\beta)=\text e^{\beta \hat a^\dagger-\beta^*\hat a}$ is the displacement operator and $\hat \rho$ is the density matrix of the state bei... |
Can anyone explain why do free protons dont decay in respective or Particle physics basis. ON the basis of binding energy I understand that it is not possible due to mass defect and also by the fermi theory.
|
I read that 1D motion is straight line motion and 2D motion is the motion when the two coordinates change with respect to time , so what would be the the motion by the graph here
|
I have the Schrödinger equation:
$$\dfrac{-\hbar^2}{2m} \nabla^2 \Psi + V \Psi = i \hbar \dfrac{\partial{\Psi}}{\partial{t}},$$
where $m$ is the particle's mass, $V$ is the potential energy operator, and $(-\hbar^2/2m) \nabla^2$ is the kinetic energy operator ($p^2/2m$).
The state function can be expressed as the prod... |
Knowing that the free Dirac Lagrangian is :
$$\tag{1} \mathcal{L}= \bar{\psi} (i \gamma^\mu \partial_\mu -m ) \psi$$
and that the Euler-Lagrange equation is:
$$\tag{2} \frac{\partial \mathcal{L}}{\partial \psi}= \partial_\mu \left( \frac{\partial \mathcal{L}}{\partial(\partial_\mu \psi)}\right)$$
I am trying to obtain ... |
Long story short,
how can I qualitatively explain what is the Lorentz transformation and why it does so?
I am looking for a description of its general behavior instead of "it works due to an XYZ mathematical equation".
Long story,
I am reading a famous book about Special Relativity
The ABC of Relativity
by Bertrand ... |
Wolfgang Demtröder writes this in his book on Experimental Physics,
The future destiny of a microparticle is no longer completely determined by its past. First of all, we only know its initial state (location and momentum) within limits set by the uncertainty relations. Furthermore, the final state of the system show... |
I know that for transverse waves, the particles themselves have a different speed to the wave itself but is this also true for longitudinal waves? It seems intuitively that since the displacement is parallel to the direction of the wave, particles that are displaced positively (or in same direction as the direction of ... |
I do not get the idea that how does the torsion balance result in a damped oscillation. Two big and small masses separately attract each other. I naively think that after a while big and small masses stick together, which stops the motion. But it is wrong. Where is my mistake?
|
In many text books and exercises, it is stated the the phase transformation is constant under differentiation iff the argument is real, which is necessary to show the invariance of the Lagrangian under such transformations. But why is this? That is, why does the following hold, and why only when the argument is real?
$... |
I have read a lot about why sign conventions are used in ray optics. It is because the formulas are different for different lens and object.
My teacher also said that sign conventions are like the coordinate system. In the equations, we specify the coordinates of the object. lens and image. This is why we use sign con... |
The following question on Philosophy SE https://philosophy.stackexchange.com/q/73366/ relies on this "given"
"suppose that the instantaneous velocity of object A is $1$m/s and that the mean velocity of object B is also $1$ m/s..." .
I'm not interested here in the question that is asked under this assumption, but i... |
In several textbooks I read about solid state physics, the way to introduce the first Brillouin zone and the energy band structure is like the this:
Step 1: The Hamiltonian could be diagonalized by a set of eigen functions:$H|\psi_{n,k}>=E_{n,k}|\psi_{n,k}>$
Step 2: The Hamiltonian is invariant under the lattice transl... |
The wavelength of light of specific colour increases as we go from left to right in the visible colour spectrum: "VIBGYOR".
Wavelength of green lies between wavelengths of blue and yellow. To me, this makes logical sense because when blue and yellow are mixed, it gives green. (By "mixed", i mean the simultaneous pres... |
I just read the University of Helsinki press release Researchers discover a new type of matter inside neutron stars on phys.org. It states that a Finnish research group has found strong evidence for the presence of exotic quark matter inside the cores of the largest neutron stars in existence. I want to know whether th... |
Given that the Schroedinger equation states that a particle can be found an infinite distance away from its "center" and the universe is infinite, why don't we find infinite particles at any given point?
|
The question come from the fact that I've seen for the first time in my life the quantization of a field, in particular of the free em field.
I've study how it is possible to write the energy of the em field as a function of canonical coordinates $p_\lambda$ and $q_\lambda$ and how to substitute them with operators $\... |
Consider a simple electric circuit.
I just not understand what is the difference between heat emited from resistor and power that is on the resistor that emited to heat
why one is $p=I^2R$
and the second is $U=\int I^2Rdt$
|
Magnitude of induced EMF in a loop is given as $|\frac{d\phi}{dt}|$.
If the loop has n turns then induced EMF is given as $|n\frac{d\phi}{dt}|$. As we can consider each turn to be a battery which is connected in series, so net EMF is the algebraic sum of individual turn's EMF.
But the question is, as in first turn, whe... |
In one of my exercise, I got following differential equation for density matrix $\rho$,
$$
\frac{d\rho}{dt}=-i[H_1,\rho]+\{H_2,\rho\}
$$
where $H_1$ and $H_2$ are the Hermitian Hamiltonian, and $[.,.]$ is commutator, and $\{.,.\}$ is anti-commutator. I know that the commutator part on the r.h.s. causes rotation to our ... |
Let $|q\rangle$ be the eigenvectors of the position operator, let $|\psi\rangle$ be a state and let $\hat{p}$ be the momentum operator.
In my book it's stated that i can interprete the quantity:
$$\langle q|\hat{p}|\psi \rangle$$
as the elements of matrix of the momentum operator in the base made by the eigenvectors of... |
We can clearly see in page $6$ of Pozar's Microwave Engineering Faraday's law written under this form
$$\nabla \times \bar{\mathcal{E}}= \frac{\partial \bar{\mathcal{B}}}{\partial t}-\bar{\mathcal{M}}$$
$\bar{\mathcal{E}}$ is the electric field, in volts per meter (V/m).
$\bar{\mathcal{B}}$ is the magnetic flux densi... |
$$ΔE_e=\frac{1}{2}k(x_f^2-x_i^2)$$
Where $k$ is the spring constant and $x$ is the displacement from equilibrium position.
Are we allowed to select an arbitrary reference level of elastic potential energy? As in, does elastic potential energy have to be strictly $0$ at the point of equilibrium? I think it does, becau... |
Given some area that can tile 2d space and which contains 1 point of a lattice and given a second area that also only contains 1 lattice point and can tile the whole space how can i prove they are equal areas?
|
We know that black holes are actually "black" because no light can escape them due to their gravity and that's why they appear black. That means the mass of the black hole most be extremely large even in a cosmological scale.
If light cannot escape black holes due to the their gravity, and the more massive an object t... |
How to represent graphically the relationship of $Z$ and $\gamma$ to $W_3$ and $B^0$ ?
I made these two schematics below, but I'm not sure which one is correct, nor if we we should put $W_3$ or $B^0$ in $x$ axis or in $y$ axis.
-If this would be the schematic of the left, it could not work, since $Z$ has a positive y a... |
I don't understand. If I look at a picture of Halbach array
I see it is apparently symmetric. At least both pairs of opposite sides are.
Then how can it have "weak" and "strong" opposite sides?
|
What happens to the Coulomb electric field produced by the electron beam moving helically? In principle it would be like considering several rings of charges, in the center of the ring the electric field is zero, but what happens if we cover half of the ring with a material that does not let the electric field pass? th... |
From Wikipedia:
In celestial mechanics, the Roche limit, also called Roche radius, is the distance within which a celestial body, held together only by its own force of gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction.
Inside the Roche li... |
We know that special relativity is just a special case of general relativity and we can consider the space time to be flat in constant velocity motions like in special relativity.
If that's the case then how can general relativity managers to explain the increased mass (relativistic mass) due to relativistic effects at... |
it is given the angular momentum with $J = \int x \wedge(E \wedge B) dx $. Therefore I get the operator $J = \sum_k (x \wedge k) N_{k,\lambda} $ where $N_{k,\lambda} $ is the number operator, $k$ is the momentum and $\lambda $ is the polarization of the photon.
Now I have to consider the component of $J$ in the directi... |
I'm having trobules understanding the solution of the following problem.
In the problem we have a solar cell, which is impacted by a green light of $\lambda = 560nm$ and, as a consequence, there is some current. When we apply a voltage of $0,95 V$ the current dissapears.
So the probelm is asking for the work function.
... |
In my physics class we currently have to do research about a motion and preform an experiment and write an essay on it. The idea I had was to drop two parachutes with different areas from the same height and use video measurement and a modeling program to graph the motion. I bought parachute soldiers off the internet o... |
When a capacitor reaches its maximum potential, and charge is still being given to it, it just leaks through.
A teacher asked us to consider it similar to trying to pour a jug of water into a relatively smaller glass. When the glass is full, the water just overflows.
But when you suddenly flip over a jug trying to fil... |
Recently, I noticed that most devices that produce X-rays are somewhat 'crude'. It is usual for these devices to either heat something up to the point where the bremsstrahlung is in the X-ray region - for example implosion backlighters in big laser facilities.
Another more commercial method is using cathode ray tubes -... |
Consider two points in the Schwarzschild coordinates with a line-element $ds^2=-(1-\frac{2M}{r})dt^2 + \frac{1}{1-\frac{2M}{r}}dr^2+r^2(d\theta^2 + \sin^2\theta d\varphi^2)$, where $M$ is the mass of a black hole.
For those static points on the radial axis, $dt=d\theta=d\varphi=0$, one can evaluate the proper distance... |
I watched on a derivation of coaxial cable and when we want to calculate the self inductance per unit lengh we first find the flux of the magnetic field,so we take the integral $\int_{a}^{b}\vec{B}\cdot ds $ and we say that $ds=dr$ and my question is why it is not $rd\theta dr$ because ds is the area of the surfate el... |
Is this sentence always true? "The temperature rises as the kinetic energy rises"?
If it's not, do we have any limitations for it?
|
For my homework i am considering a harmonic oscillator which´s wavefunction at $t=0$ is the superposition of the eigenstates $\psi_n$.
$$
\psi(x,t=0) = \sum\nolimits_{n} c_n \cdot \psi_n(x)
$$
Now i am asked for the probability of the oscillator occupying eigenenergies $E_n > 2\hbar\omega$ at some point in time which ... |
When a slab is placed in front of one of the slits of YDSE , the path difference irrespective of position of point on screen is always written as Mue-1t. Shouldn't be only when the light travels exactly perpendicular to the slab. Is it true that optical paths across slab is true for any angle with which it travels acro... |
The Fourier transform of $1$ is the (one-dimensional) Dirac delta function:
$$\delta(x) = \frac{1}{2\pi} \int_{-\infty}^\infty dp\ e^{-i p x}. \tag{1}$$
Now I would like to replace the RHS with:
$$\frac{1}{2\pi} \int_{p_0}^\infty dp\ e^{-i p x}. \tag{2}$$
What happens to the LHS of $(1)$?
|
If somebody is able to output $3750$ $\text{N}$ lifting weight on the back doing squats, why can't they jump at $150$ $\text{km}/\text{h}$ without weight?
With weight:
$$(300 \text{ kg of load} + 75\% \text{ of }100 \text{ kg of the bodymass}) \times (9.8\text{ m}/\text{s}^2 + 20 \text{ cm}/\text{s}^2 = 10\text{m}/\t... |
As I understand it, the Lie groups $U(1)$, $SU(2)$, and $SU(3)$ correspond to the electromagnetic, weak, and strong forces respectively (ignoring electroweak mixing) and the generators of their associated Lie algebras correspond to their respective gauge bosons. Are there groups that describe fermions or do these also ... |
I’m trying to figure out why raising zero to the zeroth power equals one. What kind of a scenario would occur in a laboratory experiment where something with a quantity of zero would be raised to the power of zero and you end up with one? How do I explain how something is created out of nothing? What is happening?
|
If you were to watch your friend approach a black hole, I understand that you'd see their clock slow until they appear frozen and redshift within a few seconds. But if you were to detect the increasingly long wavelengths coming off of your friend, you would still see them frozen above the event horizon for infinite tim... |
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