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I am trying to figure out how to approximate the spot size of a laser beam that is focused using a microscope objective where the size of the laser beam is smaller than the diameter of the objective. I have tried googling and reading various other questions online but still haven't been able to cobble a coherent plan ... |
In gravitoelectromagnetism, changing gravitomagnetic fields can induce standard gravitational fields, much in the same way that changing magnetic fields induce electric fields. This analogy extends to the case of transformers; where electricity and wires are replaced by dense fluids and pipes.
Given that the Schwarzsch... |
I am currently deriving the matrix form for 2D Hookes Law equation with poissons ratio, where $y$ is longitudinal and $x$ is lateral
$$v = -\frac{\epsilon_x}{\epsilon_y}$$
We can derive the total elongation from the forces in the x direction as so where L is the width or length of the shape
$$d_x = (\epsilon_{x1} + \e... |
The embers of a fire glow with an appealing shimmering light. I've often wondered if this shimmering is well-understood. For example, it seems to me that the frequency with which the patterns of light move might be explainable somehow; also perhaps the size of the brighter and darker areas. I have been unable to fin... |
I am trying to prove that the Carnot efficiency for a heat engine with maximum power is $1-\sqrt{\frac{\tau_l}{\tau_h}}$, where $\tau_h$ is the high temperature, $\tau_2$ the lower temperature, and we have the working temperature $\tau_{hw},\tau_{lw}$ such that $\tau_h>\tau_{hw}>\tau_{lw}>\tau_l$. During the hot isothe... |
This question answers the conservation of energy in many worlds by stating that the overall energy of the system is still conserved by adding up the overall probabilities of and energies of the different states, but glosses over the particle portion of particle wave duality. When an electron splits off into two differe... |
If I understand it correctly, in Quantum Field Theory, a vacuum state is a state with zero particles in each mode. However, if a photon is "created" with a specific momentum, it will be spread throughout all of space (i.e. photons are non-local). Since the total number of photons in the universe is enormous, does thi... |
In many experiments like the Delayed Choice Quantum Eraser Experiment, scientists use entangled photons.
How do scientists make/obtain them?
What is the realistic level of control scientists have over those photons?
In what rate range can we shoot them and measure them?
|
My friend phrased the original question like this:
If I tied a rope to myself and wrapped it all the way around the earth and then pulled (assuming the rope was already taut), which direction would I go and how long would it take for me to feel the tension force from the pull?
I then started to think about how long w... |
A particle whose initial mass is $m_0$ is projected vertically upwards at time $t=0$ with speed $gT$, where $T$ is a constant and $g$ is the uniform gravitational acceleration. At time $t$, the mass of the particle has increased to $m_0e^{t/T}$. If the added mass is at rest relative to particle when it is acquired, fin... |
I am looking at the following textbook problem (please note that I am not asking for a solution to the problem, only using it as a motivating example):
A host pours the remnants of several bottles of wine into a jug after a party. The host then inserts a cork with a $2.00$-cm diameter into the bottle, placing it in di... |
I am currently reading the 2nd volume of Feynman Lectures and I am stuck in the part where he solves the Maxwell's equation to find the potentials and wave equations. I can't understand the thing he calls choosing a gauge.
He changed both of the potentials in a way that despite the change the electric and magnetic fiel... |
Title says it all.
When we take the angular momentum of the solar system into account, we know that it is a net positive value. From where, how and why did our solar system acquire such a huge angular momentum?
|
I am reading statistical physics currently, and I'm on the topic "Grand Canonical ensemble-condition of equilibrium". They've introduced a new term "Chemical Potential" which is Gibbs free energy per particle of a system.
Q1. How to relate Number of microstates with Gibbs Free energy?
Q2. How do we say that chemical po... |
I found this question in a quantum mechanics exam:
What is the physical interpretation of the continuity equation $\frac{\partial\rho}{\partial t}+\frac{\partial j}{\partial x}=0$? Here $\rho(x,t)$ is the probability density and $j(x,t)$ is the probability current.
I assume they want a one liner like "probability is co... |
Why is the stress on the rocks at the bottom of a mountain due to the weight of the mountain shear stress and not compressional or longitudinal stress?
If we try to understand why a mountain cannot grow taller than 10km on Earth, the explanation is that the shear stress on the rocks at the base of the mountain for a mo... |
Someone can explain briefly how to treat with perturbation theory a free electron gas in a sinusoidal external magnetic field ? I'm trying to understand the paramagnetic response of an electron gas to a non uniform magnetic field
|
We know that the entanglement state is a very fragile state and it can be disturbed by very minimum interaction with environment, so how many times can we measure(spin direction) the same entangled pair before the decoherence occur and the entanglement is broken?
|
The Hamiltonian of the system of bosons ($a$, $a^{\dagger}$, $b^{\dagger}$ & $b$ are Bose operators) is:
\begin{equation}
H=\epsilon_{1} a^{\dagger}a+\epsilon_{2}b^{\dagger}b+\frac{\Delta}{2}\left(a^{\dagger}b^{\dagger}+ba \right)
\end{equation}
where $\epsilon_{1}$, $\epsilon_{2}$, and ${\Delta}$ are real and posit... |
When I first studied physics in my first year at university, one thing that struck me was the way the gravitational and electrostatic forces look so similar:
$F = k_e\frac{q_1q_2}{r^2}$ (Coulomb's law) vs $F = G \frac{m_1m_2}{r^2}$ (Newton's law)
To the naive observer, the only differences seem to be that we know of po... |
I have been previously advised that any horizontal hydrostatic forces on the curved face of the piston will cancel out but I thought it would have an effect on the movement of the piston.
Am I wrong?
Based on the drawing attached:
Q1. What is the vertical hydrostatic force acting on the piston?
Q2. What is the horizon... |
Given a wheel like a disk with some angular velocity $\omega$, will it precess in microgravity?
|
I have just discovered the ideas of Lagrangian and Hamiltonian formulation of mechanics. I wish to self-study further.
I (believe I) grasp the very basic idea that both approaches are based on the energy of the system; Lagrangian the difference between kinetic and potential energy, Hamiltonian the total energy of the s... |
first >> we know that quantum mechanics works with a probabilistic nature so that we can't say " what will happen? " but " what might happen? "
second >> we can ask how quantum mechanical systems evolve in time and indeed we obtain a time evolution operator for state ket so now we can simply answer this question "at ti... |
What is the "Critical impact parameter" for photons of a Black hole with a Radius $r$?
Here I'm defing the Critical impact parameter $C$ as the value such that.
A photon with an impact parameter > C will be deflected by the black hole.
A photon with am impact parameter < C will be pulled into the black hole.
|
At this link https://en.wikipedia.org/wiki/Partition_function_(mathematics), it is claimed that the following partition function:
$$
Z=\int D\phi \exp (-\beta H[\phi]) \tag{1}
$$
is a consequence of taking the usual partition function of statistical physics $Z=\sum \exp (-\beta H)$ but for an uncountable amount of rand... |
I am seeing a lot the expression that the phase angle $\theta$ between the current and the voltage of the circuit can be expressed in term $tan\theta=\frac{IM(Z)}{Re(Z)}$ when $Z$ is the total impedance of the circuit, and I do not understand why is it true? what is the logic behind it? I understand that $Z$ is complex... |
What makes us feel heavy on Earth?
$F=m\cdot g$ is the gravitational force that earth exerts on us and $N$ is the force that the surface has on us (Normal force), so which one makes us feel heavy?
My professor claims that $N$ gives us this feeling, but I don't understand why. Could someone clarify or correct this for m... |
I developed my question, Below is a special box with no gravity and vacuum. Let this box be of infinite length. Here an object moves at a speed of 50m / s. If the object has energy here, would we have produced infinite energy. ? Or while this object is pushed by a person, did the energy lost by man turn into the speed ... |
I have calculated time taken to travel a fixed distance by the object from two different frames of refrence. One frame was moving with uniform velocity wrt other . But time taken to cover the equal distance was different in both frames
|
Say I measure a quantum particle at some place, and then I find it at another place.
According to my understanding of wavefunctions the particle can get from one place to another without traversing the space in between
Is this phenomena a consequence of Quantum Mechanics or have i got it wrong?
|
There is a 10N force on the object in the figure. Here I showed the forces on the figure. But how can I calculate the moment and shear force at points in the object or AB Surface? Figure drawing is mine. And it's never a question of homework.
|
It seems to be a well-known fact that the Schroedinger equation doesn't hold for macroscopic systems (e.g. an animal), except maybe for very short time durations until decoherence effects take place. On the other hand I haven't found this anywhere explicitly stated and haven't found any explanation/reasons for this wel... |
In mean-field parton theory of Heisenberg model, the hamiltonian can be written as
$$H_{MF} = \sum_{\langle i j \rangle} Tr(\psi_i^\dagger U_{ij} \psi_j) + \sum_i Tr(\psi_i^\dagger (\vec{a}_i\cdot \vec{\sigma}) \psi_i)$$
where $\psi = \begin{pmatrix}
c_{i, \uparrow} & c_{i, \downarrow}\\
c_{i, \uparrow}^\dagger & - c_{... |
In Young double slit experiment the photons interfere with themselves destructively and constructively. So when there is an optic fiber with a mirror end the photon should return back and one can calculate the length of the fiber in order the incoming and the reflected photons wavefunctions are over imposed so it vanis... |
I am learning about Majorana fermions in topological quantum computation, and more particularly about the Kitaev chain, described by
$$ H = -\mu \sum_{i=1}^N c_i^\dagger c_i - \sum_{i=1}^{N-1} \left(t c_i^\dagger c_{i+1} + \Delta c_i c_{i+1} + h.c.\right) $$
where $c_i = (\gamma_{2i-1} + i\gamma_{2i})/2$ is the annihil... |
I am trying to understand free particle in both cartesian and spherical coordinate. So a free particle going in, say $x$ direction with some energy $E$. We know the wavefunction of such particle is:
$$\psi(x)=Ae^{ikx} + Be^{-ikx}.\tag{1}$$
Now lets do the same calculation in spherical coordinate and derive the wave fun... |
The position of an electron is often discussed in physics. My question is simple. How does one go about measuring an electron’s position ? It seems like an impossible task.
|
Consider an infinitesimal canonical transformation from the (symplectic) coordinates $z$ with Hamiltonian $H(z, t)$, to the coordinates
$$
Z = z + \epsilon J \frac{\partial G}{\partial z}
$$
with the transformed Hamiltonian
$$
K(Z, t) = H(z(Z, t),t) +\epsilon \frac{\partial G(z(Z, t),t) }{\partial t}
$$
where $G = G(z,... |
Usually the NS momentum equation for an compressible fluid is written in its convecting form, in the absence of external forces, as
$$
\rho\frac{\partial \vec u}{\partial t} +\rho(\vec u\cdot\nabla)\vec u+\nabla P = \mu\nabla^2\vec u
+\frac{\mu}{3}\nabla(\nabla\cdot \vec u)
$$
However, from the Wikipedia, this can be w... |
I'm currently studying QM, and in my class tunneling effect was mentioned, but with no details.
I was wondering what exactly causes this effect?
Is this due to the wave characteristics of the particle, so that waves with appropriate momentum can pass through while the others can't?
or is it due to the uncertainty princ... |
https://www.youtube.com/watch?v=1NnyVc8r2SM
In this video quicksilver moves plastic bullet's with his finger from a different time reference. Needless to say, if bullets were in contact with an ordinary hand in the same manner, it would have some effect of friction and heat etc. I'm just wondering whether for quicksilv... |
I'm studying the online course "Topology in Condensed Matter", in the QSHE section (<https://topocondmat.org/w5_qshe/fermion_parity_pump.html>), I've studied the Fu-Kane formula
$$ Q=\Pi_{n,j} P_{n,j} \quad(n\text{ is band index, }j\text{ is TRIM index})$$
which tells us in a TR topological insulator with inversion sym... |
According to Sakurai's Modern Quantum Mechanics, we can choose different parity for the wave functions of relativistic hydrogen atoms.
However, when calculating the state degeneracy, we don't consider this difference. Since two wave functions with different parity correspond to one same energy, this confuses me.
|
Suppose we add to the SM the following electroweak scalar triplet with hypercharge $Y_T=-1$
$$T=\begin{pmatrix}
t^0 & t^-/\sqrt{2} \\
t^-\sqrt{2} & t^{--}
\end{pmatrix}$$
where the superscript indicates the electric charge of each component field. It couples to the Higgs $H$ with the following Lagrangian:
$$ L_T=... |
If we imagine a hypothetical perfect fluid with no pressure, then in its inertial rest frame its stress-energy tensor would only have one component:
$\quad T_{00} = \rho$
Solving the field equation would give us a diagonal Ricci tensor with equal components:
$\quad R{\mu\nu} = \frac12R$ when $\mu = \nu$ and $0$ otherwi... |
I am designing a simple Mass Spectrometer.
I need to find radius of $Pb_{204}^{-}$ when deflecting. I have this equation:
I know everything in that equation except the mass. I have
How can I find the mass for the equation?
|
When we solve the twin paradox we say something like the traveling twin has a Rindler Metric while the stationary twin has a Minkowski metric, or more plainly, the traveling twin experiences non-zero proper acceleration, while the stationary twin experiences zero proper acceleration.
We define proper acceleration to be... |
I am looking to work out the orientation between two quaternions to establish if they are parallel face-face orientation, side-side orientation or perpendicular orientation. At the moment I am taking the absolute of the dot product of two quaternions i.e.
tmp = abs(q1.dot(q2))
If tmp = 1 I identify them as being parall... |
I am currently implementing the model proposed in this publication (1983). I already figured out, that it probably uses cgs units. (The units of $1/\epsilon_0$ would be missing in eq. (24,25), if it were SI units.). To get the actual numbers, i would like to find out, which version of the cgs system is used. The value ... |
I'm interested in approximating the mean free path of an electron in air. I think I'm going to need to add something more into my approximation because currently I calculate $400m$ for the mean free path at atmospheric pressure. Say the mean radius of an air molecule (either $\text{O}_{2}$ or $\text{N}_{2}$) is about $... |
I've been teaching myself physics through the internet and I came to a question about ballistic pendulums. Usually, I have seen these questions asked in regards to energy, but not forces. Assuming that the block has mass, immediately after a bullet strikes a mass hanging from a string (which before the collision, the t... |
I am studying Srednicki book of Quantum Field theory. In chapter 6 regarding the path integral there was derived equation of transition probability for hamiltonian of type:
$$H(\hat{P},\hat{Q})= \frac{1}{2m}\hat{P}^2+V(\hat{Q})\tag{6.1}$$
between two adjacent space points (eq. 6.5):
$$<q_2|e^{-iH\delta t}|q_1> = \int \... |
In the following circuit involving a potentiometer;
Assume $V$ to be the voltage produced by the cell in the primary circuit across the length $AJ$ of the potentiometer wire, and $E$ to be that produced by the cell of the secondary circuit.
In the case of $V=E$, it's known that there is zero current through the second... |
I'm studying Matvei Bronstein's 'Quantum theory of weak gravitational fields' and in the general remarks whilst he gives the correct expression for the Riemann-Christoffel curvature tensor in first order approximation, when he describes the equation of gravitation in empty space he sets
the Ricci tensor to zero but wit... |
I'm trying to understand the justification for using the Minkowski metric. It's clear to me that it's the natural choice of metric given that spacetime separations denoted by $(-c^2\Delta t^2+\Delta x^2+\Delta y^2+\Delta z^2)$ are invariant across inertial frames of reference. So the next step is to show that spacetime... |
there was an almost the same question here, but there was no appropriate answer(the answer there was incomplete and not to the point). now there is an updated answer to the question.
|
I have been researching for countless hours and I can not find any relevant information on calculated/predicted Higgs Boson mass for my physics report. I have looked into super-symmetry, breaking symmetry and academic papers which was incomprehensible.
If someone could point me in the right direction for a year 12 (fin... |
In natural basis $| 0 \rangle = \begin{pmatrix} 1 \\0 \end{pmatrix}$, $| 1 \rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix}$, what physical situation/model does the following Hamiltonian represent: $H = \alpha \Big( |01 \rangle \langle10| + | 10 \rangle \langle 01| \Big)$?. Here, $| i j \rangle = |i \rangle \otimes |j \r... |
The RN metric in asymptotically flat spacetime is given here: Wikipedia page on RN metric.
From the metric, we can work out the Bekenstein-Hawking entropy to be S = Area/4 , which explicitly would be:
S = $\pi (M+\sqrt{M^2-Q^2})^2$, where we choose the units appropriately($\hbar = G_{N} = 1$).
The temperature can be e... |
I am having trouble understanding a calculation done by V. Mukhanov in his book "Physical Foundations of Cosmology". In the beginning of the chapter 9, the following arguments are stated:
The state of a single photon with a given polarization at conformal time $\eta$ is completely characterized by its position in the ... |
Suppose we had a bowling ball that we took to space. Also suppose we stopped completely and released the ball. At which point would the gravitational pull of Earth be so weak that the ball would not fall towards Earth, but rather some other object?
I realize this might vary based on how close the Moon is, if there are ... |
Suppose we have an observer standing still in an inertial frame of reference. We will consider a scenario where there are no real forces acting on them in the inertial frame.
If we define a non-inertial, accelerating, frame with respect to the observer's inertial frame, we find that the observer must feel a non-zero ps... |
I've been reading a bit about finite temperature quantum field theory, and I keep coming across the claim that when one Euclideanizes time
$$it\to\tau,$$
the time dimension becomes periodic, with period related to the inverse temperature $\beta$. Can someone please explain where the periodicity comes from and how we kn... |
How can I get from:
$$
\overline{A}_L^{ij} = \frac{6}{r^3} l^{(i} \overline{\epsilon}^{j)kl} J_k l_l
$$
(where $l^i \equiv \frac{x^i}{r}$) and
$$
W^r = 0, \; W^\theta = 0, \; W^\phi = -\frac{J}{r^3}
$$
that:
$$
\overline{A}^L_{r \phi} = \frac{3 J}{r^2} \sin^2 \theta.
$$
I've checked it several times, but my answer is w... |
So, I understand the basics of how a railgun works - the current in the conducting rails and the armature sets up a magnetic field, which, via the Lorentz force acting on the current in the armature pushes the armature out of the loop formed by the rails, armature and power supply, accelerating it down the rails.
Howev... |
When satellite is return from space orbit to earth how they lower the potential energy? Do satellite need to fire engines as they launch?
How we apply energy conservation laws?
|
I have a misleading picture of a point source in electromagnetic waves. The solution is the Green function. I can understand how a oscillating dipole generates a wave, but I can not see how a point source can generate a wave. Is it a point charge at the origin which at time zero vanishes? Thanks
|
I am a bit confused by the difference between $T$-odd and $T$-violation. For example, I read that the existence of a fundamental particle EDM is a violation of time symmetry. However, placing an electric dipole in an electric field, would produce a hamiltonian (non-relativistically, which is usually the region of inter... |
I'm reading a text on special relativity ($^{\prime\prime}$Core Principles of Special and General Relativity$^{\prime\prime}$, by James H. Luscombe, Edition 2019), in which we start with the equation for composition of velocities in non-standard configuration. Frame $S^{\prime}$ is moving w.r.t. $S$ with constant veloc... |
In N. Zettili’s book of quantum mechanics, I came across this problem:
Consider a pendulum undergoing small oscillations with angular frequency $\omega$ =$\sqrt{g/l}$. Show that quantum energy levels and the corresponding degeneracies of the pendulum are given by E=(n+1)$\hbar$$\omega$ and g=n+1.
Now, I have been try... |
In elementary statistical mechanics, one can think of temperature as arising from the average kinetic energy of particles in the ensemble. Is there a similar way to think about the temperature of a quantum field theory?
I know that we can talk about the temperature as being related to the periodicity of Euclidean time,... |
In a problem I'm facing, friction acts on the system that I wish to apply conservation of linear momentum. Why can't I take the surface as a part of system and conserve momentum? As the surface is basically earth, as it's mass is so huge it's velocity change is negligible and I can cancel it's momentum on $LHS$ and $RH... |
I have to derive a formula for the symmetry factor of the diagrams of the form
in $\phi^4$-theory, where $\phi$ is a real scalar field. By symmetry factor I mean only the number of possible contractions, which lead to the same diagram (without the factor $1/n!$ for $n$th order of pertubation theory and without the fac... |
Jackson, 3rd ed., section 2.2 states the formulas for the image charge and position, dependent on an equality of the magnitudes of two vectors:
$$
|\bar{u}-k\bar{u}'|=|\bar{u}'-k\bar{u}|
$$
Where $ |\bar{u}|=|\bar{u}'|=1 $, $k<1$. My question is how you prove this equality.
There are two unknowns in this method of imag... |
How are superconducting materials classified as gapped or gapless, also is this same as saying that a superconductor is conventional or unconventional? Could you explain how this is linked to topology or the topological order in the material?
|
This is taken from the first example in Griffith's intro to QM:
Suppose I drop a rock off a cliff of height h. As it falls, I snap a million photographs, at random intervals. On each picture I measure the distance the rock has fallen. Question: What is the average of all these distances? That is to say, what is the ti... |
In the $1s,2s$ electronic configuration, I've found that the possible states are 1S0 and 3S1.
$L=0$ for both of these terms, so would the parity of the spatial wave function not be $(-1)^L=1$, and therefore symmetric, for both of these terms?
The first singlet state was straightforward but for the triplet states where ... |
I am reading the book Nonlinear Solid Mechanics A Continuum Approach for Engineering by Gerhard A. Holzapfel, Chapter 2.3 and find one equation confusing, which is displayed in the pitcure.
Here in the pitcure, $F$ is a smooth material field, denoted with $F(X,t)$.
The equation (1.266) is as follows,
I am wondering w... |
I have come across topological twists on numerous occasions but I have never actually seen them explained in an understandable way. So, I was wondering
What does it physically mean to topologically twist a theory?
What does it mathematically mean to topologically twist a theory?
What is the motivation for talking abou... |
In several textbooks and papers, like this one for example, a claim like the following is made:
The EDM of a system $\vec{d}$ must be parallel (or antiparallel) to the average angular momentum of the system $\hbar\langle\vec{J}\rangle$.
What is the motivation for making such an assertion? It seems not to make much se... |
I took a photo of my computer screen through my mobile phone camera. Why are these color distortions in hyperbolic shape?
|
I’m confused about the force that is experienced by a small piece of a continuous massive spring from the rest of the spring to its left and right. On the one hand, the wave equation says the force is (in general) nonzero. On the other hand, it seems that the forces from either side of the small piece are both proporti... |
Consider this:
$$\langle \mathbf{r} | \hat{\mathbf{P}} | \psi \rangle = \displaystyle\int d^3\mathbf{r}'\displaystyle\int
d^3\mathbf{r}''\langle \mathbf{r}|\mathbf{r'}\rangle\langle\mathbf{r}'|\hat{\mathbf{P}}|\mathbf{r}''\rangle\langle\mathbf{r''}|\psi\rangle = \\ = \displaystyle\int d^3\mathbf{r}'\displaystyle\int ... |
could you say to me if white light in a prism with refraction => if we recompose the spectrum we will have white light again ? or what else ? since brown and magenta are not on the spectrum. What is the "frequency" of a natural white light and the "frequency" of a recomposed "white" light from a spectrum?
|
I have been trying for quite some time now to find a satisfactory justification of a standard assumption we usually do in time-independent perturbation theory, but I am still puzzled.
Here is the problem: We consider a Hamiltonian of the type $H=H_0+\lambda V$, where $V$ is a perturbation and $\lambda$ is a small param... |
Say we have a motor coil like this:
We hang a mass (red ball) on the motor to prevent it's rotation. We make the mass heavy enough such that it's Weight Force directly opposes the motor force produced by that wire.
$$mg = BIL$$
Does this motor turn? I feel like the answer is no, because that wire has no net force acti... |
I was reading about the reason why we think neutrinos have mass, and it said that because they evolve over time, they must have mass because they feel the flow of time.
But don't photons also evolve over time? They get red shifted, isn't that evolution over time?
|
The reason why the weak nuclear force is weak is because the mediators, the $W$ and $Z$ bosons, need to take on a ridiculously high mass compared to the mass that they are usually found at (which is very rare). This is only possible because of the time-energy uncertainty given by the uncertainty principal.
But if boson... |
If we have two flat surfaces touching each other and apply a force parallel to the surfaces, one may move relative to the other.
An example would be a polymer block gliding on another.
Dependent on the surface properties, they could smoothly and easily glide,
or be hard to move, or just stick together, with no relative... |
Looking at the periodic table, group II elements like magnesium are known to be metallic, and yet they have full outer shells. So this means they should have full (valence) bands.
Now, last time I checked a completely full band does not conduct.
In a similar way, group IV elements like silicon, germanium, and tin (whic... |
Why do objects with big size break easily? For example: if I drop a chalk of length $L$ from height $h$ then there is a greater probability that it might break, when compared it to a chalk of length $\frac{L}{2}$ dropped from that same height $h$. And if I repeat the same experiment with same chalk after it gets broken... |
This is from chapter 4 of David Tong's notes on Classical Dynamics (Hamiltonian Formalism).
Let's say you make an infinitesimal canonical transformation (with $\alpha$ as the infinitesimal parameter) as follows
$$q_i\rightarrow Q_i=q_i+\alpha F_i(q,p) \qquad p_i\rightarrow P_i=p_i+\alpha E_i(q,p) \qquad \qquad(1)$$
By ... |
I am currently studying Classical Mechanics, fifth edition, by Kibble and Berkshire. Problem 2 of chapter 1 is as follows:
The two components of a double star are observed to move in circles of radii $r_1$ and $r_2$. What is the ratio of their masses? (Hint: Write down their accelerations in terms of the angular veloc... |
I feel that the answer should be yes. While the entire journey isn't straight, the journey between successive collisions is straight. But the internet and my book says the opposite (the path is curved). Please clarify this.
|
Given two domains with different speed of sound, what are the acoustic transmission conditions?
I know, that there is continuity of velocity and acceleration in the normal direction
$$\frac{\partial\mathbf{u}}{\partial t}\cdot\mathbf{n} = -\nabla \psi \cdot \mathbf{n}$$
with $\mathbf{u}$ being the mechanical displaceme... |
In the Davisson Germer Experiment, we assume that the incoming beam of electrons undergoes surface diffraction when it hits the nickel. That is, we assume all the electrons hit the top most layer of nickel atoms, and that they then scatter in random directions. We then suppose that upon hitting the top layer of nickel ... |
Recently I came across a question which stated that a small electric dipole is placed at the centre of a sphere(insulated). I'm required to prove that the potential due to this dipole is always zero on a circle on the surface of the sphere. What does a circle on the surface of a sphere mean here? Is it the planar secti... |
I'm trying to justify whether the parity operator is an observable in quantum mechanics, and if so, why. I'm at a loss here, any advice on how to tackle this problem?
|
I have come to this as the Time Dependent Equations for the Density Matrix for a Two Level System.
$$\frac{d}{dt}\Big(\begin{matrix}ρ_{11}&ρ_{12}\\ρ_{21}&ρ_{22} \end{matrix}\Big)=\Bigg(\begin{matrix}\frac{i}{\hbar}(V_{21}ρ_{12}-V_{12}ρ_{21})+\frac{1}{T_1}ρ_{22}&-\frac{i}{\hbar}V_{12}(ρ_{22}-ρ_{11})+(iω_{21}-\frac{1}{T_... |
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