I have a problem question related with angular and linear momentum. I watched many tutorials including, MIT online courses about angular and linear momentum of a rotating body, but I still struggle to solve the problems. Below I attach the problem question and my solution: I believe my solu...

I need to get model evidence of a model. This is formally defined as the integral across all the parameter space (which is composed of vectors $\vec{x}$ , 3x1 column vectors with real entries between 3 ranges (i.e. one for each coordinate) [1,20] [0.5, 6] [0.5, 7]) of the likelihood function time...

To be clear I have indeed reviewed the question asked by helios321 (Classic man on boat problem). But i have something else to ask related to man on a boat problem. The man on a boat problem goes like this: A man is standing on one side of a boat and the boat is stationary. We ignore fricti...

Imagine that you have some model with an enlarged scalar potential, such that there is, for instance, a quartic coupling $\kappa$ between the Higgs charged component and three other scalars, which do not get a vev. After electroweak symmetry breaking in the Feynman-t’ Hooft gauge ($\xi=1$), one ...

On page 35, right after equation 1.4.61, Sakurai says that the anti-commutator $$\{ \bigtriangleup A, \bigtriangleup B\}$$ is hermitian. Here, $\bigtriangleup X = X - \langle X \rangle$, and $A,B$ are both hermitian operators. I have worked out $\{\bigtriangleup A, \bigtriangleup B\}$ explicitl...

Question Attempt I tried taking a system in which there was visibly no external force and applied momentum conservation. But my answer came wrong. Where did I go wrong? Please help. I am in high school so I dont know much advanced concepts.

What is the Energy-Momentum Tensor? I know that this equation appears in Einstein's Field Equation. I would like to know what the Energy Momentum Tensor stands for as an equation, like if $F = ma$ then the Energy momentum tensor equals_______________? (I would also like to know what each element...

I have multiple doubts in vectors. Please help me. They are as follows. 1) Can a vector have components perpendicular to itself? 2) Is the sum of the components (rectangular or non-rectangular) of a vector a always equal to it? 3) Can the magnitude of a component of a vector a be greater its...

Question Attempt In this question if I take system as whole , there seems no external force acting. Gravitational force is balanced, tension and normal reaction are internal. Is my assessment right? Then how came the Ans is not 0? Where am I wrong? Please help.

An electron in first orbit in hydrogen atom is given appropriate amount of energy so it moved to another orbit, the electron now has an angular momentum of ( 2.11*10^(-34) (kg.m^2)/sec ) , find in that moment the difference of the magnetic field in the core hint: use Bohr's model

Given the Bateman equations $$ N_1(t)=N_1(0)e^{-\lambda_1 t} \\ N_2(t)=N_1(0) \frac{\lambda_1}{\lambda_2-\lambda_1} (e^{-\lambda_1 t}-e^{-\lambda_2 t}) $$ And given that the activities $A_1$ and $A_2$ are related by $A_2=A_1$ at $t=t_A$ and $A_2=3A_1$ at $t=2t_A$, I'm asked to compute $\lambda_...

Time travel is highly theoretical and according to many people impossible (including me), but nevertheless something bothers me. There are some theoretical proposals (see this Wikipedia article) implying the past is "eternally present" (eternalism as opposed to presentism), which I interpret tha...

My question revolves around this lecture notes on page $109$ equation $(5.1.10)$. Let's stick to $\mathbb{R}^3$ and consider a particle in $3$-space with position vector $\mathbf{x} = (x, y, z)$. Denote its velocity by $\mathbf{v} = \dot{\mathbf{x}} = (\dot{x}, \dot{y}, \dot{z})$. Basically, w...

So, I was doing a problem in one of the problem sets of 8.04 Quantum Mechanics Course MIT (Problem Set 10 Problem 7 part c,d ) which has an excellent problem relating the band structure with scattering processes in symmetric potentials. The problem asked us to show that - When the potential ...

What is an EFT, and why all the observable interactions until one scale are only a finite number that we know? Is SM an effective field theory, till what distances? I real "introductions" to EFT, but they are examples, not an explanation what it is

Consider a simple transverse wave propagating along a rope. We understand it's propagation stating that each point is pulled by its neighbors, making it act along with them, this will create a similar motion for the neighboring points. But, how come they follow with exactly the same shape with no...

I recently asked a similar question to this, but i still have a query related to such type of question. Well, the question is Two men A and B are standing on two ends of a boat. A on left end and B on right end. Assuming there is no friction in between the boat and the water, there are no ex...

I'm using parallel-axes theorem in both the following methods to calculate $I$ of a rod about a point (say $P$) at $x=l/4$, $\perp$ to the rod. Method 1: We know, $I$ about the centre, $\perp$ to it is $ ml^2/12$, then $$ I_P = \frac{ml^2}{12} + m\bigg({\frac{l}{4}}\bigg)^2 $$ Method 2: We know...

How do I take the covariant derivative of the Ricci Tensor? Could someone be so kind as to give me the process of how it is done?

I have just started studying Classical Mechanics and I just can't wrap my head around why we legendre transform lagrangian to hamiltonian if it just reverses velocity and conjugate momentum.

I am trying to answer a question that asks to find the branching fraction of $\tau^{+}$ decays to leptons. I know the decays are: τ$^+$→ν$_τ$ e$^−$ ν$_e$ τ$^+$→ν$_τ$ μ$^−$ν$_μ$. In the answers, it gives that the widths are as follows: $\Gamma(\tau \rightarrow ν_{\tau} d \overline{u}$) = $3\co...

When searching for QFT's applications, most articles and answers tend to mention how it is used to expand our understanding of physics, e.g. with the LHC. So I'm wondering if you know of any examples (outside of particle/theoretical physics) where QFT has been used to develop new forms of techn...

Is the absorptivity of light affected when the temperature of the solution it passes through changes? For example consider a Beer Lambert experimental set up. If the temperature of the solution changes does the intensity of the emitted light change too?(Given that the incident light has not chan...

There are a plethora of mini ultrasound transducers available. Many of which have a Sound Level SPL > 110dB. This seems extremely "loud". If you were to listen to one of these transducers, would they have the same effect (disregarding frequency) on your ears as a 110dB chainsaw? Listening to a ch...

I have been quite obssessed with basic physical concepts such as equality,how we assign values to physical quantities,what is a physical property etc.Please follow the link and suggest anything to help me https://en.m.wikipedia.org/wiki/Defining_equation_(physics)

I am studying Thermodynamics in my first year and I don't quite understand the process of isothermal reversible expansion. Below is a P-V graph I found on Google, just to help me illustrate my question here. I understand how we define the work done by an ideal gas when expand and I know how to...

I'm reading through Xiao-Gang Wen's Quantum Field Theory of Many-body Systems, and I just begin reading $Z_2$ lattice gauge theory. In page 255, the author constructed a four-fold denegerate (in the sense that they give rise to the same $Z_2$ flux $F_i$) link variable configuration with the sta...

Please help! How do I calculate the internal resistance of these circuits with 2 different voltmeter readings and no given emf? Thank you!

Two particles in an inertial frame $F$ are moving along the $x$-axis in opposite directions with equal speeds. They fuse to form a single particle with mass $M$, before this decays to form two particles of mass $m$ moving in opposite directions along the $y$-axis. Now suppose that the initial p...

How can I derive Newton's gravitational law? $$G=\frac{m_1 m_2}{r^2}$$ Is it impossible to derive? Did Newton get this just by obervations?

There are two ways that I think that this problem may be able to be solved, however, they give different answers, therefore at least one of them is incorrect. Let's start with a simpler problem, the classic example of lifting a weight $m g $ with a vertical force $F$, a distance $\Delta z$ give...

Question:there is a point charge +q placed at the centre of a cube ,find electric flux through one of the side. Through the logic that total flux through the cube will be q/€ so owe to symmetry flux through one side will be q/6€. But when I tried by finding integral E.dA I got kq/(l/2)² *l² w...

It is known that the 1D Ising spin chain $$H = -J\sum_{j=1}^N (Z_j Z_{j+1} + g X_j)$$ can be written in terms of complex fermions $\mathbf c_j$, and then Fourier transformed, to obtain $$H = J \sum_k^N (2(g-\cos \frac{2\pi k}{N})\mathbf c_k^\dagger \mathbf c_k-i \sin \frac{2\pi k}{N}(\mathbf ...

Consider a quantum field theory in $d$ dimensions with a symmetry $G$. For the purpose of this discussion let's say that $d$ is even and $G$ is a compact, connected Lie group. We say that the symmetry has a 't Hooft anomaly if it is not possible to gauge $G$. To detect this we couple the theory t...

I'm studying Conformal Field Theories and I recently read that one of the first implication of extending the Poincaré group to the Conformal group was that there where no more concept of mass as this would imply some inherent scale length in the theory. I don't understand why mass would imply a s...

The neutrino decoupling and the photon decoupling happened after the big bang, though at different times. The CMB is very detectable, and although there is no universal reference frame, the CMB is quite often used as some kind of a reference frame. Understanding the CMB background as a reference...

After generation of the kinetic energy operator matrix in 2D of the form: using the finite differences method where V=0 and hbar^2/2m = 1 so the Schrödinger equation simplifies to: -(dψ^2/dx^2 + dψ^2/dy^2) = E*ψ, where the matrix displayed above is equivalent to the left hand side of the ...

I wanted to calculate centripetal acceleration $a_c=rw^2$,however since centripetal acceleration is pulling the object then shouldn't radius also decrease and increase depending on the position of the object that is rotating in circular motion?

I'm studying cavity QED and I'm confused about Vacuum Rabi Splitting. Mostly, Vacuum Rabi Splitting has been described when the two-level atom are in the excited state at the beginning with no photon in the cavity, and then it emits the photon with the atom in the ground state. With interactio...

suppose that we have electron in the first orbit then the electron is given enough energy to jump to other orbit how can we express the change of magnetic field in the moment the electron jumped to the orbit we are talking about Bohr's model why when electron is in any orbit we consider there is...

I'm confused about the conductivity and the edge states in the IQHE. On the plateaux, we zero the longitudinal conductivity and resistivity, right? So is it really true, that on the plateaux, there is no current flowing in the longitudinal direction, only in transverse? From this image, it loo...

I'm trying to solve the following exercise: Construct the physical states of the $\mathcal{N} = 4$ massless graviton supermultiplet, starting from a Clifford vacuum of helicity $λ_0 = 0$. Decompose the $\mathcal{N} = 4$ massless graviton supermultiplet into a direct sum of $\mathcal{N} = 1$ mas...

I want to know which publication to cite when I reference the "Associative axiom of multiplication" in the Bra-Ket notation of Quantum mechanics. Sakurai only attributes it to Dirac, but doesn't name the source. As far as I can tell, it was not introduced in "A new notation for Quantum mechanics".

The Electric Field must be zero inside the Metallic cube but as per the text book answer there is electric field at Point P which is closer to the left side of the Metallic cube. There is a possibility that Diagram is incorrect i.e. the Point P is outside the conductor. The second point was o...

First, If something is unclear because of my English, let me know. Assume I have a two-board capacitor connected to a power supply which delievers constant voltage value,and I am willing to fill it in with dielectric material in order to streamline its capacity. Obviously, its capacity will incr...

A car increases speed from 40 km / hr to 60 km / hr in 5 sec. What is the accelaration? A simple approach is 60 - 40 = 20 Km in 5 sec = 4000 m /s From other approach it is: 40 km / hr = 11.11 m/s 60 km / hr = 16.66 m /s So accelaration is = 5.55 m / 5 sec = 1.11 m/sec What is wrong in my fi...

Assume a 1 kg mass extends a spring .49 m, and that when the mass is moving with a velocity of .5 m/s the medium in which the mass is moving exerts a viscous force of 3N. mass is m, k is spring constant, L is the spring displacement from the initial position, g is the gravitational constant: Th...

I'm doing finite element analyses. My model was simple: a sharp object penetrates a rubber cube, and then I would measure the pressure exerted on the cube, keeping in mind that P = F/A, so smaller area = greater pressure, means sharper object. But the hurdle is that instead of penetrating the cub...

I want to learn the basics of radiative transfer for my reasearch, which is on planetary sciences. I am looking for a book that would give me the basics of radiative transfer (the mathematics involved) so that I can perform numerical modeling of the radiative transfer process in planetary atmosph...

Is it faster to get warmer in warm water vapor or in warm water in liquid form?

So, I am working on a perturbation theory problem where the hamiltonian is, $$H = \frac{p^2}{2} + \frac{\omega^2 x^2}{2} + V$$ $$V = \lambda x^3$$ Also mass and $\hbar$ can be assumed to be 1 So, I have to find the correction to the first excited state energy to second order. Here's what I ha...

DaVinci's Vitruvian Man purports to be the anatomically perfect human, built on the mathematical ratio of the golden rule and divine proportions. It is curious that the Left foot is the only part of the body NOT in alignment. It is also possible since DaVinci draws and writes in a mirror techni...

The work-energy theory states: $\Delta$ K = W John Taylor breaks work into conservative and non-conservative work: $\Delta K = W_c + W_{nc} $ One type of non-conservative work is friction, which i beak up into friction work and other non-conservative work $\Delta K = W_c + (W_{fr...

Okay, so I had a problem for homework, and even though I know how to solve it the intended way (using energy analysis), I was wondering why my method (using force analysis) gave a slightly wrong answer. Also, it is not a rounding error as I tried both methods on my calculator to full precision. T...

In a book about semiconductors, I found the following formula for the density of states: In that book, the important lesson from this formula is that density of states grows like a square root of energy, and increases with the mass of a particle in question (electron or hole). But I'm confused...

If I understand it correctly, temperature is the measure of the average kinetic energy of a substance. Why is it then that T≠Eₖ,ₘₑₐₙ or something similar? Why is the kelvin a base unit and temperature a base quantity in The International System of Units (SI)?

Say i have a bucket of water. I can understand that at any point inside the bucket there will be a force hence a pressure acting downwards, but why is there a pressure acting side ways as well at the same point ? Could anyone give me a intuitive understanding of it. Thank you

Well, if they exist, they are very few probabilities to generate in a nuclear reaction. But, what is an stimation for this bound to probability basing in accelerator experiments?

If an object is moving at a constant velocity, and starts spinning as a result of some internal torque, would its linear velocity decrease or stay the same? Since no external forces are applied, the objects total energy should stay the same. This means the sum of its translational kinetic, rotat...

I've made a very simple colorimeter. An RGB LED illuminates transparent liquid samples with red, then green, then blue light. A detector detects the intensity of light that comes through the liquid. I put blue food coloring into water and tested it. I was surprised that it seemed that blue light...

I have seen ... ... a classical description in [1], ... a semi-classical-description, treating the molecules in the crystal quantum mechanically and the presence of the electromagnetic radiation as a slight perturbation in [1] where a huge part of the calculation is left out with reference to (...

I'm currently taking Physics II and I'm tasked to solve for the voltage $U_R(t)$ in this circuit. It's driven by a current source $I(t) = I_0*e^{i*\omega*t}$ and I can neglect the switch on process. I'm currently at the point of having the differential equation to solve this problem but I'm no...

When an ac source is connected with a pure inductor (when ac voltage is at its peak) then how it is possible that when voltage is decreasing current is increasing , when voltage is zero current is maximum and when voltage reverses polarity and becomes negative, current remains positive and decrea...

Using d’Alembert principle, one doesn't require any assumption like the one made in other case where particle has to follow the path of least action.

I was reading about Einstein-Hilbert action, and in some point in this page they use this identity $$\sqrt{-g}A^{a}_{;a}=(\sqrt{-g}A^{a})_{,a}$$ I Know that $\nabla_{\sigma}g_{\mu\nu}=0$. And $\sqrt{-g}=\sqrt{-g^{\mu\nu}g_{\mu\nu}}$. However I can't see how to get the equation $\sqrt{-g}A^{a...

Suppose there is an object motionless behind me. Now suppose I (almost) instantly accelerate away from it. In my perspective, this causes the time of the object behind me to be set back. Now this is not a contradiction, as he cannot possibly know I've accelerated before the time on his watch (...

When I look at the NED database, I see the Luminosity quoted for six different bands (X-Ray, UV, Visible, Near IR, Far IR, Radio). My issue is trying to interpret the M/L ratios I've seen referenced in several articles to the values in the NED database. Sometimes the band is included (e.g. M/Lv)...

This is a sample problem from the book by Resnick Halliday & Krane (5th edition), page no 98-99. I understand the kinematics and force equations used in this problem. I don’t understand a few things. 1) How did they come up with that FBD (free-body diagram) for the horizontal forces acting ...

Suppose I have a model composed of two parameters $(a,b)$ that I want to describe a set of data points with. In CASE A, I fit the model taking into consideration the correlations between the data points (that is, in the chi square formulation I use the full covariance matrix for the data) and in ...

Barometric formula is fit up to 86km. Is there a sufficiently nice approximation for what happens above (e.g. thermosphere where molar mass isn't constant anymore)? I understand air is much thinner that high, but how negligible it is, e.g. for a long-distance rocket cruising at that altitude? I'...

In Gubser's famous paper on breaking Abelian gauge symmetry near a black hole horizon, he talks about how to connect the asymptotic behavior of the scalar field $\psi$ to the scaling dimension $\Delta$ of the dual operator. Solving the equation of motion for $\psi$ (Eqn. 9 in the text), $$\psi''...

The question is in the title. Can a Poincare invariant Lagrangian lead to a path integral that is not Lorentz or Poincare invariant? If so, can I have an example? A related confusion: on page 426 of Weinberg I, he seems to show that this is not the case, at least for the translation subgroup. Ho...

The task would be: Prove, that the dispersion relation is periodic, in other words: k-> k+(2*pi/a) will give the same result if we defined the lattice vibrations as: u_s=e^(-i*omgea * t+i* k * a *s)

I've been curious about the concept of categories in physics and tried finding some more information about the subject. There are lots of textbooks about category theory, some from mathematicians and some written specifically for physicists (example), but I'm having a hard time seeing in which ar...

I came across these equations in a fluid mechanics textbook and wish to differentiate the first equation w.r.t. time to obtain that second equation. Any help is much appreciated! $c(f_1+f_2)=a^2(\frac{1}{2}\dot{a}^2 -ca+h)+2af'_2$ $c(1-\frac{\dot{a}}{c})(f'_1+f'_2)=ca(-2\dot{a}^2 (1-\frac{1}{2...

I read at the end of this question that Matta wrote: "If I put a quantum field on a spacetime and boost to an accelerating reference frame then the field modes undergo squeezing which is a Bogoliubov transformation (or, as I come from quantum optics, a symplectic transformation)" I wonder if this...

We know that the second order Born approximation in low-energy limit is given by, $$f(\theta =0, \phi =0) = \frac{-m}{2\pi\hbar^2}\int V(r) d^3r + (\frac{m}{2\pi\hbar^2})^2 \int \int \frac{V(r) V(r')}{|r - r'|} d^3 r d^3r'$$ This would be for a soft-sphere scattering. I wonder how this would ...

I'm confused about the scattering mechanism in the Integer Quantum Hall effect. I often read the statement, that at a hall plateaux, the particles can't scatter, since an integer number of Hall plateaux is occupied, so the particles have no available state to scatter into. So then I don't underst...

Question: What are conceptual physics books which are written by masters of the field, without compromised explanations, and which are useful for building intuition and/or seeing general principles in physics (preferably accessible and/or useful to a reasonably technical audience)? Definitions o...

I'm trying to get through Sakurai The Aharonob Bohm Effect where on page 141. According t0 Eq 2.7.53, if the original equation was transformed by a gauge $\tilde A=A+\nabla \Lambda$, then the solution for the new system was just the original solution at $\Lambda=0$ multiplied by a phase, i.e. $...

My interest here is to understand the following: The quasi-particle approach in say, Fermi liquid theory makes several predictions like temperature dependence of resistivity etc. which can be verified. I am wondering if there are some experiments which directly show us the existence of quasi-part...

Hamilton's principle states, that the action $S$ along the real trajectory $q(t)$ ist stationary \begin{equation} 0=\delta S=\delta \int _{ { t }_{ 0 } }^{ { t }_{ 1 } }{ L\left( q,\dot { q } ,t \right) dt } \end{equation} For fields there is a similar principle \begin{equation} 0=\delta S=\delt...

Do the cancelling moments of an antiferromagnet create a magnetic scalar potential, the same way that cancelling electric fields create electric scalar potential? Is there a formula for calculating this?

During a walk immediately after the end of a 6-inch snowfall two weeks ago, I threw or dropped several snowballs (each 3 or 4 inches wide) into a blanket of the stuff. The snow was rather dense but quite dry, and the temperature was exactly at the freezing point. While landing, each snowball fo...

A 5g piece of ice at -20°C is put into 10g of water at 30°C. Assuming that heat is exchanged only between the ice and water, find the amount of ice melted. (P.S. No other details have been given in the question. However, options have been provided as follows. (a) 3.125g (b) 5.000 g (c)4.950g (d)...

I'm doing a project about any TIR phenomenon and was wondering if anyone has a cool idea of what to do. I talked with my teacher about mirages, but she wanted something that was a little more unique. However, I am currently having trouble finding other phenomenons. I would greatly appreciate any ...

I am trying to compute the fermion massless propagator in two dimension: $i \int \frac{d^2k}{(2 \pi)^2} e^{ik \cdot x} \frac{k^0 \gamma^0 + k_1 \gamma^1}{k^2 + i \eta} = \frac{i}{(2 \pi^2)} \int dk^1 e^{ik^1x^1} \int dk^0 e^{eik^0x^0} \frac{k^0 \gamma^0 - k^1 \gamma^1}{(k^0)^2 - (k^1)^2 + i \eta}...

Disclamer Before I continue, I'd like to state clearly that I'm by no means an expert in this field. What I regularly do is read popular literature on this topic (if such a thing could be considered 'popular' :) ), and follow several YT channels. Ocasionally (and these occasions are getting fewe...

In quantum field theory, a global symmetry group that can't be gauged is said to have an 't Hooft anomaly. One of the most familiar examples is the free massless Dirac fermion in $3+1$ dimensional spacetime: it has a global $(U(1)_V\times U(1)_A)/\mathbb{Z}_2$ symmetry, and we can gauge the $U(1)...

In every chargeable device, from phones to electric cars, the charging time is always a problem. Yet, charging a single phone takes the same time as charging two phones. Assuming that the power source isn't an issue, and with the goal of speeding up the charging process, what are the downsides o...