Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework questions.

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2
votes
1answer
146 views

Derive non-linear $\sigma$ model from a theory of SU(2) matirx

It's said in Chapter VI.4 of A. Zee's book Quantum Field Theory in a Nutshell, a theory defined as $L(U(x))=\frac{f^2}{4}Tr(\partial_{\mu}U^{\dagger}\cdot\partial^{\mu}U)$, can be write in the form of ...
2
votes
1answer
519 views

Equations of motion for a pendulum in 3D?

I am trying to solve for the equations of motion to simulate a pendulum. I decided to use the spherical coordinates. The Lagrange equation is: where L = length of the rope ϕ= angle of the ...
1
vote
2answers
183 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec ...
-1
votes
2answers
176 views

How many mirrors placed perpendicular to each other shall make a light ray completely reverse its path?

The answer is 3. But according to me 2 shall also work in 2 Dimensions? Does anyone has a theoretical proof?
2
votes
1answer
119 views

How to quote answer when error is smaller than significant figures of data?

We have these rules: Can't quote answer to more significant figures than original data. Error quoted to one significant figure unless first significant digit is a one. In which case quote error to 2 ...
4
votes
0answers
350 views

How to prove that Weyl tensor is invariant under conformal transformations?

I need to verify that the solution for vanishing Weyl tensor is conformally flat metric $g_{\mu\nu} = e^{2\varphi}\eta_{\mu\nu}$. The most convenient way to show this is to prove that Weyl tensor is ...
1
vote
1answer
151 views

Combining relativistic velocities in the same direction using Lorentz transformation matrices

It is known that when combining the Lorentz Transforms of two frames with velocities $v_{1}$ and $v_{2}$ in the same direction it is equivalent of computing a Lorentz Transform of a single frame with ...
1
vote
1answer
107 views

Molar heat capacity of gas defined by relation $p=kV$

we have this problem where relation between Pressure($p$) , Volume($V$) is defined by relation $$p=kV$$ where $k$ is a constant and we have to find the molar heat capacity of the gas. Note:Ideal gas ...
6
votes
2answers
609 views

Infinitesimal Lorentz transformation is antisymmetric

The Minkowski metric transforms under Lorentz transformations as \begin{align*}\eta_{\rho\sigma} = \eta_{\mu\nu}\Lambda^\mu_{\ \ \ \rho} \Lambda^\nu_{\ \ \ \sigma} \end{align*} I want to show that ...
3
votes
1answer
323 views

Atwood machine problem [closed]

Sorry for the bad drawing, but I hope that this will help you get a hold of the problem. Consider an Atwood Machine with a total of two blocks, a mass less pulley, ideal string. One block rests on ...
0
votes
0answers
125 views

Solve a problem without using separation of variables

There's an additional exercise from Introduction to Electrodynamics by Griffith. Problem 4.34 A point dipole p is imbedded at the center of a sphere of linear dielectric material (with radius $R$ ...
0
votes
1answer
289 views

Eigenvectors of the angular momentum operator $S_x$ [closed]

For a spin of $\frac{1}{2}$ the angular momentum operator can be written as $\vec{S} = \frac{\hbar}{2} \vec{\sigma}$ in matrix form. Find the eigenvalues and eigenvectors of $S_x$ where $\sigma_x = ...
1
vote
1answer
63 views

How does the following commutator for measured observables and this operator relation imply the following relation?

$$ \hat{\Omega}_j{(\tilde{q}_j)}=\Omega_j(\tilde{q}_j-\hat{q}_j) $$ $$ [\hat{q}_j,\hat{q}_l]=ik_{jl} $$ Implies $$ [\hat{q}_j,\hat{\Omega}_l]= ...
1
vote
1answer
1k views

Ground State Wavefunction of Two Particles in a Harmonic Oscillator Potential

Question: Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by ...
0
votes
0answers
53 views

Flow of water through sand

Imagine a set up with a column of sand with porosity $\phi$ and permeability $k$ contained in a cuboid container. When one pours water evenly (let's say $V_w/A$ cubic meters per square meter) on the ...
0
votes
1answer
135 views

What is the tension in the string of a spherical pendulum? [closed]

Can some one solve it by using Lagrange's undetermined multiplier method or any other method that explains the physics in spherical pendulum system? book references: 1) Classical mechanics by ...
6
votes
1answer
88 views

Temperature of a phase transition

A solid can exist in two phases, with energies $$U_{1}(S,V)=\frac{S^2}{a_1}+b_{1}V(V-2V_{0})$$ $$U_{2}(S,V)=\frac{S^2}{a_2}+b_{2}V(V-2V_{0})$$ where $a_{1},a_{2},b_{1},b_{2},V_{0}$ are positive ...
0
votes
1answer
260 views

Work done on gas by piston [closed]

In this problem there is a cylinder that is closed at both ends and has thermally insulated walls. It is divided into 2 parts by a movable, frictionless, thermally insulated piston. There is a ...
0
votes
1answer
102 views

Confusing Classical Mechanics Question

I don't want this to be a "do my home work question" so please tell me how I can make this question helpful for other people. In my physics assignment I found the question below. I'd think that both ...
1
vote
1answer
1k views

Commutator of Momentum with a Position dependent function

I heard from my GSI that the commutator of momentum with a position dependent quantity is always $-i\hbar$ times the derivative of the position dependent quantity. Can someone point me towards a ...
1
vote
0answers
78 views

How to analyze this constraint question

Let $\gamma$ be a smooth curve in the plane, and introduce curvilinear coordinates $q_1,q_2$ on a neighborhood of $\gamma$; $q_1$ is the direction of $\gamma$ and $q_2$ is distance from the curve. ...
2
votes
2answers
63 views

Difference between a central potential that is a point and one that is a sphere?

In quantum physics there is a special case known as a particle in a spherically symmetric potential. I have a problem which is similar to the case of a hydrogen atom in that there is one free ...
3
votes
2answers
143 views

Srednicki's book on QFT

I am reading Srednicki's book on QFT and there's a thing I don't quite see in chapter 6 (Path integrals in QM) equation (6.7) is ...
1
vote
1answer
65 views

How to calculate thrust ratios for an object with a non centered mass [closed]

I am trying to figure out a formula that, given an initial thrust value, will give me the thrust value that I need to apply to each thruster (red) to make the overall thrust be straight up with no ...
-2
votes
1answer
182 views

What is the maximum mass that the airplane can have and still maintain enough lift to fly? [closed]

A commercial airplane travels at a speed which is 85% of the speed of sound. The wings of the airplane are designed such that the bottoms of the wings are flat and the tops of the wings are curved ...
0
votes
0answers
37 views

Determine the current and voltage for every component in the following circuit [closed]

Determine the current and voltage for every component in the following series circuit What is the voltage and current through R1 and what is the voltage and current through C1? $V_1= 20\,V$ $R_1= ...
0
votes
1answer
624 views

Problem with Velocity of efflux [closed]

I am stuck in this problem- I need to find the velocity of efflux at the hole of the container. [We can assume that the area of the hole is negligible in comparison with the base area of the ...
8
votes
5answers
885 views

How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
-5
votes
1answer
517 views

Tesla to Newtons [closed]

Is it possible to convert Tesla to Newtons of force? Or magnetization force H:(A/m) to newtons?
1
vote
0answers
57 views

A problem about special relativity [closed]

i can't understand it clearly, so please help me!
2
votes
1answer
175 views

Is there a better, faster way to do this projectile motion question? [closed]

The question is In a combat exercise, a mortar at M is required to hit a target at O, which is taking cover 25 m behind a structure of negligible width 10 m tall. This mortar can only fire at an ...
1
vote
1answer
102 views

Confused about elasticity and collisions

I was solving the following problem and the explanation to it confused me. There are two objects with mass $m$ and $M$, respectively. The object with mass $m$ has a velocity of $\sqrt{2gl}$ and ...
0
votes
0answers
36 views

Increasing number of neutrons in nucleus

I understand that the neutron-proton bonds in the nucleus creates the strong nuclear force but,how does increasing the number of neutrons in a nucleus affect electrostatic force, nuclear force and the ...
0
votes
1answer
56 views

Tungsten Wire Heat discipation

Background Information: I'm doing an experiment in which I place a bare tungsten wire in to various liqids, to measure a coefficient $\alpha $ in the equation $$ Power Dissipated = \alpha * \Delta T ...
0
votes
1answer
132 views

Proof of diffraction equations

If light incident on a grating makes an angle φ with respect to the normal to the grating, show that dsin(θ)=mλ becomes d[sin(θ-φ)+sin(φ)]=mλ. I began by showing: d[sin(θ-φ)+sin(φ)]=mλ, θi=φ=θ at ...
1
vote
2answers
414 views

Neither Biot-savart nor Ampere Law can solve this problem?

I'm confused about the use of the Ampere's Law and the Biot-Savart Law due the inconvenience of each law. I want to calculate the magnetic field due to current carrying a circular loop over itself, ...
0
votes
1answer
132 views

Voltmeter Question [closed]

I understand that a voltmeter is used for measuring potential electrical difference, but how exactly should said voltmeter be connected with the resistor in circuit?
2
votes
3answers
231 views

Mirror reflection

Question Create a set-up, as shown in the Figure, consisting of two mirror tiles (A and B) and a bird face, facing to the right . Make sure the two mirrors are perpendicular to the table and ...
3
votes
0answers
86 views

Electrodynamics and induced EMF question [closed]

A very long straight wire carries a current I. A plane rectangular coil of high resistance, with sides of length $a$ and $b$, is coplanar with the wire. One of the sides of length $a$ is parallel ...
2
votes
1answer
91 views

Calculate required voltage in mixed circuits [closed]

Q: Calculate the voltage that V1 has to provide Given: The following circuit. The voltage through LAMP1 is 5.0V. A (U,I) chart (not shown). LAMP1 and LAMP2 are identical, non-ohmic lightbulbs. ...
4
votes
1answer
364 views

Problem in Youngs double slit experiment

This is from Young Double slit experiment. But How to prove the the two $\theta$ are equal, I meant, how $\angle EAD= \angle PEC$? I see from the both triangle have $90^0$ but what about others?
1
vote
0answers
350 views

Current flowing through a square loop - Magnetic Field [closed]

A square conducting loop of wire of side $2a$ carries a uniform current I. Calculate the magnetic field at the centre of square due to the current in the loop.
1
vote
3answers
268 views

Electric flux for a rectangular surface? [closed]

I have the following homework problem: A line of charge $\lambda$ is located on the z-axis. Determine the electric flux for a rectangular surface with corners at coordinates: $(0, R, 0)$, ...
2
votes
0answers
102 views

Conservation of Mechanical Energy [closed]

I am currently trying to tackle the problem: A 2.0 kg bundle starts up a 30° incline with 125 J of kinetic energy. How far will it slide up the plane if the coefficient of friction is 0.30? ...
3
votes
0answers
56 views

Charge distribution and potential in a 1-dimensional quasistatic system

Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution ...
-3
votes
1answer
43 views

Acceleration on an inclined rail [closed]

I have to use $\vec{P}+\vec{R_N}+\vec{F_f}=m\vec{a}$ with $\|\vec{F_f}\|=\mu\|\vec{R_N}\|$ to express the acceleration as $$a_{x'}=g\sin\alpha(1-\frac{\mu}{\tan\alpha})$$ The configuration is (sorry ...
0
votes
2answers
164 views

Not so simple problem using momentum, energy and angular velocity…?

I have an object in free space (no gravity) with angular momentum $ = \omega_i $, and some velocity vector $=\vec{V_i}$. To simplify we will say it has a mass-less rigid rod length $ = \ell $, ...
0
votes
0answers
70 views

Transformation of a time-dependent acceleration to another frame

How do I transform a time-dependent acceleration between to rest frames? I was given a particular problem and while I found possibilities [1] [2] for acceleration-transformations when the acceleration ...
2
votes
2answers
400 views

Probability of Different States - Canonical Ensemble - Partition Function

Consider a canonical ensemble of $N$ ideal gas atoms, which could have spin up or spin down. Why is it that the probability of finding the particle in a spin up state generally only involves the ...
0
votes
1answer
265 views

Light bulb filled with air inside volume of helium [closed]

I have a question on my homework I can't really figure out. It's from Reif, problem 3.6, Fundamentals of Statistic and thermal physics Question: A glass bulb contains air at room temperature and at a ...