The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [homework-and-exercises]

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-like questions.

2,367 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
27
votes
0answers
2k views

How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
15
votes
2answers
751 views

Bottle stability optimization

A few days ago some friends and I played a game called "flunkeyball" where you need to upset a bottle with a ball. Then a question occurred: "How much water do we need to put into the bottle that its ...
13
votes
0answers
335 views

The dual of a surface element in 4-space

In reading the classic text, "The Classical Theory of Fields", Third Edition, by Landau and Lifschitz, I found an "obvious" statement not so obvious to me. It is on p.19, the statement of the ...
11
votes
0answers
197 views

Simple argument for unexpected behavior in SUSY model

Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential $$ W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ ...
10
votes
3answers
553 views

Magnetic scalar potential far above a magnetic film

The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization $\bf{M}$. I would like to find the the magnetic field far above the plate. My expectation is that ...
9
votes
1answer
586 views

Deriving the Poisson bracket relation of the Ashtekar variables

I'm trying to figure out how to calculate the orthogonality of Ashtekar variables with respect to the ADM hypersurface metric and conjugate momentum. $$\{{A_a}^i(x), {E^b}_j(y)\} = 8 \pi \beta \delta^...
9
votes
0answers
888 views

Can spheres leaking charge be assumed to be in equilibrium?

I am struggling with the following problem (Irodov 3.3): Two small equally charged spheres, each of mass $m$, are suspended from the same point by silk threads of length $l$. The distance between ...
8
votes
3answers
6k views

Basic Thermodynamics: Quasistatic Adiabatic Process

I'm going through the exercises in a Thermodynamics book, just to revise and build my intuition. Right now, I'm working on: Show that for a quasistatic adiabatic process in a perfect gas, with ...
8
votes
1answer
575 views

Force problem related to adhesive and bonding

I have two PCBs (printed circuit board), and they are glued by adhesives, as show in the pictures. And the location of the adhesives are indicated on the picture (please notice that NO adhesive is ...
7
votes
0answers
252 views

Path Integral on Feynman Hibbs: Interaction of EM field and matter, how can we get to equation (9.68) from (9.67)?

On Feynman Hibbs "Quantum Mechanics and Path Integrals", the equation (9.67) describe the transition amplitude of the matter (for example an atom) to go from the state $M$ to the state $M$ when it ...
7
votes
1answer
476 views

Escape velocity for Schwarzschild metric

I can't fill in the gaps in my solution to this and assistance or a reference would be appreciated. The question begins with the straightforward derivation of the EoM for a massive particle orbiting ...
7
votes
3answers
1k views

Drag - Dimensional Analysis / Buckingham $\pi$

I'm working on dimensional analysis and I'm having trouble. Here's a problem from my book I'm working on. I'm supposed to consider a small sphere experiencing acceleration due to gravity $g$. The ...
7
votes
1answer
521 views

General motion of a cone on an inclined surface

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight? I know that its motion depends on the ...
7
votes
1answer
927 views

Question about superconductivity

A long cylinder of radius $R$ is made from two different material. Its radius $r<r_0$ $(r_0<R)$ part is a material with superconducting transition temperature $T_1$, and its $r_0<r<R$ ...
7
votes
1answer
836 views

Analytical solution of two-level system driving by a sinusoidal potential beyond rotating wave approximation

A quantum mechanical two-level system driven by a constant sinusoidal external potential is very useful in varies areas of physics. Although the widely used rotating-wave approximation (RWA) is very ...
7
votes
2answers
652 views

Express Laplace transform of voltage across a capacitor in terms of charge

In Charge Tunneling Rates in Ultrasmall Junctions section 2.1, the authors consider the problem of charge relaxation in a simple circuit shown in Figure A. The implicitly use an assumption made about ...
6
votes
0answers
185 views

Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)

I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
6
votes
0answers
222 views

Sphere half-submerged on a dielectric

This is a classic problem in electrostatics with a twist, so I thought it could be useful for others here. I did have a problem with the integration at the end, but on general I think the idea can ...
6
votes
1answer
476 views

Charge over 2 layer dielectric, image method

If I have a charge $Q$ located over a 2 layer dielectric as represented: According to the image method : the charge $Q'1$ will be located at a distance $h_1$ under the first interface and the $Q'2$ ...
6
votes
1answer
400 views

Trying to solve 2D Toda Lattice Equation with Lax Pair Approach

I am working on this Hamiltonian: $$ H = \frac{p_1^2 + p_2^2}{2m} + e^{q_2-q_1} + e^{q_2} + e^{-q_1} -3 $$ Thank you for the hint that it is a modification of the Toda Lattice Equation. Let me sketch ...
6
votes
4answers
900 views

Distinguishable, indistinguishable paramagnetic ideal gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
5
votes
1answer
205 views

Examples of central forces on the path of orbit?

In solving a problem from Goldstein (3.13), I solved for multiple properties of a circular orbit with the attractive central force where the path of orbit crosses the point of the force (at origin). ...
5
votes
1answer
457 views

How to understand Bloch sphere representation?

I'm really new to quantum computation. Now, I'm going through a tutorial article Quantum Computation: a Tutorial (NB: PDF). I was confused by certain points over there. So, on page 5, when the ...
5
votes
0answers
553 views

Two-point function of a free massless scalar field in Euclidean space-time

Let $\phi(x)$ be a free massless scalar field on $d$-dimesnional space-time with Euclidean metric. I am interested in the operator formalism, i.e. $\phi(x)$ is an operator satisfying $\Delta \phi=0$ ...
5
votes
1answer
277 views

How the Poisson bracket transform when we change coordinates?

I'm studying the book Geometric Mechanics by Darryl D. Holm and there's one exercise in the book I'm not quite getting what has to be done. The same discussion the author makes in the book is made on ...
5
votes
1answer
171 views

Polchinski equation 11.2.7

In Polchinski's string theory volume 2, when discussing the GSO projection for the heterotic string he says: In the IIA and IIB superstrings the GSO projection acted separately on the left- and ...
5
votes
1answer
391 views

Sum of energy for 2 solids in rotation

I would like to compute the sum of energy of the following case: Two solids are turning (disks). Yellow solid is turning at $w_1$ radians per second around its center of gravity and blue solid is ...
5
votes
0answers
436 views

Action of Parity operator on Impulse representation

Is my derivation of the action of the parity operator $\mathbb{P}$ on the $|p\rangle$ representation correct? $$\left( \mathbb{P}\tilde\psi \right)(p)= - \tilde\psi (p).$$ Obtained from $$\left( \...
5
votes
0answers
2k 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 ...
5
votes
0answers
875 views

Goldstone modes and Heisenberg model

The ideia is to show that, because of Goldstone modes, 2d systems are quite different from 3d ones. So, considering the Heisenberg model, I'll post here what I'm asked to and my current thoughts on ...
5
votes
1answer
741 views

Ray tracing in General Relativity

I would like to find out what one would see at the Schwarzschild radius of a massive non-rotating black hole, if the black hole is surrounded by a bright ring. For that, I would place the observer at ...
5
votes
1answer
145 views

Taking pivot about an accelerating point

Given this question: A small ball of mass $m$ and radius $r$ rolls without slipping on the inside surface of a fixed hemispherical bowl of radius $R>r$. What is the frequency of small ...
4
votes
0answers
138 views

Importance of an extra total derivative term in Liouville theory

In this paper on boundary Liouville theory, the authors have introduced an extra term, $-\partial_{\sigma}^2\phi$, (the last term in the equation below) in defining the stress tensor of the Liouville ...
4
votes
1answer
33 views

Deriving equations of rotational motion for connected rods

I'm working on a problem involving deriving equations of rotational motion for a system of connected rods (see the picture), and I'm a bit confused about a few things to do with rotational motion. I ...
4
votes
0answers
249 views

Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
4
votes
0answers
174 views

Free Field Realization of Current Algebras and its Hilbert space

I have some conceptual confusion regarding the interplay between current algebras, their free field representation and the Hilbert space generated from it. Let's sketch a simple example, $\mathfrak{...
4
votes
0answers
102 views

Equilibrium points of three masses on a rigid spring ring with gravity

I'm trying to find the equilibrium points of a given system using Lagrangian mechanics (the system is still not rotating at the beginning). should I find the diagonal matrix for the characteristic ...
4
votes
1answer
48 views

What are the scalar equations for velocity and displacement if acceleration obeys the inverse-square law?

In basic high school physics/calculus you learn that you can formulate equations for velocity and displacement under constant acceleration as: $a(t) = a_0$ $v(t) = a_0t + v_0$ $x(t) = \frac{1}{2}...
4
votes
1answer
224 views

Komar mass for rotating black hole

I am trying to calculate the Komar conserved quantities for black hole having Killing vectors. I followed the standard procedure and calculated the Komar mass for Reissner-Nordstrom black hole (plz ...
4
votes
0answers
382 views

Goldstein Classical Mechanics exercise 5.17 (3ed) conceptual

I am having difficulty understanding a concept in the "Heavy symmetric top" type of problems. I will include all of my efforts as to hopefully have someone easily point out what it is that I'm missing....
4
votes
0answers
193 views

Feynman rules for this perturbative expansion in Grassmann variables

I'm given the integral $$ Z[w] = \frac{1}{ (2 \pi)^{n/2}} \int d^n x \prod_{i=1}^n d \overline{\theta}_i d \theta_i \exp \left( - \overline{\theta}_i \partial_j w_i (x) \theta_j - \frac{1}{2} w_i(x) ...
4
votes
1answer
599 views

Solving the Lindblad quantum master equation in matrix form

I have just started learning density matrix and quantum master equations, and I am given a problem set that asks to find the solution to the Lindblad equation with $H$, $L_+$, $L_-$, $L_z$, and $\rho(...
4
votes
0answers
330 views

How can I see where this formula for a general vertex factor comes from?

I have been reading Srednicki from the beginning and doing all the exercises, and I hit a big roadblock at Q10.4, as I can't seem to figure out what Srednicki is doing in his solution. Luckily, I ...
4
votes
0answers
227 views

1D Quantum scattering from $V(x) = e^x$

Define $V(x) = e^{x}$, $x \in \mathbb{R}$ and consider the Hamiltonian $H = - \frac{d^2}{dx^2} + V(x)$. The eigenvalue problem is $$ -\psi''(x) + e^{x} \psi(x) = E \psi(x)\,, \quad x \in \mathbb{R}\,. ...
4
votes
0answers
95 views

Constructing the Kruskal diagram for a 2-dim metric of the following form

We are given $ds^2 =- \frac{du\,dv}{M - uv},$ where $$v=t+x\, \qquad u= t - x\qquad -\infty < t, x < \infty$$ and $M$ is a positive constant. The Riemann curvature tensor is proportional to $\...
4
votes
0answers
214 views

Generating function of point transformation

I am asked to show that the generating function corresponding to a point transformation in Lagrangian mechanics can be taken as null. The point transformation consists of $$ Q_i=Q_i(q,t), $$ and ...
4
votes
0answers
145 views

Where is wrong in the derivation about adiabatic theorem

There is a homework in Quantum Mechanics which is about adiabatic theorem. Let us argue where is wrong in following derivation. $$i \partial_t |\psi(t)\rangle = H(t) |\psi (t)\rangle \tag{1}$$ if $\...
4
votes
1answer
177 views

OPE of Lorentz current with tachyon vertex

This is a question related to chapter 2 in Polchinski's string theory book. On page 43 Polchinski calculates the Noether current from spacetime translations and then calculates its OPE with the ...
4
votes
0answers
56 views

LFRW Universe - equivalence principle and Hubble flow

After a suitable change of coordinates, the metric for the (flat) FLRW universe becomes $$ ds^2 = (1 + 2 \Phi(\vec{x},t))dt^2 - (1-2\Psi(\vec{x},t))d\vec{x}^2, $$ where $$ \Phi(\vec{x},t) = -\frac{1}...
4
votes
0answers
158 views

How does one extract classical results from QED Lagrangian?

A well known result from classical electrodynamics for the total energy density of a charged spherical shell is, $$ u = \frac{3e^2}{32 \pi^2 \varepsilon_0 r^4}, $$ How would you extract that result ...