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.
6
votes
0answers
225 views
exponential potential $ \exp(|x|) $
For $a$ being positive what are the quantization conditions for an exponential potential?
$$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$
with boundary conditions $$ y(0)=0=y(\infty) $$
I ...
6
votes
0answers
224 views
Capacitance of this unusual capacitor
This capacitor is composed of two half spherical shelled conductors both with radius $r$. There is a very small space between the two parts seeing to that no charge will exchange between them.
...
5
votes
0answers
125 views
Find $x$ operator given $p$
This is problem $1.2$ of Molecular Quantum Mechanics by Atkins, 4th edition. I'm given the momentum operator
$$p=\sqrt{\frac{\hbar}{2m}}(A+B)$$
with
$$[A,B]=1$$
and I need to find $x$ in this ...
3
votes
0answers
64 views
Effective mass in Spring-with-mass/mass system
Suppose you have a particle of mass $m$ fixed to a spring of mass $m_0$ that, in turn, is fixed to some wall. I'm trying to calculate the effective mass $m'$ that appears in the law of motion of the ...
3
votes
0answers
179 views
Shape of a string/chain/cable/rope?
The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc ...
3
votes
0answers
296 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 ...
3
votes
0answers
116 views
Matter-wave interference from free falling cold atoms
and another exam question, this is about current research:
Interference of matter waves has been studied using ultra-cold atoms. The phase of a matter wave for free-falling cold-atoms at time $t$ ...
3
votes
0answers
453 views
How do I derive the critical temperature for bose condensation in two dimensions?
In class we derived the 3D case, but there's a step I don't understand:
$$ N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p = ...
2
votes
0answers
28 views
5D Ricci Curvature
As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper ( http://arxiv.org/pdf/1107.5563v2.pdf ). I was wondering if there is some ...
2
votes
0answers
60 views
Wald problem 11.4
Consider a stationary solution with stress-energy $T_{ab}$ in the context of linearized gravity. Choose a global inertial coordinate system for the flat metric $\eta_{ab}$ so that the "time direction" ...
2
votes
0answers
47 views
Parton Distribution Functions, average cross section of the nucleon
Say we are given the scattering cross section for neutrinos from $d$ and $\bar{u}$ quarks as $\frac{d\sigma^{d}}{dQ^2}=\frac{G_F^2}{\pi}$, $\frac{d\sigma^{\bar{u}}}{dQ^2}=\frac{G_F^2}{\pi} (1-y)^2$, ...
2
votes
0answers
42 views
Analytical solution of two level system driving by a sinusoidal potential beyond rotating wave approximation
A quantum mechanical two-level system driving by a constant sinusoidal external potential is very useful in varies areas of physics. Although the wildly used rotating-wave approximation(RWA) is very ...
2
votes
0answers
171 views
Pauli paramagnetism for electrons with external magnetic field
Apparently it is to be shown that for electrons under an external magnetic field, in the limit as $B\to 0 $
$$
\chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)}
$$
...
2
votes
0answers
67 views
Classical scattering of two particles by a Yukawa potential
A point-like particle $A$, coming from minus spatial infinity, heads at another one, $B$, with an impact parameter of $b$.
Initial momenta are $p_A$ and $p_B=0$.
They repel each other via a Yukawa ...
2
votes
0answers
46 views
Calculating the minimum Lawson parameter for sustained d-d fusion
Calculate the minimum Lawson parameter for sustained deuterium-deuterium fusion in a plasma with an energy of 10 keV.
I have been given the above question as part of a homework assignment and help ...
2
votes
0answers
142 views
How is parity relevant to determining angular momentum?
Question:
Particle A, whose spin $\mathbf{J}$ is less than 2, decays into two identical spin-1/2 particles of type B.
What are the allowed values of the orbital angular momentum $\mathbf{L}$, ...
2
votes
0answers
91 views
Internal moment in the hull of a pressure vessel
This question is related to the course structural analysis. As part of our exam grade every student has been given different multiple homework assignments which we have to solve.
One of the problems ...
2
votes
0answers
495 views
Rotate vector in spherical coordinates
I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia ...
2
votes
0answers
303 views
How to calculate uncertainties of a natural exponential function?
(I apologize if this should be posted in mathematics, however I chose to post it here as it's technically about physics)
I conducted an experiment in which position of items were shifted on an ...
2
votes
0answers
123 views
Angular momentum confusion
Could somebody please explain what is going on here?
We have a system of two indistinguishable spin-1 bosons. We shall adopt the center of mass frame.
Let
$S$ = total spin
$L$ = relative orbital ...
2
votes
0answers
86 views
Bandgap Spacing in Photonic Crystals
I am doing some self-study on photonics and have encountered the following question:
We know that amorphous electronic crystals such as amorphous silicon have a bandgap. Can amorphous photonic ...
2
votes
0answers
161 views
include the stretch of the spring own weight in potential energy for spring pendulum?
we are given a problem with spring with its own mass $m$. I am confused how to set up the
PE term in the Lagrangian.
Assume the spring has length of $L_{0}$ when it is laying on a table
horizontally. ...
2
votes
0answers
75 views
The force exerted by a ~10 Tesla magnet on a C13 isotope?
How much force would a ~10 Tesla magnet exert on a weakly magnetic C13 isotope? If I made a molecule of diamond with $N$ C13 atoms, how large would $N$ need to be for me to pull on it with something ...
2
votes
0answers
69 views
Randomly sampling a “well-mixed” solution of Brownian particles
I place $N$ Brownian particles in $V$ liters of solution, shake until I assume that the particles are "well-mixed", and sample and randomly sample an $S$ liter volume. What is the probability ...
2
votes
0answers
187 views
Cerenkov light - a practical calculation
I need to calculate the approximate total amount of energy radiated, via Cerenkov, by a muon as it traverses $10\:\rm{cm}$ of quartz glass. Unfortunately I've spent so much time fiddling with ...
2
votes
0answers
251 views
kinetic energy in collisions
We were hoping you could help us understand collision energy.
Vehicle A is driving West at 35mph and weighs 1437kg.
Vehicle B is driving North at 35 mph and weighs 1882kg.
Vehicle B crashes into the ...
2
votes
0answers
405 views
When do I know if energy stored in an object is 0 or nonzero? (Heat transfer)
There is uniform internal heat generation at $\dot{q}=5\times10^{7} \frac{W}{m^{3}}$ is occurring in a cylindrical nuclear reactor fuel rod of 50 mm diameter and under steady state conditions the ...
2
votes
0answers
152 views
Solar wind and the Earth's magnetic field
I have again an old question from a comprehensive exam I took a couple of months ago. Lucky for me one could pick 5 out of 8 questions, because on some of the problems I didn't even know how to start. ...
2
votes
0answers
374 views
Bungee jump physics
Question:
A bungee jumper jumps from a bridge. The length of the loose rope is 30 m. When the jumper reach the lowest point possible, the rope stretches 10 m. What is the final stretch of the rope, ...
2
votes
0answers
312 views
Amplitude of a Forced Harmonic Oscillator
For an assignment in one of my maths units at uni, I've been asked to derive and solve the differential equation of motion for a forced harmonic oscillator, with the forcing function having the form ...
2
votes
0answers
647 views
Measuring the spring constant in a system with hydrostatic buoyancy
I have a physics lab tomorrow and I would appreciate it if you could give me your opinion on whether my reasoning is correct for this situation or not:
http://i.stack.imgur.com/WMzA7.jpg
The title ...
1
vote
0answers
31 views
Maxwell-Boltzmann distribution
The short story is, that I have to calculate some transport coefficients, but using the the MB distribution as my distribution function.
What I currently need to solve is:
${{\mathcal{L}}^{\,\left( ...
1
vote
0answers
18 views
How to find outflow pressure/force of air through a pipe
I have been trying to find the correct method for determining the outflow force resulting from a certain amount of air being forced into a pipe of a certain dimension. Essentially i'm trying to ...
1
vote
0answers
51 views
+100
Induced current using a reference system bound with a moving charge
Let's suppose to have a charge moving at velocity $\textbf{v}$ and a square wire.
If I choose a reference system bound with the square wire, since the charge is moving at velocity $\textbf{v}$, in ...
1
vote
0answers
28 views
Power transfer in a transformer
Can it be proved using the concept of induced emf that power supplied at the primary coil equals power consumed at the secondary. I tried following. Let primary coil be called 1 and secondary be ...
1
vote
0answers
51 views
A slender rod with a ball at the end
A slender rod is attached to a block accelerating horizontally. The rod is free to rotate without friction. At the end of the rod is a ball.
As the block accelerates, the slender rod will be deviated ...
1
vote
0answers
32 views
Mercury's Orbital Precession in Special Relativity
I am researching Mercury's orbital precession. I have considered most perturbations and general relativity. I am still not satisfied. I need your help.
I need a solution to Exercise 13, Chapter 6, in ...
1
vote
0answers
32 views
Calculating the change in entropy in a melting process
I have a homework question that I'm completely stumped on and need help solving it.
I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
1
vote
0answers
47 views
What defines the adiabatic flame temperature?
In a case, I have to solve, I need to describe the combustion of natural gas (Groningen natural gas to be more specific). However I am having some problems understanding the adiabatic flame ...
1
vote
0answers
54 views
Stress-energy tensor of point particle when the trajectory is a transcendental equation?
I'm working through Carroll's GR book, and Problem 7.8 is not coming together. I'm missing something idiotically simple, but I'm not sure if I can cleanly write a stress-energy tensor for a point ...
1
vote
0answers
42 views
Proton scattering off electrons
I'm looking at a question which starts off as:
A proton is travelling through a material and scattering the electrons in the material. Express the scattering angle in terms of the impact parameter, ...
1
vote
0answers
81 views
General physics question involving Heisenberg Uncertainty Principle
Question:
An unstable particle produced in a high-energy collision is measured to have an energy of $483\ \mathrm{MeV}$ and an uncertainty in energy of $84\ \mathrm{keV}$. Use the Heisenberg ...
1
vote
0answers
18 views
Henry's Law in metals
For fixed temperature the concentration of a gas dissolved in a solution is directly proportional to the gas pressure $p$, i.e. $c_s (T,p) = f(T)p$. Since $H_2$ only dissolves in metals as single ...
1
vote
0answers
51 views
Calculating pressure in accelerated fluids in closed and open vessels?
The question asked was "what should be the acceleration such that the pressure at both the points marked by thick dots be equal? the vessel is open and cubic with side 5m?"
Initially i considered ...
1
vote
0answers
44 views
Dust generated static space-time implications on fluid 4-velocity
Imagine we have a perfect fluid with zero pressure (dust), which generates a solution to Einstein's equations. Show that the metric can be static only if the fluid four-velocity is parallel to the ...
1
vote
0answers
65 views
linear response for a simple harmonic oscillator
Really sorry for this simple question, but I think it will be useful/interesting in general.
Consider a quantum simple harmonic oscillator.
Add a perturbation $H_I = -\lambda \hat{x}$
Calculate ...
1
vote
0answers
55 views
Feynman Diagram for Interaction of Deuteron with Oxygen-16
I have to draw a Feynman diagram for the interaction of a deuteron with Oxygen-16.
The interaction is as follows:
$ d + {}^{16}O \rightarrow p + {}^{17}O . $
I am generally ok with Feynman ...
1
vote
0answers
104 views
Use of Principle of Equivalence
Let $x^\mu$ be the coordinates of a reference frame, $K$, where all bodies feel the same constant and uniform acceleration $\textbf{a}=\textbf{g}=-\nabla\varphi$; let $\xi^\mu$ be the coordinates of a ...
1
vote
0answers
31 views
What is the meaning of $h_L - h_H$ for a heat engine?
My problem gives me a Carnot cycle heat engine with water as its working fluid, with $T_H$, $T_L$, and the fact that it starts from saturated liquid to saturated vapor in the heating process.
I need ...
1
vote
0answers
56 views
Concentration of Proteins
You release a billion protein molecules at position $x = 0$ in the middle of a narrow capillary test
tube. The molecules’ diffusion constant is $10^{−6} \ cm^2 s^{−1}$. An electric field pulls ...
