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80 views

Is my method of calculating thermal conductivity of a metal wrong?

I am trying to determine the thermal conductivity of pure copper at various temperatures using the Weidemann-Franz Law but for some reason it is not matching up to textbook data. I used the Bloch ...
2
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0answers
62 views

Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation

I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral ...
2
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0answers
153 views

Lagrange's Equations for a Tetherball

I'm trying to write down the equations of motion for a tetherball moving around a pole while the string is getting shorter. --- MAJOR EDIT --- I started with Lagrange: $$ x(t)=l(t) \sin (\theta) ...
2
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0answers
60 views

Statistical Mechanics: Most probable orientation of grain particle in gas chamber?

I'm in an introductory statistical mechanics course, and we've been posed the following situation: Long-shaped dust particle (so imagine something like a grain of rice) is placed in a gas chamber (so ...
2
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222 views

Equation of motion for a falling rod (with one end touching a frictionless surface)

I have a quick question about the equation of motion for a falling rod (with one end touching a frictionless surface). The end touching the surface is not fixed. I am given the moment of inertia about ...
2
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67 views

The proof that Dirac's hamiltonian commutes with inversion operator

I tried to check the statement that Dirac free Hamiltonian commutes with inversion operator. For $$ \hat {P}\Psi(\mathbf r , t) = i\hat {\gamma}_{0}\Psi (-\mathbf r , t), \quad \hat {H} = (\hat ...
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75 views

One more relation with spherical spinors

Let's have the spherical spinors: $$ \mathbf {Y}_{j, m, l = j \pm \frac{1}{2}} = \frac{1}{\sqrt{2l + 1}}\begin{pmatrix} \pm \sqrt{l \pm m +\frac{1}{2}}Y_{l, m - \frac{1}{2}} \\ \sqrt{l \mp m ...
2
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0answers
69 views

Finding internal energy using equation of state

I have an equation of state as a function of $p$ (pressure), $T$ (temperature) and $V$ (volume) for a real gas and need to find an expression for the internal energy $U$. I know this is given by the ...
2
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0answers
84 views

Momentum representation of a state

I am trying to figure out the momentum representation of the state which has the properties $$\langle \psi |\hat q |\psi \rangle=-q_0,$$ $$\langle\psi|\hat p|\psi \rangle=p_0, $$$$\Delta q\Delta ...
2
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0answers
92 views

Pauli matrices product identity

How to prove the identity $$ \tilde {\sigma}_{\alpha}\sigma_{\beta}\tilde {\sigma}_{\gamma} = g_{\alpha \beta}\tilde {\sigma}_{\gamma} + g_{\alpha \gamma}\tilde {\sigma}_{\beta} - g_{\beta \gamma} ...
2
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0answers
54 views

Can I use the reduced mass principle in a spring-damper system?

http://hyperphysics.phy-astr.gsu.edu/hbase/orbv.html#rm I want to know, if I can use the reduced mass principle to solve a two object spring-damper system. In the books and webpages that I have ...
2
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335 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 ...
2
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0answers
191 views

Stationary Perturbation Theory : Estimating higher order corrections for anharmonic oscillator

Note $\hbar = 1$. $$H = H_0 + \lambda V =\frac{p^2}{2m} + m\omega^2x^2 + \lambda m^2\omega^3 x^4$$ Supposedly the perturbation expansion diverges. We are supposed to estimate for what order we have a ...
2
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0answers
51 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 ...
2
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0answers
99 views

Transmission + Reflection coefficients >1 For Potencial Barrier with Negative Complex Part Contradicts Paper

I am studying reflection and transmission coefficients for a barrier consisting of a a step potencial defined by: $$V(x):=\begin{cases}0&{\rm if}\,|x|>a/2 \\ V_0+iW_0 & {\rm ...
2
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0answers
92 views

Two spinor tensors and Maxwell's equations

Let's have two symmetric (by the indices) spinor tensors $F_{ab}, F_{\dot {a}\dot {b}}$ and conditions $$ F_{ab}, \partial^{\dot {a} a}F_{ab} = 0, \quad F_{\dot {a}\dot {b}}, \partial^{\dot ...
2
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0answers
83 views

Jacobian matrix of Galilean transformation

If we want to transform to another inertial frame of reference using Galilean transformation in 4-dimensional space-time, what is the Jacobian matrix of Galilean transformation?
2
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78 views

Approximate energy levels for the following potential

Let's have potential $$ U(r) = -U_{0}e^{-\frac{r}{a}}. $$ I need to find energy levels for particles moving in this field (for an arbitrary values of orbital number $l$). This task isn't exactly ...
2
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79 views

Commutators with function

I have following exercise: If $[C,D]$ is a c-number and $f(x)$ is a well-behaved function (i.e. all derivatives exist and are finite), show that: $$[C, f(D)]=[C,D]f'(D)$$ where $f'(D) = ...
2
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0answers
38 views

Likelihood of the creation of a single unbound quark in the collision of very high energy particle beams

I am going over old exam and am not understanding the logic behind the answer given in the mark-scheme. A beam of protons and antiprotons attain energies of 1400 GeV in a synchrotron. Why is it ...
2
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321 views

Radial Wave Function for Spherical Squared Well Potential and $S$-Matrix

I have a problem with this exercise because I really don't know how to proceed. It's related with the "S-matrix". In class we saw this example: Consider the spherically symmetric potential: ...
2
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0answers
171 views

Conservation of energy in a quantum harmonic oscillator after a sudden change in spring constant

At a given instant of time, a harmonic oscillator undergoes a sudden change in spring constant from $k$ to $k'$. Show that for energy to be conserved in the accompanying transition, $\sqrt{k/k'}$ must ...
2
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230 views

Calculating Electric Field from a Potential Difference w/o Charge

So here is my homework question: Two long cylindrical shells of metal (radii $r_1$ and $r_2$, $r_2 > r_1$) are arranged coaxially. The plates are maintained at the potential difference ...
2
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0answers
67 views

Spin of a decay product

A particle A decays into particles B, C and D. The spin of A, B and C particles is 1/2 each. What are the possible spins of particle D? My attempt is the following: Since B and C have spin 1/2 ...
2
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0answers
196 views

How should I think about reciprocal lattice and Miller indices?

When I hear someone talking about a (100) plane or a (111) plane or an (hkl) in general, my first thought is, is the system cubic. The reason I think this is because I tend NOT to think of the planes ...
2
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0answers
112 views

mathematical model of one electrostatic problem

I am trying to find direct-current electric field in a specific domain: it is a brick made from a low-conductive material with a number of more conductive inclusions of different shapes - spheres, ...
2
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0answers
80 views

A question about inverse Green's function

(The background is in a book, An introduction to String Theory and D-brane Dynamics 2nd, by Richard J Szabo p87, Eq. (6.31)) Given $$N(\theta,\theta')= - \frac{1}{\pi} \sum_{n=1}^{\infty} \frac{ ...
2
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0answers
105 views

How to understand the transmission coefficient from the following question?

I want to understand the transmission coefficient and construct a time-independent Schrodinger equation where $$ V(x)=\left\{ \begin{array}{c c} \delta(x), & |x| < 1 \\ + \infty, & ...
2
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0answers
138 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 ...
2
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0answers
110 views

Definition of a 'tunneling lifetime'

I'm given a one-dimensional potential with two wells, one local minimum at some higher energy and one deep global minimum next to it, separated by a barrier of own shape and height (phase qubit). I ...
2
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0answers
54 views

Manipulating a formula for a relativistic Doppler shift

Lets say we take the standard configuration when $x'y'$ is moving away from system $xy$ (image 1). By knowing that the phase is constant in all frames $\phi=\phi'$ we can derive the Lorenz ...
2
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0answers
52 views

Is there an equation that tells you more about the amplitude of an object which is in resonance?

I'm a high school senior and I have to write a paper about resonance and differential equations. I've been searching the Internet for a long time, but I haven't found an equation that is properly ...
2
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0answers
159 views

Current to cancel Earth's magnetic field

I'm making a lab report where I've used a Helmholtz coil and a magnet to find Earth's magnetic field intensity in the area by relating the frequency of oscillation of the magnet when a certain current ...
2
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0answers
232 views

Trouble with calculating Christoffel symbols of FLRW metric using Lagrangian method

The FLRW metric which I am using is $$ds^2 = dt^2 - \frac{a(t)^2}{c^2} \left( dx^2 + dy^2 + dz^2 \right)$$ where $a(t)$ is the so-called 'scale factor'. I did not want to calculate the Christoffel ...
2
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0answers
59 views

error propagation and collision in ideal gas

When dealing with gas, a statistical approach is needed because For N particles, you have to solve 6N equations which cant be done analytically. To know our time step for numerical solving, you can ...
2
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0answers
112 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
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0answers
194 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
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0answers
408 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
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0answers
161 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
81 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
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0answers
159 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
2k 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
104 views

Showing that the Ricci scalar equals a product of commutators

I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor ...
2
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0answers
1k 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
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0answers
281 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
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0answers
95 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
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0answers
398 views

Dielectric in Parallel Plate Capacitor

Given a parallel plate capacitor of width $w$, length $l$, with a dielectric moving along the length $l$. Let the dielectric be from $x$ onwards. The capacitance will be $\frac{w \epsilon_0}{d} ...
2
votes
0answers
283 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
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0answers
1k 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
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0answers
215 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. ...