Homework Statement
Find the Lagrangian for the double pendulum system given below, where the length of the massless, frictionless and non-extendable wire attaching m_1 is l. m_2 is attached to m_1 through a massless spring of constant k and length r. The spring may only stretch in the m_1-m_2...
Homework Statement
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Consider a mass m moving in a frictionless plane that slopes at an angle \alpha with the horizontal.
Write down the Lagrangian \mathcal{L} in terms of coordinates x measured horizontally across the slope, and y,
measured down the slope. (Treat the system as...
I'm supposed to find the magnetic field, the scalar electric potential and magnetic vector potential for the following electromagnetic wave:
\vec{E} = E_0 cos (kz - \omega t) \left \{ \hat{x} + \hat{y} \right \}
Alright, the magnetic field goes as
\vec{B} = \frac{1}{c} \hat{k} \times \vec{E}...
Homework Statement
Suppose a proton and an antiproton collide producing a pair of top-antitop quarks.
What would be the minimum required momenta of both proton and antiproton in order for this pair creation to occur?
p + \bar{p} \rightarrow t + \bar{t}
(Answer: 173 \frac{GeV}{c^2}, 59.9...
Homework Statement
I'm trying to confirm the speed of an antimuon in the \pi^+ \rightarrow \mu^+ \nu_{\mu} decay through the laws of conservation but it doesn't add up.
Homework Equations
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1.Energy-momentum relation:
E^2 = (pc)^2 + (mc^2)^2
2. Rest masses:
m_{\pi} = 139.6 \...
Homework Statement
A body at rest in a frame of reference S disintegrates into two pieces moving in opposite directions. The masses of each fragment are 3.0kg and 4.0kg and their velocities 0.8c and 0.6c, respectively. Find the mass of the body before it disintegrated. (Answer: 10kg)
Homework...
Bonjour Patrick! Merci pour ta réponse. Ça va? As for your question, I'd say it's the operator being self-adjoint, i.e. A = A^{\dagger}, also I believe I know where you're going at, I should have written A = i \frac{\partial^4}{\partial t^4} instead?
Hello, could you please give me an insight on how to get through this proof involving operators?
Proof: Given an eigenvalue-eigenvector equation, suppose that the vectorstate depends on an external parameter, e.g. time, and that over it acts an operator that is the fourth derivative w.r.t...
Hello, I've been having some trouble with a paramagnetism problem from my Statistical Mechanics class textbook (F. Mandl, Statistical Physics, 2nd edition, p. 25). The problem is as follows
1. Homework Statement
2. Homework Equations
1. The temperature parameter
\displaystyle{ \beta =...
Homework Statement
I'm supposed to find the Laurent expansion of sin z/(z-1) at z=1.
The Attempt at a Solution
I thought about expanding the sine as a power series of (z-1) but I'm not so sure if that would be correct since the sine is a function of z and not z-1.
I can see that for z=0 it's a pole of order 2 due to it's taylor series
f(z) = \left( \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!} z^{2n+2} \right)^{-1}
as for n=0 we have our first singularity z^{-2} which I can verify it as a pole by it's definition "The coefficients a_n are zero for n<-k and...
I've been studying the residue theorem and I've been having some difficulty with classifying singularities.
For example, let's use the function
f(z) = \frac{1}{z sinz}
I know it has two singularities, one at z=0 and the other at z=2kπ for k ={0,1,2,..}, I don't know what kind of singularities...
Homework Statement
Evaluate the following integral,
I = \int_{0}^{2\pi} \frac{d \theta}{(1-2acos \theta + a^2)^2}, \ 0 < a < 1
For such, transform the integral above into a complex integral of the form ∫Rₐ(z)dz, where Rₐ(z) is a rational function of z. This will be obtained through the...
That's nice to hear. How competitive is it? High or low demand?
I see, I just thought there were some strong background requirements such as a deep knowledge in programming or even in finances. But I suppose these are not entirely necessary? Quants basically use applied physics and basic...