Hi, I have this code that solve the equation of motion of a relativistic electron.
from math import sqrt
from scipy.integrate import odeint, solve_ivp
import numpy as np
import matplotlib.pyplot as plt
e = 1.602 * 10 ** (-19)
E = 10 ** 6
m = 9.106 * 10 ** (-31)
def d2vdt2(t,r):
t_arr = []...
dv/dt is the acceleration, so I thought I could find the acceleration from F = qE = ma = dp/dt. But this is a relativistic case, so the proper acceleration is a = F/mγ3, where v in the gamma is the v of the electron and F = eE. However, I'm not sure if this is correct, because the constant τ...
Hi, I have been taught that quarks don't exist individually on their own, as they has with be with at least another antiquark to form a colorless state. But in the quark-gluon plasma, do we have individual quarks in a color state or do they still, somehow, are in a color-neutral state?
Thanks!
So if we find the variance of a distribution to be infinity, it is equally valid to say that the variance is either infinity or doesn't exist? Are there cases where we should interpret it as being infinity, and not say that it doesn't exist, and vice versa?
The problem is actually split into 3 parts: a) it asks if this distribution is normalized, which it is, b) find the mean and c) find the variance. I calculated the mean both by hands and by using integral calculator, 0 is the result. I suppose the calculator loosens the definition of the...
\frac1\pi ∫
So if the mean is 0, but <x^2> diverges, what can we say about the variance? Also, the problem directly states that this is a "Lorentz distribution", does this help me decide whether to say that the mean is 0 or that there is no mean?
So, the integral of x/(x^(2)+1).
Let u = x^(2) + 1 => du = 2x dx => du/2 = x dx, and substitute
changing limits : for x = inf => u = inf ; for x = -inf => u = inf.
We have same upper and lower limits, therefore the integral = 0.
I found that <x> of p(x) = 1/π(x2 + 1) is 0. But its <x^2> diverges. I don't know if there are other ways of interpreting it besides saying that the variance is infinity. I usually don't see variance being infinity, so I'm not sure if my answer is correct. So, can variance be infinity? And does...
I used the two equations above to solve for u_x and u_y and got u = 0.987c, where u_parallel = u_x and u_perpen = u_y. I wonder if I can use velocity four-vectors to solve this problem. Modify η'μ = Λμνην so we can use it for velocity addition?
Ok, I forgot and treated A as a scalar when calculating ∇^2. So,
∇2A = ∇(∇⋅A) - ∇ × (∇ × A) = ∇(∂Ax/∂x) - (∇ × B)
First term, we have partial A_x / partial x, but x-component of A doesn't depend x, so it's zero, thus, the first term is zero. The second term is μ0J, which is zero, unless there is...
Lorentz gauge: ∇⋅A = -μ0ε0∂V/∂t
Gauss's law: -∇2V + μ0ε0∂2V/∂t2 = ρ/ε0
Ampere-Maxwell equation: -∇2A + μ0ε0∂2A/∂t2 = μ0J
I started with the hint, E = -∇V - ∂A/∂t and set V = 0, and ended up with
E0 ei(kz-ωt) x_hat = - ∂A/∂t
mult. both sides by ∂t then integrate to get A = -i(E0/ω)ei(kz-ωt)...