I'm just starting my undergraduate Quantum Mechanics course. I had a homework problem to show that \Delta S_x = \sqrt{\langle S_x^2 \rangle - \langle S_x \rangle ^2} = 0 , S_x being the spin in the x direction. I managed to solve it, but the physical interpretation is confusing me. If I...
Note this is in our Lagrangian Mechanics section of Classical Mechanics, so I assume he wants us to use Calculus of Variations to solve it.
The surface area is fixed, so that'll be the constraint. Maximizing volume, we need a functional to represent Volume. This was tricky, but my best guess for...
I changed how the potential is handled with a simple function
def potential(x):
if (abs(x)<=1):
return 0
else:
return V0
So now my stepping function is
Which surprisingly yielded the same plot. I will look into starting at x = 0. Will come back with updates.UPDATE:
I...
Every one of those would represent the first point in the list, corresponding to the very left of it's domain. wavefunction[0] and x_axis_wave[0] correspond to the their function at -1, while with potential and it's domain's 0th element is their function at -3. I have constructed the lists so...
The book's procedure for the "shooting method"
The point of this program is to compute a wave function and to try and home in on the ground eigenvalue energy, which i should expect pi^2 / 8 = 1.2337...
This is my program (written in python)
import matplotlib.pyplot as plt
import numpy as...
This is in python:
#ELECTRIC POTENTIAL
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import numpy as np
import matplotlib.pyplot as plt
dx = 0.1
dy = 0.1
xrange=np.arange(-1,1,dx)
yrange=np.arange(-1,1,dy)
X,Y = np.meshgrid(xrange, yrange)
max_dV = 10e-5
blockRadius = 3...
Okay it turns out I was making a fatal error. These damn negative signs. The second differential equation yields
$$\frac{-v_t^2 \ln\left(\frac{v_t^2-v_f^2}{v_t^2}\right)}{2g} = -y_{max}$$. I forgot cancel negatives and dropped it when i subbed y_max. A lot of canceling yields...
I chose coordinates where down is positive. So the force going up is $$F_{up} = mg - cv^2$$
$$a = g + \frac{c}{m}v^2$$
$$a = g + \frac{c}{m}v^2$$
$$a = g \left(1 + \frac{v^2}{v_t^2}\right)$$
$$a = \frac{dv}{dt} = v\frac{dv}{dy} = g \left(1 + \frac{v^2}{v_t^2}\right)$$
I used normal separation of...
Damn, that was the problem! I went ahead and each 6 arrays and added their 0th component by hand, and now the plot is display (roughly) what I need! Just need to clean it up a bit.
import matplotlib.pyplot as plt
import numpy as np
#constants and conditions
initial_velocity = 49.1744 #m/s, book has 110mph
velocity_angle = 35 * np.pi / 180 #coverted to radians because numpy only likes radians
gravity = 9.8 #m/s^2
dt=0.1
windspeed = 4.4704 #m/s book has 10mph
#calculating...
Sorry I confused myself when making this thread. I was tired. I should also specify the level of the course too. Quantum Physics I is the course name, but the other course is Classical Mechanics I. As for textbooks, I haven't figured out my Quantum book but I know for Classical Mechanics it's...
Hello! I'll be entering my second semester of my junior year of my Physics Degree. My uni doesn't have a bad physics program, but it's really small so I have to take my upper level classes as soon as they're offered or I won't take them for another 2 years or so. They are on a cycle so I will be...
So I'm reviewing old lectures to prepare for an exam soon. This is about polarization. E fields, D Fields, etc. My professor labeled this diagram like so. The figures my professor drew are cavities in a dielectric if you can't read her handwriting. However, I can't seem to figure out why the...
From Griffiths E&M 4th edition. He went over solving a PDE using separation of variables. It got to this ODE
\frac{d}{d\theta}\left(\sin\theta\frac{d\Theta}{d\theta}\right)= -l(l+1)\sin \theta \Theta
Griffths states that this ODE has the solution
\Theta = P_l(\cos\theta)
Where $$P_l =...