Homework Statement
My question is more about understanding the task itself, not about calculation.
I am supposed to use the poisson equation, to derive the potential inside a semiconductor for a barrier with potential height ##\phi_B## and a donator doping with ##N1 > N2##. Then I should use...
But it has acceleration in the x- and y- direction namely a_x = sin(\theta)*0,4 and a_x = cos(\theta)*0,4 . Particle B starts with zero velocity and starts the origin so \vec{x_0} = 0 , \vec{v_0} = 0
Homework Statement
I am currently solving a problem and I am not sure if it is correct.
There are two particles A and B. A has a constant velocity with |\vec{v}| = 3 and starts from y = 30
B has constant acceleration with |\vec{a}| = 0,4
The goal is to find the angle between the...
In Shankars "Principle of Quantum Mechanics" in Chapter 4, page 122, he explains what the "Collapse of the State Vector" means.
I get that upon measurement, the wave function can be written as a linear combination of the eigenvectors belonging to a operator which corresponds to the...
I did perform that step as I wrote in my post and I get the same equation, though my derivative might be wrong.
Let's differentiate the solution from the book with respect to x:
\frac{d}{dx}\left(\frac{l^2a^2x^2}{12x^2+l^2}\right) = l^2a^2 \frac{d}{dx}\left(\frac{x^2}{12x^2+l^2}\right)
Using...
It means :\frac{d\dot{x}^2}{dx} = \frac{d}{dx}\left(\frac{dx}{dt}\right)^2
For the result from the book there where no steps shown.
For my result: \frac{d\dot{x}^2}{dx} = \frac{2l^4a^2x}{(12x^2+l^2)^2} \Longrightarrow \int d\dot{x}^2 =2 l^4a^2\int \frac{x}{(12x^2+l^2)^2} dx
Apply...
Homework Statement
I've got an equation which I need to integrate. However, integrating it and checking with the solutions, I get two different results. I get the same result as using wolfram alpha, but a different result from the book.
If I differentiate both results, I get back to the orginal...
Homework Statement
We've got a line element ds^2 = f(x) du^2 + dx^2 From that we should find the geodesic equation
Homework Equations
Line Element:
ds^2 = dq^j g_{jk} dq^k
Geodesic Equation:
\ddot{q}^j = -\Gamma_{km}^j \dot{q}^k \dot{q}^m
Christoffel Symbol:
\Gamma_{km}^j = \frac{g^{jl}}{2}...
Homework Statement
Mass 1 can slide on a vertical rod under the influence of a constant gravitational force and and is connected to the rod via a spring with the spring konstant k and rest length 0. A mass 2 is connected to mass 1 via a rod of length L (forms a 90 degree angel with the first...
Wouldn't it reduce to \frac{\partial U(r_{k})}{\partial r_k} j = r_{k+1} because only for j=k+1 the kroenecker delta would give me a 1? And when you would have \frac{\partial U(r_{k+1-1})}{\partial r_k} = \frac{\partial U(r_{k})}{\partial r_k} and then I would have two \frac{\partial...
Homework Statement
In this exercise, we are given a discrete Lagrangian which looks like this: http://imgur.com/TL0P61r. We have to minimize the discrete S with fixed point r_i and r_f and find the the discrete equations of motions.
In the second part we should derive a discrete trajectory for...