That's one thing I'm confused about too. In the place I read about, (it's the second link in my "Relevant equations"), they put the equation of movement in like that. I tried figuring it out but I'm not really sure about it.
So the force would be perpendicular to the particle's tangential...
Homework Statement
Consider a charged particle, of mass m and charge q, confined in a device called a Penning Trap. In this device, there is a quadrupole electric field described in cartesian coordinates by the potential
Phi[x,y,z] = U0 (2z^2 - x^2 - y^2) / (r0^2 + 2z0^2)
Where U0 is...
Oh. Thank you so much, I was messing up somewhere - I got exactly the same eigenvectors as I got for B. I probably should have gotten B's and compared them with A too.
Turns out they form a complete basis.
Thank you so much again!
I just did that. Considering a vector a = β*[0 1 0] + μ*[0 0 1], (both transposed) and applying B to it, I get the vector [0 -2μi 2βi] transposed.
Plugging in the eigenvalues and equalizing them, the only solution is μ and β equal to zero for both of them... so I'm at a loss.
Am I going...
I did not get B's eigenvectors -- I got A's, the three unitary vectors, and applied B on them. Only one gave me an eigenvalue of B's (I got [2 0 0] transposed from applying B to [1 0 0] transposed). The others gave me stuff like [0 0 2i] transposed and [0 -2i 0] transposed, which are NOT...
Homework Statement
In a given basis, the eigenvectors A and B are represented by the following matrices:
A = [ 1 0 0 ] B = [ 2 0 0 ]
[ 0 -1 0] [ 0 0 -2i ]
[ 0 0 -1] [ 0 2i 0 ]
What are A and B's eigenvalues?
Determine [A, B].
Obtain a set...
That's the uncertainty, no? For example, in the y direction, at t = 0, the particle could be anywhere within the slit, from one border to the other.
The thing is, now that I propagated (using the partial derivatives of y in respect to y_0 and vy_0), I have a few questions: are the initial...
(Confirmed! It really is an initial v_z.)
So, taking this:
[;\sigma_{py} \geq \frac{\hbar}{2\sigma_{y}};]
[;\sigma_{y_0} = 10^{-3};]
[;\sigma_{py_0} \geq 5.275 \times 10^{-32} ;]
Which means... (dividing by the proton mass)
[;\sigma_{vy_0} \geq 3.153 \times 10^{-5};]
Do I...
I'm not sure either, actually!
And well, according to the Uncertainty principle:
[;\sigma_{py} \geq \frac{\hbar}{2\sigma_{y}};]
But since they mention the propagation, and even with this info, I'm really lost.
Homework Statement
A given particle is confined to a certain potential. At a given instant that potential is turned off and the particle is accelerated by gravity. In the initial instant t = 0, when the potential is turned off, it has an initial speed of vz = 1 m/s.
In the instant t = 0...