Thanks for your remark, but I'm afraid having a wave function with a unit is not the problem, but only the symptom.
Many sources on the net [1],[2] calculate the Fourier transform of a circular aperture to be
\begin{equation}
\mathcal{F}(A) = \frac{J_1(2\pi Rq)}{Rq},
\end{equation}
but...
Hi there,
I have a little problem in wave optics: I have a wave function \psi_{ap} that depends on some geometric parameters, but that has no units itself (as one would expect). But unfortunately when I calculate the Fourier transform of this wave function the Fourier transform has a unit...
Your equations can be solved without big problems:
\Lambda(r,\,\theta,\,z) = \frac{1}{2}r\theta^2+\left\{\begin{array}{cc}
\frac{2k_1\mathrm{ln}(r)}{\theta(\theta+\pi)} & r>r_0\\
\frac{k_2r^2}{\theta(\theta+\pi)} & r<r_0
\end{array}\right.
The gradient of this expression does not show a...
That's exactly what I thought when I started out with this adventure: "just" integrate.
Yes, it would be helpful for \Lambda to be continuous at r=r_0
But one has to keep in mind, that I'm talking about a 3 dimensional vector potential \vec{A} and a scalar function \Lambda of 3 variables...
It's me again.
After checking back to some books I decided to perform a Gauge Transformation of the form
\vec{A}' = \vec{A}+\mathrm{grad}\Lambda=0
such that the solution to the initial Schrödinger equation becomes
\psi = \psi'*\mathrm{e}^{\frac{ie}{\hbar c}\Lambda},
where \psi' is the...
Hi Mat,
as usual m,e and E are constants (mass, charge and kinetic energy of an electron).
I did not bother to insert for A², but that would be equal to 1/r² or 1/r²_0 (r_0 is an arbitrary constant].
If you have any other regards why equation (8) should be wrong, please let me know.
CU Andi
Hi there,
during my work on my PhD thesis as an experimental physicist I ended up with a very theoretical problem:
What does the wavefunction of an electron traveling through a magnetic vector potential look like?
I chose a cylindrical coordinate system with a magnetic vector potential A...