Hey everyone,
I seek help regarding the Faraday-effect (change of the polarization angle of a linearly polarized wave in an electric field). I have asked my professor about the topic and learned a lot, but I think I am still lacking one or some crucial points. Here is how I understand the cause...
I am basically just rewriting a question that was posted on other forums.
While watching videos of a MIT lecture on the eigenstates of angular momentum (video: '16. Eigenstates of the Angular Momentum II' by MIT OpenCourseWare) the professor visualized different spherical harmonics for low...
Ah, I think I see the error in my thinking. Also, what I meant to write was that the integral of the Real part would have to add up with the factors squared to be equal to one.
I see now, of course the two wavefunctions that make up the superposition would have to be eigenstates of some...
It would be the double product of ψ1 with ψ2: $$\lambda = \alpha^* \psi_1^* \beta \psi_2 + \beta^* \psi_2^* \alpha \psi_1 = 2 Re(\alpha^* \psi_1^* \beta \psi_2)$$
which can be seen as some complex number plus its conjugate, thus twice its real part and a real number.
This ought to be some simple gap in my knowledge, but it bugs me nonetheless. Let me present the argument as I see it, I'm fairly certain that there is just some tiny part that I didn't learn correctly.
Let us assume a wavefunction $$\Psi$$ is defined as a superposition of two wavefunctions...
This is basically just a comprehension question, but what makes elements of the Hilbert space exist in infinite dimensions? I understand that the number of base vectors to write out an element, like a wavefunction, are infinite:
\begin{equation*}
\psi(x) = \int c_s u_s (x) ds = \sum_k^{\infty}...