Recent content by Coltrane8

Ok, and this I assume is valid for any ##C^1## or bounded and continuous function expanded on any complete set of orthonormal basis of a Hilbert space. I would like to see the proof and the formal statement of the theorem. May you provide some references were I can look to? Say I have a...

Ok, where can I find this result/theorem? Because it seems to be pretty strong if for any basis in ##L^2##. I know that for spherical harmonic expansion, you would need the function to be ##C^1##, so it seems just not true to me what you affirmed. Moreover when you talk of a basis of ##L^2##...

In the contex of ##L^2## space, it is usually stated that any square-integrable function can be expanded as a linear combination of Spherical Harmonics: $$ f(\theta,\varphi)=\sum_{\ell=0}^\infty \sum_{m=-\ell}^\ell f_\ell^m \, Y_\ell^m(\theta,\varphi)\tag 2 $$ where ##Y_\ell^m( \theta , \varphi...

In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase seems to me puzzling. What I know is that if I know the direction of motion, I know the spin projection onto that direction, say ##\hat{z}##-direction. But to not violate...

Hi everyone, I'm an undergraduate student at physics department. In this time of trouble I hope to find a warm community to share and discuss some hopefully interesting topics! It's my first time on a forum and it seems so curious. Thanks