Recent content by Thomas Michael

Ok, I think that makes sense. So just use the chain rule: $$ \frac {d^2v} {dx^2} \frac {dx^2} {d\phi^2} $$ With ##x=\cos(\phi)## the first term will have $$ \frac {d\cos(\phi)} {d\phi} = \frac {dx} {d\phi} = -\sin(\phi)$$ $$ \frac {d^2x} {d\phi^2} = \sin^2(\phi) $$ $$ \sin^2(\phi) =...

I'm reading "Differential Equations with Applications and Historical Notes" by George F. Simmons and I am confused about something on pages 431-432 He has the second order ordinary differential equation $$\frac {d^2v} {d\phi^2} + \frac {\cos(\phi)} {\sin(\phi)} \frac {dv} {d\phi} + n(n+1)v = 0...

To determine the relative stability of the reactant vs the product, try thinking about how the R group induction will stabilize the carbocation formed in the Sn1 reaction.

This paper may be of interest: https://www.biorxiv.org/content/10.1101/2021.01.07.425740v1.full.pdf It is a pre-publication of data about the effectiveness of the Pfizer vaccine against the N501Y variant. I've also made some Youtube videos on my channel going through the literature on many of...

Normally, it would look something like: $$i\hbar \frac {\partial \Psi} {\partial t}= \frac{\hbar^2}{2m}\frac {\partial^2 \Psi} {\partial x^2}+ V\Psi$$ And then the complex conjugate of $$i\hbar$$ would just be $$-i\hbar$$ thereby changing all the signs on the right hand side as well.

Sometimes doing a simple Google search isn't good enough. I would recommend looking at scientific papers, particularly the Introduction section. One place I like to search for such papers is on Protein Data Bank. For instance, I did a search for SARS-CoV-2 on PDB, clicked the first entry...

Hello, physics forums. My educational background is in biochemistry, but I love most things science (I'm also a bit of a history and philosophy buff, so just all around nerd, I guess). My highest degree is a Masters, due to having to drop out from a PhD program due to mental health and...