Well, the title isn't quite right. I want to study (pure) math, but this probably isn't the most employable STEM major out there. So, since I do plan on pursuing a BA in mathematics, I've also been thinking about what I can do/take additionally in the coming years that would allow for avenues...
There used to be a chess feature on this site. Unfortunately, this existed and was eliminated well before I became a member. I enjoy playing chess and from what I understand, so do many other members here. Is there a possibility of bringing back PF chess? I think it would be a great way for...
Can one show that strict charge conservation ##\nabla_{a}J^{a} = 0## follows directly from ##\nabla_{a}F^{ab} = 4\pi J^{b}## alone?
Also, how does ##d^{\star}F = 4\pi ^{\star}J## follow directly from that same equation where ##\star## is the Hodge dual operator?
In class, my teacher was motivating Schrodinger's Equation, but there is one step that I do not understand or even have intuition for. I'll give the argument leading up to the step I do not understand for context.
Let \hat{U}(t) be the operator that gives the wave function after time t, given...