/sqt/ - Stupid Questions Thread

Last one is about to die.

Post your retarded questions here, brainlets.

Please direct all brainlets to this thread.

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Is 1/2 spin always taking into account the magnetic dipole moment inherent to the electron? Is that why it takes 2 rotations for the electron to face the same direction?

I'll ask again because it's really stupid

biochemistry or chemical biology (in terms of job expectancy?

I love both biology and chemistry equally

You mean organic chemistry or molecular biology?

Molecular biology probably has greater application in future technology.
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So when you're doing integration by substitution with a definite integral, the upper and lower limits have to be plugged into u, right? Because I keep getting answers that are completely wrong when I do this, but then the answer comes out fine when I keep the limits what they are.

Are you substituting back in for u AFTER you change the limits? Because that will fuck things up.

Consider [math]\int_0^\pi x \cos(x^2) \, dx[/math]. If we say u = x^2 and substitute, we need to change the limits because everything has to be in terms of u. So we have [math]\int_0^{\pi^2} \frac{1}{2} \cos(u) \, du[/math]. Then when we integrate we get [math][\frac{1}{2} \sin(u)]_0^{\pi^2}[/math]. We can do one of two things at this point. You can either just plug the limits in and get your answer, or you get change everything back in terms of x. If we do the latter, we have to change the limits back to what they were before, so we would have [math][\frac{1}{2} \sin{x^2}]_0^{\pi}[/math]. Notice that you'll get the same answer if you evaluate either of these.

funny, I am studying molecular biology atm, and was thinking of changing

Thanks for your help. I'll try it out.

Pedantic question about notation but my autism prevents me from leaving it unanswered.

Is [math]\mathbf{Set}[/math] the only category where [math]f \in \text{Hom}_{\mathbf{Set}}(X, Y) \rightarrow f: X \rightarrow Y[/math]?

Like if you're in [math]\mathbf{Top}[/math], is it still proper to say [math]f \in \text{Hom}_{\mathbf{Top}}((X,\mathcal{O}_X),(Y,\mathcal{O}_Y))[/math] even though [math]f: X \rightarrow Y[/math]? Or do I have this wrong and it is simply that [math]f \in \text{Hom}_{\mathbf{Top}}(X,Y)[/math]

What value is there in knowing whether the momentum operator^2 is hermitian for certain hydrogen states?