Thanks for the reply!
By "have physical significance" I simply meant "correspond to values that could be calculated from measurable quantities". I gather from your answer that all hermitian operators fall under that category.
Quick question: when you say all observables are represented by...
I'm trying to prove that for n>2, member of Z, exists some prime p s.t. n<p<n!. I have successfully proved it by saying there's no prime btw n and (n-1)!, but I want to prove it with my original thought:
first prove for 3, then for n>3:
p=1+∏pi (where pi is the ith prime less ≤n) is a prime...
My question is about both sides of the same coin.
First, does a hermitian operator always represent a measurable quantity? Meaning, (or conversely) could you cook up an operator which was hermitian but had no physical significance?
Second, are all observables always represented by a...
But if it's not hermitian, then the operator may not commute with its Hermitian transpose (right?), so how would we know whether [C2]=[C] [C]* or [C]* [C], and generally wouldn't there be some commutator relationship in there?
If we have a hermitian operator Q and we know it's matrix representation [Q], does that mean that [Q2] = [Q]2?
For example, I'm pretty sure that's the case for p2 for a harmonic oscillator. We have p=ic(a+-a-) and so
p2=c2(a+-a-)(-a++a-)*=c2(a+-a-)(a+-a-)=p p
Which tells us that [p2]=[p]2...
That would seem to indicate that flux through a wire loop is very dependent on the thickness of the wire. That doesn't seem right to me. Furthermore, I would be able to make a similar argument for a solenoid for which (to any reasonable approximation) wire size makes no difference. Are you sure...
If B~1/r2, then if we have a simple loop, B near the inner edge of the loop will be infinite (or close to it). Why then, would our flux not be infinite?
I also get infinity if I take
∫ ∇ X A *da =∫B*da =∫(closed)A*dl
Since A ~1/r and r~0 at the limit of our surface integral.
I know I am...
My intuition says that it will be something like
cos(θ)[Forig- vxtan(θ)]
where Forig = the force you would get on a flat surface
and vx is your horizontal velocity.
I don't have any proof, but I can explain my reasoning:
The angle lessens the force because the normal force can only oppose...
I would like to be able to write my integrand before my integral and then have my integral be more compact. However Mathematica does not seem to like when I try and substitute in my dq's. Is there a way to tell mathematica to evaluate the substitution before evaluating the integral?(and, I...
OK, I've solved the problem. phyzguy, your notebook worked fine, until I cut and pasted it into mine. Long (~hour) story short, it turns out I had made gravity a double negative, and that was throwing the whole calculation way off. I've decided that tiny errors and typos are the worst things...
Does that mean that you agree that this issue is either unsolvable or not easily solvable at all? That's disappointing...
To make sure we are on the same page, though, in my version, g, rho, and Cw had all been previously defined. the only undefined constants I had were the ones specified in...