E = hf = hv/λ = hp/mλ = p^2/m ? Is that right? (non-relativistic)
SQT - Stupid Questions
Carson Lewis
William James
I thought it was p^2/2m.
I'm reading Babby Rudin and he says if m^2 =2, then we could write m = p/q where p and q are not both even. How does he know that? I'm in calc 2...is this book too advanced for me?
Samuel Wright
Is that part of the proof that the square root of 2 is irrational?
He is probably just saying that for any number m, we can say m = p/q, where p and q are two other numbers to be determined, and you can make it so that they aren't both even.
For example, if m=5, then we could use p=15, q=3, p/q=15/3. There's never a situation where the only possible values for p and q are both even, because then you could simply divide p and q both by 2 until one isn't even, and the value m remains unchanged since you're dividing the numerator p and denominator q by the same value.
It's all very simple and pedantic, but these subtle properties are important later on in the proof.
Juan Gutierrez
Oh ok. Thanks. That last part was very helpful
Jordan Kelly
How would you go about proving this?
“Prove that if f is continuous on R and f(x + y) = f(x) + f(y) for x,y within R, then f(x) = ax for some a within R.”
Cameron Carter
Prove it for all rationals and then use the density of Q in R.
Aaron Lopez
Nope. The product [math] f \lambda [/math] (called phase velocity) is, in general, not the same as [math] \displaystyle \frac{ p }{ \beta m }[/math] (group velocity) (\beta is the relativistic factor, which is almost 1 for small velocities).
But they are the same in the case of pure electromagnetic waves - both equal c.
Aiden Stewart
This is the most basic application of density desu...
Prove that an increasing function has a countable set of non-continuous points is harder.
Luke Ross
Is this right?
David Morris
scipy-cookbook.readthedocs.io
Can anyone explain how this smooths data? or point me to a paper explaining this method.
Also what exactly is the line 45 doing:
"s=numpy.r_[x[window_len-1:0:-1],x,x[-1:-window_len:-1]]"