someone has an idea ? said: Still stuck on the following problem : Let $f:\Bbb{R}^2\to \Bbb{R}^2$ be a $1-$Lipschitz function, how can I prove, the $n-$th iterated function noted as $f^n$, that $f^n/n$ converges.
I tried to prove that $(f^n/n)$ is a Cauchy sequence
chemistry largely being applications of QM + E&M + StatMech/Thermo
(which, of course, is a bit like saying engineering is largely 'just' applied classical mechanics. doesn't mean i could build something without it falling down.)
I wonder why this post (question) had no downvote ... (I mention that I don't downvote users here - but compared with my questions that are often downvoted here, I'm sure this should have got some downvotes) - math.stackexchange.com/questions/1774602/…
Planck said $E = h\nu$ Bohr had something to say too de Broglie explained by $\lambda = h/p$ and Heisenberg formulated his principle of uncertainity Then Sommerfeld introduced his model of atom which seemed to appeal to everyone At last Schroedinger wrote down his equation hip-hip-hooray for the wave function!
We were just told about Schrödinger equation that it gives the first there quantum numbers as its solution . I have no clue about the fourth quantum number
In math, the continuous is often easier to do than the discrete (e.g. the formulae of difference calculus can sometimes be more awkward-looking than the analogous formulae for continuous calculus); that's why it's convenient to treat things in physics as continuous, unless forced by nature to do otherwise. Hence, QM.
$\newcommand{\Integers}{\Bbb Z}$ Does this sentence make sense to you guys: "[...] where $\Lambda_\Integers[\alpha_1,\dots,\alpha_n]$ denotes the exterior ($\Integers$)-algebra over $\{\alpha_1,\dots,\alpha_n\}$."
I'll consider very well returning here after seeing that Ramanujan picture has only one star on such a place. This annoys me more than any stupid thing addressed to me during the time.
@Danu ROFL. I'm far away from my books, and my memory can get hazy at times. :D (I think The Rise of the New Physics has the complete tale.)
@Semiclassical I would say that the weirdness comes out of trying to conclude things from the assumption that stuff comes in chunks, not that the things themselves are in chunks.
So, I don't understand the uncertainty principle. I can understand that $\sigma_x \cdot \sigma_p$ is always greater than some positive constant, but why $h/4\pi$ in particular? The same $h$ that appears in $E = h\nu$? I can't make the connection.
@Semiclassical That is one point, but to fair, that question could have also been closed without no problem. Just look at my closed questions for a small comparison. In general, from my posts one can learn a lot by working on the question.
@Semiclassical You said "hmm. the currents will also produce magnetic fields." and "and if memory serves, those induced magnetic fields will cause those two loops to attract one another"
"more generally, two parallel wires will attract one another due to the magnetic fields they produce"
@Semiclassical ah, alright . I was about to write "because of the trivial fact that any real number, divided by itself, is 1. noted :P", so good thing I noted the second message. :)
not sure where you're going with that, but it is true that the density of electrons in the lab frame would be different than that in the electron frame.
a field in space, created either by changing electric fields or by steady electric currents, which acts on moving charges and which, if it isn't static, generates electric fields
If you don't like that answer, ask yourself what an electric field is.
What you're arguing is that, if a voltage is applied, then the fact that the electrons are moving would mean that their density increases and therefore you have a net negative charge.
So, I don't understand the uncertainty principle. I can understand that $\sigma_x \cdot \sigma_p$ is always greater than some positive constant, but why $h/4\pi$ in particular? The same $h$ that appears in $E = h\nu$? I can't make the connection.
@BalarkaSen From experiment it is found that if you consider, say, an electron passing through a cloud of gas, if you measure it's position at one instant, and then try to measure it's position at the next instant, you will find it in some random place, and no amount of accuracy of measurement, or shortness in the amount of time between successive measurements, will allow you to draw out a smooth path along which the electron follows.
After using the "generalized uncertainty principle": $$ \sigma_A^2\sigma_B^2\geq \bigg(\frac{1}{2i}\langle [\hat A,\hat B]\rangle \bigg)^2 $$ the question just reduces to "why are commutators proportional to $\hbar$?"
That simple statement destroys all of classical mechanics, because the mechanical state of a system is specified by position and velocity, and you need both to specify a path
I don't think there is any fundamental reason why commutators, numerically, have to be on the order of $\hbar$---I think that physics does not abruptly change if $\hbar$ is changed by a factor 10 or so
