@SillyGoose there are some operations that you usually do in wavefunction form, that are horrendously complicated in density operator form. That makes it inappropriate for introductory texts except as a thing to show
let me back up for a second, maybe this question will enlighten me a little more: what stops us from writing the mixed state as a superposition of the pure states?
oh, i found a good answer on SE that answers this question
@Allie the set of density matrices is convex. Roughly speaking, convex sets have so called extreme elements, which cannot be written as (non-trivial) convex combinations. One can quite easily show that the extreme elements of the set of density matrices are exactly the pure states
oh, sorry, I've misinterpreted the question. just forget it
@Relativisticcucumber ah yeah it really was! I play with my partner and he carried the game xD we don't do worldle or travle every day, but we usually do whentaken hehe
the pdf article and the html don't match, is this common? the pdf had some numeric mistakes in the derivation of formulas, but some are corrected in the html
the top of the page says > Received 20 February 2016, Revised 13 June 2016, Accepted 14 June 2016, Available online 4 July 2016, Version of Record 20 September 2016.
whereas the pdf just says > Available online 4 July 2016
Please phrase criticism or opinions a little more constructively/objectively/less insultingly :P
@DIRAC1930 it's an unusual choice but I'm not sure why it's an object of discussion, it's not uncommon people are attached to seemingly random books for sentimental/personal reasons
Achim Leistner is an Australian optician of German origin. During his retirement, he was asked to join the Avogadro project to craft a silicon sphere with high smoothness.
Leistner studied optics at Optik Carl Zeiss in Jena, Germany, and in 1953 qualified as a precision optical craftsman. He moved to Australia in 1957, and worked in CSIRO on optical fabrication methods.
In addition to precision instruments, Leistner uses his hands to feel for irregularities in the roundness of the sphere. The research team has called his extraordinary sense of touch "atomic feeling". As a result the sphere is the...
> In addition to precision instruments, Leistner uses his hands to feel for irregularities in the roundness of the sphere. The research team has called his extraordinary sense of touch "atomic feeling". As a result the sphere is the roundest man-made object ever. If it were scaled to the size of the Earth, it would have a high point of only 2.4 m (7 ft 10 in) above "sea level".
My current work is heavily physics based but my chemistry background gives me a good foundation, and i was a biochem major for a short period so I have some understanding of how that all comes together
Also the first episode is an adaptation of "A Study in Scarlet", but it is missing the most important part (half the book being dedicated to slandering the Mormons)
What is an example of an unprovable statement I. Physics? Like I assume the axioms of qm and according to godel there should exist statements which I cannot prove to be either true or false?
@MoreAnonymous There's a bunch of problems known to be equivalent to the Halting problem and therefore unsolvable, you can try to check out which one could conceivably have physical interpretation :p
An example would be that some versions of quantum gravity have a sum over all spacetime manifolds, but we know that the classification of 4-manifolds is equivalent to the halting problem
In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a recursive set; see the article Decidable language. There are uncountably many undecidable problems, so the list below is necessarily incomplete. Though undecidable languages are not recursive languages, they may be subsets of Turing recognizable languages: i.e., such undecidable languages may be recursively enumerable.
Many, if not most, undecidable problems in mathematics...
it's pretty rare that undecidable problems are relevant for physics though
They tend to be problems involving very general objects
So in Bragg diffraction when we talk about the waves of, say, an electron, constructively or destructively interfering,are we talking about the wave function interfering with itself?
like, the superposition of reflections from different planes will either constructively or destructively interfere
There is a factor 2 (about which I don't even want to investigate, it's related to the particle hole spectrum), that some feature and some do not. Tinkham derives the DoS in a way you see all over the literature but I find it not motivated enough.
I would use the definition of DoS. Carsten Timm does, and gets a factor 2 which he motivates, although the connection with the other approach is not clear, but mathematically it comes from a rather questionable choice of the domain of integration ($\epsilon_k-\mu\geq-mu$). Some other people get something slightly different. Other people just copy each other word by word AAAAAAH
One thing I find frustrating compared to HEP is that, even if in HEP too I find different (not so obviously compatible) ways to handle things, at least basic results and approximations are the same
I think this level of frustration is only comparable to when I read Hawking's papers about the thermal emission of BH!
Regarding Bhabha scattering. In the case where $\sqrt{s}>>m_e$ one can find an expression for the differential cross-section: $\frac{d\sigma}{d\Omega}\propto 1\sin^4(\frac \theta 2)$ where $q^2_\gamma=-s\sin^2(\frac \theta 2)$, where $q_\gamma$ is the momentum of the virtual photon. While mathematically it is evident that the smaller the angle,the smaller the sinus function and as a result the larger the differential cross section, from a observational standpoint how does that makes sense?
For example when rutherford performed his experiment, he noticed that some particles would deflect from their trajectory a bit, some not at all and some would just return back 180
and he argued that those who went staight on, they didn't collide with anything
while those that deflected or went back, they collided with something.
So back to the Bhabha scattering, how, small scattering angles imply large differetial cross section, hence large cross section, which is a measurement of the probability of some event taking place when scattering occurs
In any case, the wave properties (quantum properties) become relevant with large wavelength and as the wavelength shrinks, you go to the classical limit. After all, think about a classical object $\lambda=h/p$, take any macroscopic sensible momentum
For another way to see this: you may consider the thermal wavelength. The context is different, but you may know that: low temperature-->quantum, high temperature---> classical (well, roughly). $\lambda_{thermal}~T^{-3/2}$, so for high temperatures it goes to zero (and as I said, high temperature corresponds to classical)
large contirbutions for $\theta \propto 0 \rightarrow q^2_\gamma $ is small $\rightarrow$ de broglie wavelength $\lambda_\gamma$ large $\rightarrow$ classical limit $\rightarrow$ electrodynamics is correct $\rightarrow$ determine luminosity ffrom Bhabha scattering for $\theta \approx 0$ 1. How does (intuinively) it make sense that $\theta \aprox 0$ implies large differential cross section. 2. Understand the train of thoughts from "de Broglie $\lambda$ large... $\rightarrow$ luminosity and bhabha scattering