@EmilioPisanty congrats on reaching 100k rep.!

I realize I sent an email a year ago beginning with "Hi Dr. Dr.,"

didn't even include the name...

What is the hamiltonian of electron-positron system?How can I find that from dirac field equation?please say or share any link

@SirCumference Townsend seems good book (haven't read full, just found free samples on the internet)

@JakeRose That is really painful to see! :'(

@ZeroTheHero well, it was triggered by the rep recalc with increased question rep, so it feels a bit meh

If the mythical 100k swag package appears then I might change my mind, though =P

no and not a cluster of gravitons

\o @Danu

@Secret there appears to be a nice answer here

@EmilioPisanty It is still a milestone that only outstanding contributors have reached. Plus clearly it was a matter of time before you reached it.

@ZeroTheHero It's more that I was purposefully staying away from reaching out just yet, via a heavy investment in bounties

I don't appreciate the change messing with my active choices

Mon: I’m saying good things about you and you shoot me down... ;) CONGRATS anyways!

well earned and well deserved.

Hi guys, I'm a bit ashamed of myself for asking this at my level but here goes anyway

I'm looking at the quantum mechanical density operator

So the expectation value of a "one point correlator" so to say, number operator at a spatial parameter of your choosing

I have an expression for this density $j(x,t)$ which I implemented

So to be clear, the observable quantity for the normalised density operator between two states is |<psi|j(x,t)|phi>/(<psi|psi>\cdot<\phi|\phi>)|, right?

In particular: no square on the right absolute value bar

Which I implemented numerically****

Sorry, that last bit got lost

So my expression for $j$ has a complex exponential, business as usual, basically some sort of $exp(ikx-iomega*t)$-like term

It would seem that at zero time and space an absolute value would lead to very abrupt behaviour of the density

This is not expected afaik so I'm confused now :p hopefully someone can offer some sort of insight

@ACuriousMind, hi. I have one question, which is discuss with @PM2Ring, it is there in the yesterday transcript.

@1010011010 I don't understand how that's supposed to be an "observable quantity".

@yuvrajsingh You won't get transcripts if the question is deleted

\o @EmilioPisanty

@skillpatrol hello

hi

where are @skullpetrol and @skullpatrol ?

in other rooms :P

@skillpatrol do you know how to solve any differential equations? (those also whose solutions don't exist)

@skillpatrol hehehehe :)

@AbhasKumarSinha nope, sorry

@skillpatrol oh okay

@skillpatrol Do you know elon musk?

@AbhasKumarSinha I'm not sure if this is what you're thinking of, but a lot of differential equations in the engineering field aren't solved analytically (as in you don't find an equation that solves it). They are solved with numerical methods which actually allows you to find "close enough" solutions to some differential equations where you can't actually come up with an analytical "solution".

@JMac True, eqn of pendu-lum for example

@JMac I'm working on an infinite series which can solve almost all diff equations

@AbhasKumarSinha What do you mean by "solve"? There are a lot of infinite series that are already used for numerical solutions to DE's.

@JMac example?

@AbhasKumarSinha Just off the top of my head, Taylor series comes up all the time in numerical methods.

@JMac no, I'm working on a method to generate infinite series for the solution function of any DE

@AbhasKumarSinha Have you done much work with DE's; specifically ones without traditional solutions?

@JMac just a bit like pendulum's equations....

I'm afraid, I've not done much..

@AbhasKumarSinha Do you mean the linear pendulum approximation where $\sin x \approx x$, or the non-linear one where angles are considered "large"?

@JMac no, not that ones, I'm not approximating, ama trying to solve the exact ones

$$ \ddot \theta(t) + A \sin \theta(t) = 0 $$

@AbhasKumarSinha Infinite series are so 19th century. ;) We have computers now, so we can easily use other methods, like recursion. Gauss found a nice way to do elliptic integrals using the arithmetic-geometric mean, which is a bit tedious for hand calculation, but which is a breeze on a computer. And incidentally, the AGM is used in a fast algorithm for pi, due to Gauss, Brent, and Salamin. I mentioned the AGM stuff for pendulums to you a few months ago:

:5267587 I know, but those methods have their own limitations, I'm trying to develop a method to solve any such DE equations in general and it's as easy as Taylor Series

And here's my AGM pi code, in Python: stackoverflow.com/a/26478803/4014959

@PM2Ring I <3 Python and C++ and ML ;)

@AbhasKumarSinha Ok. Good luck with that. I suspect you'll run into convergence problems. Taylor series are notorious for that.

@PM2Ring yeah!!! :)

I started learning C in 1980, but I never bothered learning C++. I figured I'd wait for it to stabilize, but then it grew into a monster. ;) I've been mostly using Python for the last 15 years or so, and almost all my SO answers are to Python questions. I haven't touched ML, but a few of the SO Python room regulars are into it.

@PM2Ring :)

@PM2Ring same for me, C++ suddenly grew to monster, specially in competitive coding stuff.

C is a nice compact language, so if you put in the effort it's not too hard to become an expert. But C++ is so large it's almost impossible for a person to gain mastery of the whole language.

true

Okay bye everyone

Good Night :)

@AbhasKumarSinha Townsend does a crappy job at motivating a lot of concepts

Almost as if it assumes you've got a background in Hamiltonian mechanics

For the sake of problem solving it's an all right book, but it isn't very enlightening conceptually

Hello. I once saw a video in which Michio Kaku said that they had undergrads calculate the probability of a person spontaneously vanishing from one side of a door to the other. He said they found that one has to be living for more years than the universe has existed in seconds (or something like that). My father doesn't believe tunneling can happen with human bodies, because of 'biology'. Does anyone know a source that supports' Kaku's claims?

@Cazo Michio says a lot of stuff... Your father's objection is reasonable: a human body cannot survive for quadrillions of years. For that matter, the universe will be pretty-well dead long before a human mass can tunnel through a door. It's not too hard for things like electrons to tunnel, plenty of modern electronics (eg flash memory) relies on that. Proton tunneling is a bit harder, but fusion in the Sun depends on it.

When a radioisotope decays via alpha emission, the alpha particle (2 protons + 2 neutrons) tunnels out of the nucleus. We've even witnessed quantum tunneling of larger things. This article chemistryworld.com/news/… is about a trifluoromethyl group tunneling in a molecule.

But you're going to have to wait a very long time to witness something larger than the molecular scale tunneling.

Does semi-empirical mass formula fit in the shell-model structure?

@Student404Mus No. As Wikipedia says, it's based on Gamow's liquid drop model, it knows nothing about shells.

hi