The h Bar

@Abcd that'd depend on what state the particle was in, no?

@EmilioPisanty what do you mean by "state"?

The same thing it always means

Quantum state

In quantum physics, quantum state refers to the state of an isolated quantum system. A quantum state provides a probability distribution for the value of each observable, i.e. for the outcome of each possible measurement on the system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, all other states are called mixed quantum states. Mathematically...

maybe you are referring to "quantum state", something that I really don't know about

@EmilioPisanty sniped

lol

10:05 PM

@0celo7 yeah, those red-box links are definitely a typesetting strike if you publish in that form

three strikes and the typesetting police comes and takes you for life

@Abcd the point is, why do you assume that the box is the sole determining factor in the uncertainty?

@EmilioPisanty So we haven't been taught anything about quantum states or stuff but there's a question in my book that asks: "An electron is allowed to move freely in a closed cubic box of side 10 cm, the uncertainty in its velocity will be? "

if it's not in a box, does that mean that its position uncertainty needs to be infinite?

I am trying to use $\Delta x\Delta p \ge n{h}/4\pi$

@Abcd that's doomed to fail because you don't know the momentum uncertainty

@EmilioPisanty I'd write $\Delta p = m\Delta v$

10:08 PM

@Abcd that's just pushing symbols around without adding any physical content

i.e. expressing a quantity X of which you don't have any information in terms of some other quantity Y of which you also have no information. (It should go without saying that this doesn't normally work. ever. at all.)

Okay, then I know the value of $m$ and I asked how to find $\Delta x$

@Abcd the important bit here is that "allowed to move freely" should be interpreted as saying that the probability distribution of finding the electron is uniform over the box

you're being asked to calculate $\Delta x$ explicitly and directly from the distribution

so $\Delta x$ is equal at all places in the cube it seems.

@Abcd what?

how would $\Delta x$ be a function of position?

@EmilioPisanty Do you mind elaborating a bit?

10:15 PM

$\Delta x$ is directly determined by the probability distribution $p(x)$ via $$\Delta x^2 = ⟨(x-⟨x⟩)^2⟩ = \frac1L \int_{-L/2}^{L/2}(x-⟨x⟩)^2 p(x)\mathrm dx$$ where $$⟨x⟩= \frac1L \int_{-L/2}^{L/2}x \,p(x)\mathrm dx$$

In your specific exercise, it's a standard bit of shorthand that "allowed to roam freely" normally gets interpreted as the statement that $p(x)=1/L$.

Everything else is just routine calculation.

You need to get a single number that depends only on $L$.

My book says: If $a$ is length of cube $\Delta x = a\sqrt3$

so?

I don't get why is it so.

Dawood ibn Kareem

That's the length of the internal diagonal of the cube.

have you done any calculations that contradict it?

10:17 PM

@EmilioPisanty (I don't understand this maths, really sorry)

@Abcd then you need to spend a lot more time with the section of your textbook that precedes that exercise.

Mithrandir24601

@DavidZ No worries :) It seems to be sorted now anyway :)

@EmilioPisanty Its high school physical chemistry- chapter: Atomic Structure. Its not even given in the contents of the chapter.

@Abcd your textbook is presumably expecting an answer that's commensurate with the contents of the preceding sections

we can't know what those contents are so we're not really in a position to help with what your textbook is expecting

Its not even a textbook btw. Its a pure Exercises-only book for grade 11 and 12.

10:22 PM

the integrals I gave above really are the basic definition, cut any more and you start getting into lies-to-children territory (and we don't know what lies-to-children you've been told at this point)

i.e. if you don't understand those definitions then you should probably be asking your instructor

@EmilioPisanty wtf, why

I was told by someone to put them there

or be a heck of a lot more explicit as to how your text has previously defined $\Delta x$

@0celo7 what?

that makes no sense at all

??????????

everyone uses hyperref

@0celo7 did they tell you to use hyperref, or did they explicitly tell you to use the default colorings?

hyperref

10:25 PM

Hmm, they have stated what is Heisenberg's principle, under that written the formula and the meanings of the symbols used. That's it.

here

\usepackage[%
  bookmarks=true,
  colorlinks,
  linkcolor=blue,
  urlcolor=blue,
  citecolor=blue,
  plainpages=false,
  pdfpagelabels,
  final,
  breaklinks=true
]{hyperref}

what will this break?

@0celo7 what, keeping the red boxes?

no, your new code

@0celo7 it's unlikely to break anything

maybe cut out the breaklinks setting if you're worried it'll break stuff

possibly also plainpages

10:27 PM

oh that's much better

thanks

see? toldja

what does breaklinks and plainpages do

@Abcd "the meanings of the symbols used" is precisely what the question was. We're unlikely to be able to help at all unless you explicitly quote what your textbook defined $\Delta x$ to be.

@0celo7 breaklinks (roughly) allows line breaks inside links

possibly also inside urls?

@EmilioPisanty They didnt define it. The only thing written is "uncertainty in position"

possibly only inside urls?

@Abcd then you cannot answer the question you were given in a meaningful quantitative fashion with the tools you were given.

@0celo7 plainpages.... no idea

10:30 PM

@EmilioPisanty qualitatively possible to answer it?

@0celo7 plainpages "Forces page anchors to be named by the Arabic form of the page number, rather than the formatted form."

@Abcd you set $\Delta x$ as the length of the cube

it's not quantitatively right, but then it's only wrong to within a factor that doesn't depend on the size of the cube.

@EmilioPisanty I found this solution on the internet^

so?

Is this justification correct? Will it always work?

it isn't a reasoning.

I don't know what you expect us to say. You have specified a set of tools that you have available to solve the problem. They are enough to provide a handwaving answer which is only correct to within a numerical factor. They are not enough to provide a correct quantitative answer.

If your textbook pretends to provide the former, then it is lying to you.

Learn better tools, or get a better textbook.

10:38 PM

Real Programmers Don't Use Pascal. They write in machine code.

Real Men Don't Eat Quiche.

@lılostafa that's real scotsmen, no?

@EmilioPisanty uhh

what does that mean

sorry, true scotsmen

@0celo7 I... don't actually know =P

it's in my thesis preface

but I do not remember what it does

Do you have any other example of these? ^

@0celo7 I imagine it's used when e.g. you have front matter with pages in lowercase roman numerals and then the main matter in arabic numerals starting from 1

i.e. the displayed page numbers go i, ii, iii, iv, v, vi, 1, 2, 3, 4, ...

as displayed on the page i.e. the "formatted form"

10:41 PM

real men don’t soak up solar energy; they burn stuff instead

@lılostafa every morning, Chuck Norris does a hundred pushups with both hands, then fifty pushups with each hands, then fifty pushups with no hands?

@0celo7 anyways, hyperref options are an absolute rabbit hole, only go there if you absolutely need to

lol :)