The h Bar - 2018-04-18 (page 1 of 2)

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12:01 AM

These guys all learned everything about standard physics first and then did their anti-establishment thing

Why not use probably the hardest books of them all and just go for it

Course of Theoretical Physics

The Course of Theoretical Physics is a ten-volume series of books covering theoretical physics that was initiated by Lev Landau and written in collaboration with his student Evgeny Lifshitz starting in the late 1930s. It is said that Landau composed much of the series in his head while in an NKVD prison in 1938-1939. However, almost all of the actual writing of the early volumes was done by Lifshitz, giving rise to the witticism, "not a word of Landau and not a thought of Lifshitz". The first eight volumes were finished in the 1950s, written in Russian and translated into English in the late 1950s...

Bell translated most of them too

wrt scientific advancement, a few good/ key/ on target ideas can be worth more than 1000s of books. eg how many 19th century physics books would you recommend?

1 hour later…

1:33 AM

@bolbteppa reading all of that conversation above, I'm reminded of nothing so much as this SMBC: smbc-comics.com/?id=1777

mostly because of the disjuncture between what a 'science fan' and an actual scientist see as valuable/relevant

Yeah there is a real element of that, I've basically been trying to say 'famous anti-establisment person memorized those digits after learning how to use pi' haha

Have to stop taking the bait

plus there's the fact that "a new revolution is always possible!" is not falsifiable

1:48 AM

I'm amazed that to people who look for such Mc'-revolutions, things like susy and strings are very commonly mocked

2:00 AM

yeah

I mean, I think there's room to poke fun at how those SUSY/strings have failed to point towards any meaningful empirical predictions

but they at least do represent actual attempts to grapple with math/physics

@bolbteppa ps lol so youre a susskind fan? me too! have you read all his stuff? how about this for a "1st step"? (in all honestly was surprised myself when ran across it last yr) o_O :P arxiv.org/abs/hep-th/9409089

It looks pretty complicated compared to those videos tbh

@bolbteppa exactly. maybe hes no good at that advanced/ (~~"paradigm shifting"~~ woo) stuff anyway. anyway its over 2decades old and nobody cites it and maybe even hes forgotten. so lets just all move on now right? nothing to see here o_O

2:28 AM

@Semiclassical did you forget about bokulich? take her seriously, or not? thought you liked her ideas. (maybe am already now a bigger fan than you are? thx for the intro!) she seems to think paradigm shifts happen™

haven't had her on the brain lately

@vzn do you have any idea where equation 2.1 comes from

Though I have been thinking about dBB more lately, and right now I'm finding myself moving towards a sort of Copenhagen view of its trajectories

@bolbteppa susskind? T-H?

Susskind

2:32 AM

which basically means two things: 1) within the realm of non-relativistic QM, it offers a consistent visualization via trajectories, and 2) such a picture is not experimentally accessible and can therefore only be useful as a way of guiding intuition (and maybe getting some nicer derivations)

@bolbteppa QCD? guessing o_O

Which is more or less an epistemic view of the trajectories

@Semiclassical "a copenhagen view of dBB"? makes perfect sense :P

lol

I recognize the inherent absurdity of that, yes

I suspect that 'Copenhagen' is probably an overstatement.

@Semiclassical re (2) think that may be the lynchpin of a new theory, yeah, it really needs to be experimentally accessible somehow, suspect there is current work that is close/ on verge/ or even fulfilling it, but unrecognized maybe even by its practitioners.

2:36 AM

for my part, I see no reason for such optimism

Can we just take a second and appreciate how the power rule exists?

I mean calculus could've been hell otherwise

eh, for integer powers it's just a consequence of the product rule

that it works for rational/real powers, on the other hand...yeah, thank goodness

Well, just imagine how bad differentiation could be, if a lot of these rules didn't exist

@Semiclassical theres been a lot of wandering for decades. but on other hand, apparently something is ~~inspiring~~ motivating you to study physics...

it's hard to imagine something that doesn't exist :)

2:38 AM

@Semiclassical You get what I mean :P

@vzn yes, but the notion of going beyond QM in an experimental sense is not one of them.

@vzn from page 16 to 18 you get a sense of where 2.1 comes from ipht.fr/Pisp/francois.gelis/Physics/2006-spht3.pdf this requires knowing a good bit of background to appreciate, how can you read a paper and have no idea where it's pieces come from, at least to me this feels absolutely terrible to pretend I know what a book/paper is saying without really trying etc

There's a few things in math I'm grateful are very simple, e.g. squaring a ratio squares both the numerator and denominator, differentiation rules, etc.

@bolbteppa papers are like snowflakes, they are endless and can be studied to any degree of detail. did read the abstract :) :P

My point was, his paper is hard to read without background, that's all, his other videos would be easier and you would learn more from them, one is not able to appreciate the contents of advanced papers without preparation

2:40 AM

@bolbteppa yeah ("point taken") and you said nothing about the main point of the paper so far.

I'm more interested in exploring the consequences of QM rather than worrying about experimental possibilities which may or may not exist

particularly since, if we didn't understand such matters as well as we did, we'd not be anywhere near as successful as we are in modern technology/engineering

This looks ads-cft'ey, will look at it once I go through a proper ads-cft course

I mean, damn, in 2016 we got down to 1nm transistors

@bolbteppa ok, but think its too bad youre not willing to consider it seriously now, you seem to have strong bkg/ interest in various/ related areas. oh, and susskind wrote it. etc

And while that may not exploit quantum entanglement in the manner you'd need to get a quantum computer, it is still predicated on knowing a hell of a lot about how physics works at such scales.

2:44 AM

@Semiclassical physics is a huge field and theres lots of ways/ places to make contributions, think its in a golden age right now, yeah am very interested in QC/ other QM applications etc...

eh. in some ways, yes.

in the realm of fundamental new physics...ehhhh

New applications of known physics, yes.

@Semiclassical lol you seem to prefer it that way maybe, just like most everyone in this room... :|

Whereas you decidedly seem to prefer it the other.

← embraces all physics, quite promiscuous, does have taste for adventure :P

So long as you ignore actually worrying about all that silly math.

2:49 AM

@Semiclassical math is cool too, theres gobs in my blog etc... but also "looks can be deceiving"... :P

I'm reminded of a line of philosophy. "The light dove, cleaving the air in her free flight, and feeling its resistance, might imagine that its flight would still be easier in empty space. It was thus that Plato left the world of the senses, as setting too narrow limits to the understanding, and ventured out beyond it on the wings of the ideas, in the empty space of the pure understanding."

ah, poetic. very platonic indeed

or, to be more precise, I have the next few lines in mind: "He did not observe that with all his efforts he made no advance - meeting no resistance that might, as it were, serve as a support upon which he could take a stand, to which he could apply his powers, and so set his understanding in motion."

huh ok, the twist. who wrote it? ps it would seem that if we quote him 2K years after he lived, that (alone) qualifies as some kind of "advance"

Kant's Critique of Pure Reason, 1781.

(a surprisingly readable bit of Kant, for once)

2:54 AM

even the entire math field is related to a platonic realm, what greater honor could there be?

That's pretty good

@Semiclassical you heard the legend of Hippasus right? in my pov one of the 1st kuhnian shifts in history... and not merely an intellectual "hurl" there o_O

I wonder what Einstein thought of people who tried to understand relativity or QM without any math

It's certainly been a convenient tale for people in the modern age.

@bolbteppa he wrote a layman book on relativity. its great. maybe many have forgotten. its basically pop science, ~1century ago. written by a scientist celebrity of the era. the opposite of an elitist in many ways.

3:07 AM

"I regularly browse open access website arxiv.org to look for the latest astrophysics research. Real astrophysics, that is. But if I want to take a look at what pseudoscientists are up to, I can browse vixra.org. That’s right, “arxiv” backwards. "

I genuinely had no idea it was arxiv backwards

lol

3:29 AM

@Semiclassical ps that line could apply to modern abstract/ theoretical physicists... of which maybe plato was in some ways one of the 1st...

(wow can find almost anything with google) pbs.org/wgbh/nova/blogs/physics/2011/12/…

> In its general approach, and its ambition, Plato’s utterly mistaken theory anticipated the spirit of modern theoretical physics. His program of describing the material world by analyzing (“reducing”) it to a few atomic substances, each with simple properties, existing in great numbers of identical copies, coincides with modern understanding.

...

> The World as a Hologram (Susskind)

1 hour later…

4:58 AM

@JohnRennie...You there ?

Anyone can help me in a vector problem of boats ?

@NehalSamee No need to ask whether to ask. Just ask.

yup, "askaway" :-)

Hmmm...

A police stands on one bank and a thief on the other ... As soon as the police saw thief , he started to cross the river perpendicularly with velocity $4ms^{-1}$ . The thief ran horizontally along bank at $2ms^{-1}$ . The river current velocity is $3ms^{-1}$ ... Will police catch thief and at what time ?

When I use component of velocity, I have only $3ms^{-1}$ horizontally . This is greater than the thief's velocity , so police will reach earlier ...

So , there arise the confusion ...

Anyone interested ?

@rob can you please help ?

5:26 AM

@NehalSamee Hey, sorry, distracted.

Is the question whether the policeman's boat collides with the thief on the bank, or whether the policeman gets in front of the thief and can stand and wait to catch him?

Collides ...

I think my first approach is correct ... But can't reason why second is incorrect ...

Can the policeman steer?

Well , second approach is : I find resultant $R$ and assume time to be $t$ and draw a right angled triangle with width if river (20m) ,. $2t$ and $Rt$ ...

@rob no ... It's just a simple boat ... It's not necessary for them to reach simultaneously ... I want to know whether they can ...

6:16 AM

@JohnRennie ... You there ?

@NehalSamee let's switch to the problem solving room

OK ...

@Semiclassical The science fans really love the ~zero point energy~

Even though it's not that interesting

6:38 AM

[Random]

Slater–Condon rules

Within computational chemistry, the Slater–Condon rules express integrals of one- and two-body operators over wavefunctions constructed as Slater determinants of orthonormal orbitals in terms of the individual orbitals. In doing so, the original integrals involving N-electron wavefunctions are reduced to sums over integrals involving at most two molecular orbitals, or in other words, the original 3N dimensional integral is expressed in terms of many three- and six-dimensional integrals. The rules are used in deriving the working equations for all methods of approximately solving the Schrödinger...

Antisymmetrisation does not just occur in QFT

3 hours later…

9:46 AM

amazon.com/…

Why is everything so expensive

to make the rich richer

I wonder how much money I have in science books

several thousands, definately

I could feed an african village with those books

crcpress.com/Independent-Axioms-for-Minkowski-Space-Time/Schutz/…

looks interesting

user image

First axiom: The Page Does not Load :P

yup, me too

theguardian.com/books/2018/apr/14/…

Imagine if all of us have the superpower to rewire a causal network in any way we please, how will everyday be like if causality is no longer immutable

(this is one step higher than changing the past)

In 2017, time ceased to be continuous to me

In 2018, space started to look not so coherent to me

This is good, for the liberation of thinking of human intuition allow me to better understand really nontrivial mathematical concepts, and perhaps help me to think moe abstractly which can help my understanding of set theory

in The Symposium, Apr 1 at 13:15, by Mozibur Ullah

In fact space is more mysterious than that as we've discovered (I mean the Planck distance). ,

> Spacelessness, one of the concepts that can liberate the mind beyond its intuitive confines, in order to better understood those that cannot be expressed as a function of arguments

All that is needed to realise The Plan, the ultimate construction that promised to make all of this crystal clear...

2 hours later…

12:37 PM

@EmilioPisanty Great work on the second rung!

Hey @BalarkaSen

I think I got poisoned

I slept for 10 hours and still feel like hell

Do you have the diarrhea

Hey @Slereah

@0celo7 That happens to me when I sleep too much

I think my record for sleeping was 18 hours

That was a nice sleep

12:41 PM

I have probably slept for well over 20 hours

It confuses my biological clock

I did sleep longer one time (I think), but it was surgery related

General anesthesia is one hell of a drug

Oof

@Slereah definitely.

I mean, there is neat stuff associated with zero point energy

But it all stems from [x,p]=i hbar

Not a lot, rly

the only application I've seen for zero point energy is renormalization in semiclassical gravity

I'm sure you can do things with it, but it's a fairly small aspect of quantum theory

Well, the Wiki page for ZPE includes a few examples

12:47 PM

@Slereah nah, had a really bad headache when I got back from dinner last night tho

apparently I was the only one in the group who did tho

en.m.wikipedia.org/wiki/Zero-point_energy

@Slereah I had a length surgery to repair a broken humerus too near the ball joint for the usual remedies when I was eighteen.

When the ^%&*# anesthesiologist comes in the next day to check my breathing he hands me the little challenge toy and lets me start to take a huge breath in an effort to peg it before suggesting that I start slowly. Wracked with pain for a least a minute.

Though it’s entirely possible they’re being too broad/generous with what they consider applications

And I'm pretty sure he smirked. But I couldn't be certain through the tears.

heheh

12:49 PM

Ummm .. can anyone give me an insight about why energy and momentum is conserved in elastic collision but only momentum in elastic collision ...?

do you mean inelastic

I want to think it in this way that , only conservative forces present help in energy conservation and no external force in momentum conservation...

@Slereah yeah ... mistake ...

@dmckee there's a story in Lance Armstrong's book where he blew the meter off the scale.

@BalarkaSen thanks =)

@NehalSamee ::sigh:: Energy is conserved in both. The thing that is special about elastic collisions is that they conservere bulk kinetic energy.

12:53 PM

lemme know if you can think of other alternative ways to slice that cat

There is no general rule of conservation for that quantity. Almost every interaction fails to conserve it.

the pivoting in SQL is fiddly but I think I have the hang of it and I can probably implement other measures

@EmilioPisanty See Section 4.3 in Federer, "Slicing"

@dmckee So we can say that he felt the situation was quite, um, humerus, can we?

@0celo7 what?

12:54 PM

@BalarkaSen Low hanging fruit.

is this Roger Federer you're talking about?

But yeah, it's pretty funny.

@dmckee yeah , how ?

@EmilioPisanty I'm heading off in a few minutes to somewhere else, I have it bookmarked so I can fiddle around with it a bit when I get back

In a shocking twist, I was that doctor

12:55 PM

@BalarkaSen cool

@EmilioPisanty amazon.com/Geometric-Measure-Theory-Classics-Mathematics/dp/…

@0celo7 ah

@0celo7 hissss

@NehalSamee In the inelastic case some of the kinetic energy is converted to other forms of energy. Thermal energy, sound, elastic potential in the stressed metal that make up the tangled wreck of your car.

I thought you meant this.

12:56 PM

"Energy" generally means "all kinds of energy taken together".

huh

so is a "federer" someone who puts feathers on hats or some such?

@ACuriousMind

But the point is that you shouldn't think "inelastic collisions are special because they don't do [thing]", but instead should think "elastic collisions are special because they do this very surprising thing".

The latter puts you in a better frame of mind for thinking about energy flows in general.

@EmilioPisanty sounds about right

That book has nothing to do with feathers, however

@NehalSamee Put another way, generically, objects have all sorts of 'reservoirs' where they can put energy (in thermal and internal energy in particular) but there's no such 'reservoir' for momentum

Most interactions are messy and they push energy into all kinds of different places. Situations where you can trace the energy as it moves between just a few easily detected states are (a) enormously useful and (b) generally very hard to make happen in real life.

1:00 PM

elastic collisions are special in that they don't couple to those reservoirs

@0celo7 probably arrows more than hats though =P

@EmilioPisanty there are some commutative diagrams, yes

but in that vein: physics.stackexchange.com/questions/133759/…, physics.stackexchange.com/questions/159221/…, physics.stackexchange.com/questions/92051/…

btw @dmckee 250 rep out the door in bounties

still some 300 / 350 short of the goal though

Every time you say that I feel that I should go hunting for worthy things to bounty. But then I never put the time into it.

@dmckee =P

it's just keeping your eyes peeled for worthy questions on site ;-)

admittedly this one is an old one of mine, but this recent one by @glS is an excellent example of the sort of questions we need more of

@dmckee So, it cant be explained using concept of conservative force and external force ...?

@EmilioPisanty Isnt it ?

1:10 PM

it can, but you need to consider the internal structure of the object and the forces acting between the different parts of that structure

@NehalSamee please clarify your question.

@EmilioPisanty I want to know the reason of conservation of energy and momentum using the fact that external force conserve momentum and conservative force conserve energy...

@NehalSamee it's unclear what you want beyond that.

elastic collisions conserve the kinetic energy of the center of mass of the colliding objects because they are subject to conservative forces between them and no other forces

inellastic collisions conserve global energy, because all the forces are conservative, but they do not conserve center-of-mass energy because that motion is coupled via conservative forces to other degrees of freedom that can keep some of that energy.

Momentum is conserved in the absence of external forces because momentum is a vector quantity for which there are no ways for internal degrees of freedom to have momentum without contributing to the center-of-mass momentum, whereas with energy there are ways for particles to have energy without contributing to the center-of-mass kinetic energy.

that difference is explained in detail in

33

Q: How can momentum but not energy be conserved in an inelastic collision?

In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions?

energy kinematics momentum conservation-laws collision

If you want further information, then you will need to be much clearer about the specific aspects you don't understand. Repeating the same question over and over will just produce the same answer over and over.

1:41 PM

user image

Ghosts in chemistry

@Secret what's a CT state?

also:

@Secret figures, it's DFT.

Charge transfer

@Secret I very distinctly remember the Thursday session here birs.ca/events/2017/5-day-workshops/17w5010/videos, particularly the Kenneth Lopata talk and the ones around it

"why DFT is great, and also all the dirt we needed to shove under the carpet to get it there"

There's ultimately a lot of approximation built in DFT such as how it is not ab initio, and that if the system depends heavily on phase behaviour of the wavefunctions, then electron density will not adequately capture it

@Secret approximations are fine

1:52 PM

Some people don't consider DFT as quantum chemistry because of this regard

inventing functionals just to see which ones "work" and which ones don't is... maybe less fine

Still, it is the best we have for big systems and it so far worked really well for most systems

Which is why I think quanutm computers will greatly expand the scope of ab initio calculations, but with 1000 qubits (with suitable error correction algorithms) as the expected target, we are still pretty far from that

which functional works for which system is in general quite arbitrary (though there are some rough guidelines exists such as hybrid functional are best for organic systems while pure functional are best for transition metal systems). In general, a selection of functionals have to be benchmarked against experimental data in order to decide which functional will be most suitable for the system under investigation

For our case, we are lucky that the fastest and simplest functional PBE work best for us, which greatly shorten computation time of 120 molecules within two days

2:51 PM

@BalarkaSen is there a typo here? i.gyazo.com/45591193fa39a3d870446140514c3109.png

they probably want to have $(\alpha^{n-k}\cup\cdots\cup \alpha^a)\cap [\Sigma_n]\ne 0$, right

3:51 PM

Hello, everyone. Is there any chat group in phystackexchange solely dedicated for scientific papers (published /unpublished) ?

*reading

Can you guys tell me about such groups in the internet for reading papers?

No

@EmilioPisanty I understood it later on ... Another question ( silly though) ... If forces 4N and 5N together do an act involving a total power of 72W , then for finding contribution of each force , shall I use unitary method ... Like , $P_4=\frac{72}{9}*4$..?

Or anyone else ...

?

@Mockingbird not that I know of. You can start your own chat room for the discussions, but I doubt there would be enough interest to keep the room going.

@JohnRennie .. would you mind answering my question ?

@NehalSamee I'm not sure I understand what you are asking. Do you mean you have two forces of 4 and 5N acting on an object moving at 8m/s ? i.e. force x velocity = 72W ?

4:02 PM

@JohnRennie yes ...

Then yes, the work done by the two forces is 4 x 8 and 5 x 8 watts respectively.

@JohnRennie great ... Thanks ...

@JohnRennie .. did you go through the!Problem I posted yesterday ...?

About Glaishier constant and see point ...?

No, sorry, I haven't looked at it.

@JohnRennie 😧😧😧

@Mockingbird well, there was this

24

Q: Let's have a journal club

This idea is not totally original: there was at least an attempt at a journal club in chat in 2011. That, in turn, was inspired by mbq's (and Cross Validated) idea, which seems to have happened at least twice. We already have users do this, so I'm really just suggesting that we more actively enco...

discussion retention

it was very successful for a time

where by "a time" I mean, we managed to pull this of just one time

and by "very successful" I mean that we had one question in the series

45

Q: Can we infer the existence of periodic solutions to the three-body problem from numerical evidence?

I recently found out about the discovery of 13 beautiful periodic solutions to the three-body problem, described in the paper Three Classes of Newtonian Three-Body Planar Periodic Orbits. Milovan Šuvakov and V. Dmitrašinović. Phys. Rev. Lett. 110 no. 11, 114301 (2013). arXiv:1303.0181. I am...

mathematical-physics newtonian-gravity numerics three-body-problem

... though it didn't get answered until six months later.

More generally, though, if you want a Journal Club experience, gathering people isn't enough - you need a critical mass of people who are interested and reasonably-well-versed in the same area of physics

I would have nothing meaningful to contribute to an astrophysics journal club, say, and I probably wouldn't get much from a general-physics audience discussing papers in my field, either.

so decide on a topic and then look for groups.

4:34 PM

@Mockingbird hi, the chat rooms already serve as impromptu/ intermittent journal clubs. the trick is finding papers that others are willing to read/ discuss/ take seriously. what areas do you want to investigate?

Hello

Does anyone know a quick way to calculate $\langle x \rangle$ given some initial condition $\Psi(x,0)$ for a harmonic oscillator?

are you asking for the time dependence?

for $\langle x \rangle $ at $t=0$ you'd just compute $\int \Psi(x,0)^* x \Psi(x,0)\,dx$

No, for any given time

Right

@bolbteppa thx for ref to minkowski spacetime, looked it up some more. think thats a valid/ key point needing further analysis. didnt look at the T-H paper closely wrt that idea, agree they need to address it "head on". but heres a wild idea: there might exist an interpretation of minkowski spacetime in line with the old/ classic "ether drift" idea...

4:41 PM

One route, as you'd expect, is just to compute $\Psi(x,t)$. But for an arbitrary initial condition this isn't practical.

I had $\Psi(x,0) = A(\psi_0(x)+2i\psi_1(x)+3\psi_2(x))$ btw

I computed $|\Psi(x,t)|^2$

I think you messed up the third subscript

And making use of orthogonality

kk

orthogonality is the most obvious approach, yeah

$$\sin(\omega t)[\dfrac{\sqrt{2}}{7} \sqrt{\dfrac{\hbar}{m\omega}}\sin(\omega t)-\dfrac{18}{7} \dfrac{1}{m\omega} \sqrt{\dfrac{\hbar}{m\omega}}]$$ is the answer I got after some simplification

4:43 PM

it simplifies things a bit to note that $\int \psi_m(x)x\psi_n(x)\,dx$ is zero when $m,n$ have the same parity

But it's pretty tedious regardless

Just wondering if there was some easier way than to compute like a dozen integrals...

Hmm. The usual alternative is to use Ehrenfest's theorem

I did that for the expected value of the momentum

iirc you have $\displaystyle \frac{d}{dt} \langle x \rangle=-\frac{i}{\hbar} \langle [H,x]\rangle$

Oops, I forgot to factor out that $\sin$

4:45 PM

I may be off by a sign, I can never remember

The nice thing is that $[H,x]=-i\hbar p/m$ so $\frac{d}{dt}\langle x \rangle = -\frac{\langle p\rangle }{m}$

bah, I'm definitely off by a sign

Yeah..

yeah, should be $+\frac{i}{\hbar}$

So then you have $\frac{d}{dt}\langle x \rangle = \frac{\langle p\rangle}{m}$. You might think you haven't improved your position here---you've gotten the derivative of <x> in terms of <p>, but you don't know that either.

However, you can use Ehrenfest's theorem on $p$ as well!

You'll find $\dfrac{d}{dt}\langle p \rangle = - m\omega^2 \langle x\rangle$

And therefore $\frac{d^2}{dt^2}\langle x\rangle = -\omega^2 \langle x \rangle$

Now this is progress.

What we've deduced is that $\langle x \rangle$ should satisfy the classical equation of motion for $x$.

And this is an ODE which we can solve in closed form

Yeah that's the case for my solution

Neat

right. So you know your solution is of the form $\langle x(t)\rangle = A \cos \omega t+B\sin \omega t$

and it's not hard to show that $A=\langle x(0)\rangle$, $\omega B=\langle x'(0)\rangle = m\langle p(0)\rangle$

That still means you need to compute the initial position and momentum, so there's still some work to do

But none of the work involves the time dependence

This is a good method so long as the classical problem is one whose solution you could find pretty easily.

On the other hand, when you do stuff like spin: You can still apply this idea, but it'll end up being more complicated

Yeah, this seems very useful

4:57 PM

it's quite handy, yes

I like this trick as well $\langle p^2 \rangle = \hbar^2 \int |\Psi_x|^2 dx$

integration by parts, eh

nice

Yeah:P

which nicely gives you the fact that the expected value of the kinetic energy should still be positive in QM

5:20 PM

@BalarkaSen @ACuriousMind are you here

5:37 PM

@0celo7 hey saw your slides, like the ideas, any availability for questions?

@0celo7 it has been worked out

@EricSilva not the end of the world?

It turns out the senior was just sitting in

So no probs

ok, nice

Also André Is like an intuition monster

5:48 PM

why

The madman makes crazy leaps without even sitting down and working out the comps

@EricSilva so is G. Huisken

it's because of him saying stuff is probably right that hundreds of papers have been written

I found some lectures online he gave about mcf and they seemed p good

Yau too, apparently. You just talk to Yau and get ideas for 50 papers

of course the actual proofs might be too hard for non-Yau people

Prepare the determinant for applying Hückel method to the cyclopropyl cation (it is called the secular determinant).
Expand and get the appropriate cubic equation. Solve for the energies of the system.

How do I go about solving this?

Can I treat it like propene? :/ (makes no sense but ...)

6:18 PM

@Secret Do you know what is free mesomeric effect? I have not only searched for this in all my books (viz March, Solomon Frhyle, Peter skyes etc) but also on google books and google and I cant find it anywhere

If I have a potential like $V(x) = \cases{0, x<0 \\ V_0, 0<x<L \\ \infty, x>L} $

Does that mean particles comin from the right are going to return left at $x=L$?

so semi-infinite with a potential step?

Yeah

yeah, everything will have to be reflected

I'm trying to solve the SE

Hmm

6:23 PM

you can view this as though you had $V(x)=V_1$ for $x>L$ and then consider the limit $V_1\to \infty$

You'd expect the transmission coefficient to go to zero in that limit

Yeah

pretty sure that also means you'll have the incident/reflected amplitudes being equal in all regions

(there can be a phase shift, though)

So for $x<0$ I got $\psi_1(x) = Ae^{ikx}+Be^{-ikx}$ and for $0<x<L$ I got $\psi_2(x) = Ce^{ilx}+De^{-ilx}$ where $k=\dfrac{\sqrt{2mE}}{\hbar}$ and $ l = \dfrac{\sqrt{2m(E-V_0)}}{\hbar}$ where $E$ is the energy of the incoming particles (which is higher than $V_0$)

And if everything is reflected, I probably wanna match $Ae^{ikx}$ with $De^{-ilx}$ somehow

One handy trick here: You know that $\psi_2(x)$ should vanish at $x=L$

And I wanna say $A=D$

6:27 PM

and you're free to choose your basis solutions as you want

And also $\psi_{2,x}(L)$?

probably not

Why?

Oh

you wouldn't do that for a particle in a box

one convenient choice is $\psi_2(x)=C\sin(l (x-L))+D\cos(l(x-L))$

you can check that both of those are solutions to the SE in region 2

So $D=0$? :/

6:29 PM

but the first one explicitly vanishes at x=L, so you can drop the second solution immediately

Yeah. So you know what the solution in $\psi_2(x)$ should be

This isn't really different from what you'd have otherwise, to be clear:

If $\psi_2(x)=Ce^{il x}+ De^{-i l x}$ and you require $\psi_2(L)=0$, you have $Ce^{-i l L}=- De^{-i l L}=C'$ where I've introduced that extra constant C' for convenience

Then $\psi_2(x) = C' e^{il(x-L)}-C'e^{-il(x-L)}=2i C'\sin (l(x-L))$

So you'd end up with the same form of solution regardless. This just gets you there faster.

Gotcha

You could similarly justify taking the solutions in region one to be $\psi_1(x)=A\sin kx+B\cos kx$, but if you want to understand the relation between the incident and reflected waves then this is not so useful

So, taking $\psi_2(x)=C\sin[l(x-L)]$, you'd get $\psi_1(0) = A+B =-C\sin lL$ and $\psi_1'(0) = ik(A-B) = l C \cos lL$

I'll point out now that $l$ is a somewhat painful choice of variable in this context :P

I like $k_1$ and $k_2$ in this scenario

But regardless, the rest of the manipulations are straightforward enough

@Semiclassical Hmm we need another equation for uniqueness, no?

You would, if you expected a scattering problem to have a unique solution :)

Remember, you don't normalize your wavefunctions in this setting

user image

6:41 PM

Ohh, yeah right

(source)

I just need to find the transmission/reflection probability anyway

Well

The transmission probability should be pretty simple :)

$0$

Right. So the reflection probability should be similarly trivial

6:43 PM

$1$

Right. The point will be that, in this scenario, the incident and reflected amplitudes have the same modulus

What will be different between them is their relative phase

e.g. if $A$ is real then $B$ generally won't be

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