Are math skills necessary?

Ans426

I'm not sure about you, but if somebody gave me a ODE/PDE and just told me "This is the answer" I probably wouldn't be very happy about it, without even knowing how to derive the result.....
And I doubt that would train anyone as a proper scientist...

Of course at some point I guess everyone uses Mathematica or Wolfram Alpha when you've pretty much mastered the skills and you're just doing it for convenience....

WindScars

Well guys, I don't know. This discussion is pointless, but this topic is being very enlightening, actually. I have not much to add to it, I guess. But as you guys are coming here and seems to be interested in helping, I'll be precise in why I made this.

As I said, I would like to work on nanotech. It's a field on development and it's entire dynamics is dictated by quantum mechanics.

So, what do I do? Something is obvious: I have to understand quantum mechanics if I want to actually push the field. But what do "understanding quantum mechanics" means?

I, for instance, could simulate mechanical systems years before I could do precise calculations. I could easily program and model systems of planets orbiting, charges interacting, springs oscilatting, etc, years before I could solve a mere quadratic equation. So I can say I did understand the classical mechanics, even though I couldn't do any serious math on it. After all, it's how our world seems to act.

So, I wonder: do I actually have to go though those years and years of "mathematical maduration" if I want to understand quantum mechanics? And I'm not sure what I'll be able to do when I have the math skills for it, but will it be useful for my purposes? For instance, do getting into QM means I'll be able to calculate precisely the motion of an isoled quantized particle, the same way I am able, today, to calculate the motion of a spring in function of time? Because if this is what "learning QM" is, I guess this is not what I need.

Will not it be more useful if I just get into quantum mechanics intuitivelly and spend those years I would be spending on the math doing simulations instead? As I said, I have no idea of how the physics of nanoscale works, but if I understood it, I could play with it here. I could do simulations and use my time actually trying to figure out how I could build machines from atoms. Wouldn't this be more useful?

Well I dont know. If you guys have any idea of where I can "see quantum mechanics" - that is, actually visualizing what happens there, before those years of 'maturation', this would be very insightful.

Ans426

I doubt anyone can "intuitively" understand Quantum Mechanics...
" I think I can safely say that nobody understands quantum mechanics. " - Richard Feynman

bp_psy

How exactly did you do that? I am sorry but I don't see how someone could do that.Except for copy - paste programing.

WindScars

I can't visualizate the motion of atoms? How can it be so weird? It can be weird, but it must follow a rule.

bp_psy, why? This is easy I guess? Planets orbiting: 3d spheres as planets, position vectors atracting themselves every tick following the laws of gravitation, initial conditions to match the centripetal equilibrium. Charges iterating: basically the same. I even did a color mapping stuff when I was trying to understand eletrodynamics. This also made me understand a little better how electrons could oscilatte though a nuclei without falling on it or needing circular motion (I still don't understand many things, though). Springs oscillating: once I made several small balls glued together by a force. Then I noticed it acted as a string. Then I suddenly understood how springs works. It was beautiful. I had no idea of what I was doing. As I said, it was nothing serious or precise, yet I'm sure it followed the intuitive principles. And was fun.

Jorriss

It does follow rules. Mathematical rules. Quantum is extremely difficult to understand physically. It requires an understanding of the math that goes along with it.

Special relativity is counter intuitive, but if one accepts that the speed of light is the same in all reference frames than the arguments of what occurs physically are crystal clear and it is easy to think about special relativity physically. Quantum is not this way at all. The postulates are mathematical, the thought experiments are very hard to grasp, it is very difficult to get a grasp of what quantum says physically.

WindScars

The classical world is not easy too, we are just used to it. Well I'm already advancing every day on the math, but I'll be very sad if when I finally get into QM I realize I could have understood it just with what I know today.

What are the pre-requisites of QM by the way? I'm stuck into that horribly bulky stewart calculus 2 book, still trying to understand why I have to waste my time on all those tricks that are not challanging and not teaching me anything I couldn't do with mathematica.

Ans426

Apparently others asked for your background for a reason...
Even "Pop" QM tells you that nothing at the atomic scale is precise..

But I guess the key point here is that you won't be able to make any sense out of the system if you can't understand the mathematics behind...

If you're simulating extremely simple stuff like two charges interacting with each other, sure you'll be fine and the results will still make sense.

But just consider a slightly more complex system, and you'll understand why computational techniques alone don't do you any good.
For instance, consider a damped pendulum (Damping Force = -bv) and further driven by an external sinusoidal force with a certain frequency. (I'm sure you're aware the code is extremely simple)
Tune the magnitude of the external force a bit and you'll start seeing crazy results that will make no sense to you unless you've learnt about differential equations and some chaos theory. And this is sophomore stuff.
Merely looking at the results generated by a computer in specific cases won't give you much insight in the generalized cases.

And I can assure you that the smartest physicists in the world have not spent decades working on something that a random undergraduate could do with his computer programs.

Differential Equations, Multivariable Calculus, Complex Analysis and of course linear algebra
Again, of course you can do everything on a computer because someone HAS ALREADY done the maths...

This in fact reminds me of the Hardy–Weinberg principle
http://en.wikipedia.org/wiki/Hardy%E...berg_principle
Hardy's name is now in every genetic textbooks simply because Weinberg couldn't do high school probability and algebra

bp_psy

.
The notion of "motion of atoms" at a quantum level is very different them motion of simple particles. This makes visualization of quantum phenomena impossible. There are some useful ways to visualize some aspects of Qm but they are all in some way or another incomplete or incorrect. An example would be this: http://www.falstad.com/qm1drad/
One of the most basic reason for learning some actual physics and maths is that you might actually be understood by someone when you want to say something about them. I am sorry but I do not understand anything in that paragraph. Nothing actually makes sense.

Jorriss

The classical world is not easy, you are right but the fact we are used to it is an immense distinction over quantum.

The baseline prerequisites are calculus, differential equations and if want to get a better grasp, baby linear algebra. If you grab a modern physics book, if you can learn some things about quantum but it's an immensely tiny fraction of what the theory actually says and is about. Everything you are learning now in your math classes is important.

You just can't understand quantum without math. It, more so than most, is a mathematical theory. All the axioms of quantum are mathematical in nature (except maybe about the existence of a wavefunction which contains the information of the system).

Even in the simplest cases of quantum, such as a free particle, have subtle physical issues due to mathematical issues such as nonnormalizable solutions.

WindScars

Ans426, if I can watch QM happening on my eyes, will not it give me an insight? For instance I always tried to find a program that would allow me to create a few atoms on void and watch them interacting. This would be awesome. Of course I never found one, but I was not sure if it was not possible or nobody did it because it is theorically useless. Words on this?

And allright, if this is the only way, at least what are the pre-reqs to QM? How fast can I get them starting from where I am (calculus 1)? Can you estimate in hours?

This is all...? They said I'd need years?

What are your background, by the way? You all know QM? You think this is accurate to say understanding QM is important to nanotech?

Jorriss

What does a few atoms on a void even mean?

If you want to learn a little tiny bit of quantum, get a modern physics book.
y''+ky=0

Can you solve that differential equation? If so, you can probably follow it a bit. I suppose a modern physics book wouldn't be bad as those are mostly qualitative anyhow.


To really do quantum, yes it takes time.

To get to quantum you need Calc I-III, differential equations and linear algebra, then you can somewhat comfortably handle an upper division course on quantum mechanics that is not too theoretical nature.

That's at least 1.5 years of prerequisites.



Formally, I have one quarter of quantum chemistry and I do undergraduate research in quantum. I suppose it's some nanotech. Electron transport through molecular junctions, but it is theory.

bcbwilla

Okay, I lol'd.

bp_psy

Hours 3456H 54mins 15 secs.
But for me from end of calc 1 to quantum 1 it was 4 semesters in a physics program.It can probably be done faster.

WindScars

Actually I can't, but I just started studying differential equations so it's good news.

A few atoms on void means, for instance, creating two hydrogen atoms in an empty space and watching them react (that is, visualizing the nuclei, the eletronic clouds)? Even if aproximately. Is this absurd? Why? This would be awesome.

bcbwilla don't ;s I didn't say estimate precisely... just because in "semesters" is very relative. Well I can estimate something in hours. Use this formula: your_answer_in_semesters * hour_you_expect_me_to_study_a_day * 180

bp_psy, can you remember your colleges pre-requisites to QM?

Jorriss

No, it's not absurd. But how are you modeling them? In reality to model something like that in fullest, surprisingly enough, requires group theory.

Are you simply modeling them as two point particles interacting via a potential?

Ans426

Just do me a favor, Google "Driven Damped Pendulum", write a program, play around with a bit and tell me what you've been generalize out of it just by "looking" at it.(This is a VERY TYPICAL classical system)

It seems to me that learning too much programming has actually did you more harm than good in terms of learning Physics, despite it usefulness nowadays