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Are math skills necessary? 
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#55
Jan2412, 10:34 PM

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#56
Jan2412, 10:34 PM

P: 50

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. 


#57
Jan2412, 10:50 PM

P: 1,042

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. 


#58
Jan2412, 10:53 PM

P: 50

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 prerequisites 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. 


#59
Jan2412, 10:55 PM

P: 33

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. 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 


#60
Jan2412, 10:59 PM

P: 452

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/ 


#61
Jan2412, 11:01 PM

P: 1,042

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. 


#62
Jan2412, 11:07 PM

P: 50

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 prereqs to QM? How fast can I get them starting from where I am (calculus 1)? Can you estimate in hours? What are your background, by the way? You all know QM? You think this is accurate to say understanding QM is important to nanotech? 


#63
Jan2412, 11:10 PM

P: 1,042

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 get to quantum you need Calc IIII, 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. 


#64
Jan2412, 11:11 PM

P: 103




#65
Jan2412, 11:12 PM

P: 452

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. 


#66
Jan2412, 11:14 PM

P: 50

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 prerequisites to QM? 


#67
Jan2412, 11:22 PM

P: 1,042

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


#68
Jan2412, 11:23 PM

P: 33

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 


#69
Jan2412, 11:40 PM

P: 50

Hmm this is pretty actually, but why this? Ans426 just asking. As you understand QM, do you consider yourself to understand an atom? Can a QM expert predict if a chemical reaction will occour (without using chemistry/testing on lab)? What would you tell me if I asked you what is the path of the motion of an electron around a hydrogen nuclei?
Jorriss, I can't answer you because I don't understand the motions of an atom. That is the point. If I could create isoled atoms, put them together, and their resulting motions leads to precise reactions in relation to what would be chemically expected, this would be awesome. I'm not sure if this is possible, but why not? And group theory? What is it? (= 


#70
Jan2412, 11:42 PM

P: 1,042




#71
Jan2412, 11:49 PM

P: 50

Modeling it on my computer, so I can see it happening. For example, I create 2 hydrogen atoms. I can see a point indicating the position of the nuclei, clouds showing the orbitals. Then I can see the atoms slowly approaching and their molecular orbitals forming as they bind. I'm not sure this is what would happen but testing and playing is the idea. If this is not absurd, wouldn't it be great?



#72
Jan2412, 11:53 PM

P: 1,042




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