Tell Me How To Teach Myself Physics

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Woxor
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Tell Me How To Teach Myself Physics

Postby Woxor » Fri May 11, 2007 5:46 am UTC

I'm a first-year graduate student in mathematics, and I'd like to learn enough physics to be about on par with the average guy with a physics BS. I can google whatever textbook-like resources I need, I think, but first I'd like to see what someone who knows what they're talking about thinks.

Specifically, what subjects are the most important? I've taken courses in basic newtonian mechanics, optics, electricity, magnetism, thermodynamics, and a scattering of engineering courses that are probably somewhat relevant but weren't in-depth. Oh, and physical chemistry. So what are the main things I've got left to cover? I don't really have a great handle on quantum physics or relativity (from a rigorous perspective, that is), but is that all? Within those subjects, what concepts/equations are the most salient and useful? What types of physics problems should I be able to solve that a mathematician, in general, could not?

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Postby Gordon » Fri May 11, 2007 7:58 am UTC

Woxor wrote:I don't really have a great handle on quantum physics


No one does.

That being said. If you want help "learning" physics, it would be better of you to post 'I don't know this....' threads. Remember that Math->Physics->Chem->Bio so if you're good at general math theories you're probably going to pick up physics pretty quick (after reading your posts I guess it's safe to say you're a math guy). But much like math[s] you need to word you question fairly specifically.

You can't just say "I want to learn physics". You have to know what part of physics you wish to learn about.
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Postby demute » Fri May 11, 2007 8:40 am UTC

I would recommend spending about 50 hours on wikipedia, reading so much you can about physics. Then, hopefully, you will know what you want to learn. Since vectors are used in all kind of physics, I would recommend to learn som vector calculus first.

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Postby evilbeanfiend » Fri May 11, 2007 9:25 am UTC

after all those courses i guess you have already spotted the main trends in physics i.e. in classical physics everything is either a wave or a particle
QM and relativity both deal with stuff that doesn't fit into the wave xor particle model very well.

id recomend looking up 'second quantisation' for QM as this shows how particles are linked to quantised waves mathematically. the generally accepted physical interpretation of QM is the 'copenhagen interpretation' though you may want to check out 'many worlds' as well as this is one of the favourite things for crackpots to cite.

once you are getting a handle on QM it open the door to a lot of new physics which relies on QM effects. e.g. superconductors and superfluids (bose-einstein condensates), lasers (although you can do a lot of laser physics just with classical waves), nanoscale physics. if you are having trouble understanding QM as an abstract concept perhaps one of these would help?

one other area i can think of that is a little different to the classical stuff and doesnt rely on QM (depending on how deep u go) is the physics of plasma
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Postby Berge » Fri May 11, 2007 9:43 am UTC

Richard Feynman wrote:I think I can safely say that nobody today understands quantum mechanics


Of course it was a long time ago when he said that...but I think the point is still valid.
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Postby Zohar » Fri May 11, 2007 12:26 pm UTC

Our physics syllabus includes (roughly, without laboratories and math courses):

Classical mechanics and electrodynamics
Waves and optics.
Analytical mechanics (if you've taken a course in variational calculus, it's basically the same) and electrodynamics.
Thermodynamics and statistical physics.
Two courses in quantum mechanics.
Introductory courses for solid state physics, astrophysics and particle and high-energy physics.

Somewhere along the line we also learned a bit of special relativity.

There are about a million books on every subject and I can't really recommend one of the other, I don't know enough of them. I do know Berkely Physics series is pretty respected. Also, the Landau and Lifshitz series are good though they're very difficult (arguments aren't very detailed and there's a lot of work "left for the student").

The Feynman Lectures on Physics are a wonderful series of books. They'll grant you a lot of understanding but no practice. It's a very different and creative way to learn physics, one which isn't used a lot in our university (and I doubt many others).

Eventually, I think physics splits roughly into the three areas I mentioned above (solid-state include everything about superconductors, semiconductors and so on).
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Postby miles01110 » Fri May 11, 2007 12:31 pm UTC

Just take physics courses. Reading about concepts is useless if you can't do problems.

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Postby miles01110 » Fri May 11, 2007 3:06 pm UTC

Ok fine, I'm in the lab now and don't feel like doing work, so here are some things to think about.

There are 4 main concentrations in the normal undergraduate course.

1. Mechanics
2. Thermodynamics/Statistical Mechanics
3. Quantum Mechanics
4. Electricity and Magnetism

Mechanics is the study of the macroscopic aspect of physics. Classical mechanics forms the basis of more or less all of physics. Classical laws are an excellent approximation to nature's behavior until you get into the realm of QM. You should be familiar with orbit equations and how to find them, Lagrangian mechanics, Hamiltonian mechanics, noninertial (rotating) reference frames, coordinate substitution, rigid body rotation, collisions, conservation laws, oscillatory motion, and if you're lucky get a little introduction to chaos.
Recommended book: Classical Mechanics, 3e- Goldstein

Thermodynamics connects the macroscopic to the microscopic. Personally I find Thermo & stat mech to be incredibly dry and boring. Things you should know about include multiplicity of states, laws of thermodynamics and how to manipulate them, Free energies, gas laws, heat engines/efficiency, PV diagrams, energy/entropy/enthalpy, the ensembles (canonical, grand, microcanonical), partition functions, Fermi-Dirac statistics, Boltzmann statistics, Bose-Einstein statistics.
Recommended book: None, because I hate thermo and the book I used sucked.

Quantum Mechanics is the heart of physics. If you do not have a basic understanding of quantum mechanics then you're not going to get far. Things you need to know are the Schrodinger equation, angular momentum, spin, perturbation theory (time independent and dependent, as well as degenerate/non-degenerate), the hydrogen atom, bound states, scattering, as well as the conventions of QM like the bra-ket notation, commutator relations, Hilbert spaces, creation/annihilation operators, etc.
Recommended books- Intro to Quantum Mechanics 2e- Griffiths, Modern Quantum Mechanics 2e (?)- Sakurai, Principles of Quantum Mechanics 2e- Shankar

Classical Electromagnetism- E&M is fun but kind of nitpicky. The heart of the course should be Maxwell's equations. You should also know electrostatics, electrodynamics, magnetostatics, potentials and fields, electric and magnetic fields in matter, electromagnetic waves and wave propagation, and radiation.
Recommended book: Introduction to Electrodynamics 3e- Griffiths

Subtopics:
I don't know a whole lot about most of these so I'll just list them.
Fluid mechanics
Relativity- general and special
condensed matter physics
high energy physics
biological physics
physical chemistry
astrophysics

Keep in mind that you are going to need a strong background in differential equations to get anywhere. Most of physics is setting up a DE and solving it, or making approximations to it. Algebra is always a plus, but that's easy. Group theory doesn't hurt if you want to learn about particle physics, which is really interesting by the way. Tensor manipulation makes your life a lot easier, and linear algebra is also very, very necessary.

If you're looking for a good book on mathematical physics, check out Boas- Mathematical Methods in the Physical Sciences 3e.

Like I said before, physics classes are the best way to go. They aren't particularly interesting most of the time, but it's really helpful for someone like a professor to explain how to go about doing problems. Physics is less about doing problems than learning how to do problems in my opinion. After all, after college you don't get the luxury of looking up something in a book.

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Postby Woxor » Fri May 11, 2007 3:18 pm UTC

Thanks all, this is great! That's exactly what I was looking for: just a list of major concepts and their various aspects. Someone once asked me a similar question about mathematics, and I know it took me a while to compose a reply as in-depth as the ones above, so thanks to everyone for taking the time to respond.

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Postby Mat » Fri May 11, 2007 6:02 pm UTC

I think this site is pretty much what you are looking for: http://www.phys.uu.nl/~thooft/theorist.html
LIST OF SUBJECTS, IN LOGICAL ORDER (not everything has to be done in this order, but this approximately indicates the logical coherence of the various subjects. Some notes are at a higher level than others)
* Languages
* Primary Mathematics
* Classical Mechanics
* Optics
* Statistical Mechanics and Thermodynamics
* Electronics
* Electromagnetism
* Quantum Mechanics
* Atoms and Molecules
* Solid State Physics
* Nuclear Physics
* Plasma Physics
* Advanced Mathematics
* Special Relativity
* Advanced Quantum Mechanics
* Phenomenology
* General Relativity
* Quantum Field Theory
* Superstring Theory

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Postby Shadowfish » Fri May 11, 2007 7:54 pm UTC

The other people in this thread have done a great job with what topics there are in physics. I'll try to tell you how to teach yourself these topics.

I'm a second year undergraduate physics student. If anyone who has gone through more physics education than me sees something wrong with what I'm saying, go ahead and correct me. That said, here's what I've noticed about learning physics.

There aren't many physical laws, and the ones that you will learn in one course are usually not enough to fill one sheet of paper. What you really learn is how to apply the laws. What circumstances they can be used in, how to solve problems with them, and what mathematical tricks you can use to make them more useful.

If you want to teach yourself physics, what you should do is, while you are reading, sort out which equations are definitions(example: Work=(integral)(Force*dl) ), which are facts about the universe (example: the speed of light is constant), and which can be derived (example: E=mc^2).

After you know that, go though and see if you can reconstruct the derivations for all of the derived equations based the definitions and facts about the universe. After you have done that, find or make up some problems, and see if you can solve them.

Edit: Any physics book will go through the process I described. To me, at least, there is a big difference between doing it yourself and reading about how it is done. Try the derivations yourself. If you get stuck, see how the book did it, and then try it yourself again.

This process may be obvious after you have gone though as much school as you have, but it would have really helped me my first year if someone had told me what I just said.

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Postby tendays » Fri May 11, 2007 8:25 pm UTC

Shadowfish wrote:If you want to teach yourself physics, what you should do is, while you are reading, sort out which equations are definitions(example: Work=(integral)(Force*dl) ), which are facts about the universe (example: the speed of light is constant), and which can be derived (example: E=mc^2).


Sorry, but I just can't let this one pass.

Not "facts". "Postulates". Or "hypotheses". There are no facts in science.

Okay, I'm done with nitpicking.

Just one comment for the OP - try (assuming you have the time) to *understand* the derivations as much as possible rather than just learning forumlas by heart.
I've seen too many people learning stuff by heart without having the slightest idea those things are about. When they face a problem they just go through their formula list and see which can be applied directly. And when facing a problem where they need to apply two formulas they are lost.
That's not the right way to do science.
Of course, once you're done understanding, it's good to learn some key results by heart so you don't have to re-prove them every time.

Okay, done with ranting as well :)

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Postby SpitValve » Fri May 11, 2007 10:44 pm UTC

miles01110 wrote:Recommended book: None, because I hate thermo and the book I used sucked.


The standard text for Statistical Mechancis is Kittel and Kroemer. Everybody seems to love it.

For condensed matter physics, Kittel is the best for a newbie, Ashcroft and Meermin is the best for reference - it's fuller, but harder to get into.

Incidentally, Ashcroft was hanging around at IRL for a few weeks before this conference earlier on this year...

Also, I have to recommend Spacetime Physics by Wheeler and two other dudes I've forgotten. It's for Special Relativity and is a really entertaining book too :)

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Postby Shadowfish » Fri May 11, 2007 10:48 pm UTC

tendays wrote:Not "facts". "Postulates". Or "hypotheses". There are no facts in science.
Quite right. "Postulate" is the word that means what I wanted to say. I make mistakes like that a lot.

Back on topic:

Another thing that I wish I had known is that simple examples are valuable. Often, a book will give you a problem that is so idealized that you can't imagine it talking about something that could really exist. But, it turns out that the simple example is a good place to start when doing more interesting problems.

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Postby FiddleMath » Sat May 12, 2007 2:47 am UTC

Wow. I'm saving a link to this thread; I want to do exactly want Woxor describes, when I finally find the time.

Maybe... maybe we can get the xkcd webdude to put up a wiki, for things like this. This isn't just a conversation, this is reference material.

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Postby Pathway » Sat May 12, 2007 7:09 am UTC

There was a book I read for honors in physics last semester--a short one--on general relativity. It was for the mathematically unsophisticated reader, but it was very rigorous and clear. Really brings to the forefront our notions of speed, time, location, and how they require modification to fit our world. General Relativity from A to B, by Robert Geroch.

All that's required is that you know what geometric points and lines are. Everything else is defined independently. Great book. Read it.
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Postby adlaiff6 » Sat May 12, 2007 9:30 am UTC

Astrophysics is probably the coolest topic to let slip at the pub.
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Postby Solt » Sat May 12, 2007 10:09 pm UTC

I recommend you spend a lot of time here:

http://ocw.mit.edu/OcwWeb/Physics/index.htm
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Postby SpitValve » Sat May 12, 2007 11:35 pm UTC

adlaiff6 wrote:Astrophysics is probably the coolest topic to let slip at the pub.


Yay for me!

The problem is, having worked doing planetarium shows for a year, if people let me I'll quite happily give a one hour presentation off the cuff. Which is probably more astronomy than most people want in the pub :)

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Postby miles01110 » Sun May 13, 2007 10:28 am UTC

SpitValve wrote:The standard text for Statistical Mechancis is Kittel and Kroemer. Everybody seems to love it.


Oh right, I forgot about that one. The one I used was Thermal Physics by Schroeder. It sucks.

I avoid thermo like the plague anyhow if I can help it. I'm at CERN right now, and I'm not in charge of the superconducting magnets...so screw thermo!

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Postby Pathway » Sun May 13, 2007 4:34 pm UTC

miles01110 wrote:
SpitValve wrote:The standard text for Statistical Mechancis is Kittel and Kroemer. Everybody seems to love it.


Oh right, I forgot about that one. The one I used was Thermal Physics by Schroeder. It sucks.

I avoid thermo like the plague anyhow if I can help it. I'm at CERN right now, and I'm not in charge of the superconducting magnets...so screw thermo!


Haha... who is, and how much grief do they get?
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Postby Solt » Mon May 14, 2007 12:21 am UTC

miles01110 wrote:
SpitValve wrote:The standard text for Statistical Mechancis is Kittel and Kroemer. Everybody seems to love it.


Oh right, I forgot about that one. The one I used was Thermal Physics by Schroeder. It sucks.

I avoid thermo like the plague anyhow if I can help it. I'm at CERN right now, and I'm not in charge of the superconducting magnets...so screw thermo!


Apparently you're not in charge of supporting the very foundations of modern society either.

But I guess thermo is more of a mechanical engineering thing anyway.
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Postby EradicateIV » Mon May 14, 2007 2:00 am UTC

I remember Physics B in high school and getting back my test in thermo...
I got a C on it.

I hit myself in the head over and over again. Thermodynamics is HELL.

But alas, I'm sure it had something to do with being in high school and being an algebra-based physics class *gag me*.
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Postby Vaniver » Mon May 14, 2007 2:18 am UTC

demute wrote:I would recommend spending about 50 hours on wikipedia, reading so much you can about physics. Then, hopefully, you will know what you want to learn. Since vectors are used in all kind of physics, I would recommend to learn som vector calculus first.
*shudder* Do not do this.

I'm a big fan of my Feynman Lectures on Physics. They'll give you a good handle on the material; but he assumes all the math knowledge beforehand (which you should be fine with, given that you're a graduate student).


My advice is to ignore all the big stuff. String theory? Theoretical astrophysics? Quantum? Don't even try to touch it until you've figured out the other stuff. Science is an iterative process, and it's learned best that way.
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Postby miles01110 » Mon May 14, 2007 1:54 pm UTC

Solt wrote:Apparently you're not in charge of supporting the very foundations of modern society either.


What? Where or when does modern society use superconductors on a daily basis? MRIs are the only thing I can think of. Superconducting is more or less exclusively the domain of science at this point in time.

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Postby Vaniver » Mon May 14, 2007 4:09 pm UTC

I think he's talking about simple thermodynamics, which gave rise to devices that produce mechanical work out of heat, while are a foundation of modern society.
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Postby Zohar » Mon May 14, 2007 4:51 pm UTC

In my thermodynamics test I got the lowest score I ever received - 15 (out of 100). Truly pitiable. However, for what I can only say are "historical reasons", every course has a make up exam, on that one I improved to an 85...
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Postby Solt » Mon May 14, 2007 7:03 pm UTC

Vaniver wrote:I think he's talking about simple thermodynamics, which gave rise to devices that produce mechanical work out of heat, while are a foundation of modern society.


Yep, cars/planes exist thanks to thermo, as well as the majority of our electricity generation and modern conveniences like refrigeration/hot water/temperature control. Satellites, chemical manufacturing processes, computer technology, materials technology, etc etc would also be hopeless without thermo.

Basically, if we couldn't control heat we would be living in huts, hunting bears. Respect the thermo!
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Postby miles01110 » Tue May 15, 2007 1:28 am UTC

You know, you could argue that any area of physics forms the basis for modern society...

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Postby Vaniver » Tue May 15, 2007 2:05 am UTC

You know, you could argue that any area of physics forms the basis for modern society...
You'd be better off arguing that it forms a basis for modern society. Otherwise, someone will trounce you with their definition of "modern", which probably stems from a single source.
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Postby Solt » Tue May 15, 2007 2:53 am UTC

miles01110 wrote:You know, you could argue that any area of physics forms the basis for modern society...



Not really. For example, you don't really need optics until you get into things like the internet. It's mostly for research and specialized applications.

Quantum Mechanics? Relativity? Very few practical applications so far.

Mechanics? meh. Design of machines. We could do a decent amount without it, though it's important for what we do do. More important is the power that drives these machines. Mechanics probably exists as a complement to thermodynamics, ie the steam engine. Physicists only study it these days because it is fundamental to some of their more interesting subjects.

Electricity and Magnetism is something of a basic, though, since electricity and communication are very important to society. Of course that application would be pointless without Thermodynamics to acquire said electricity.

Usually as soon as something becomes hugely useful/well understood, physics hands it off to people who are interested in implementing the finer points, and moves on to more complex things.
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Postby miles01110 » Tue May 15, 2007 3:07 am UTC

Solt wrote:Not really. For example, you don't really need optics until you get into things like the internet. It's mostly for research and specialized applications.


Photolithography is used almost exclusively to prepare silicon for doping in computer chips and other things of that nature. Modern warfare is more or less possible due to advances in optical systems.

Quantum Mechanics? Relativity? Very few practical applications so far.


Quantum Mechanics- not many examples, but the laser is pretty important.

Relativity- GPS systems, communications, satellite TV all not possible without it.

But yeah...depends what you mean by 'modern.'

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Postby SpitValve » Tue May 15, 2007 4:03 am UTC

Quantum Mechanics? Relativity? Very few practical applications so far.


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Transistors use quantum mechanics. The very foundations of electronics are quantum mechanics. You need to know quantum to do band theory and you need band theory to know how devices like diodes and transistors and stuff really work.

Shut down your computer in shame. Because it runs on quantum.

Edit: Apologies for the rantiness, but quantum is just the way physics works... it's used in every bloody device... how could you say it has no applications? gah! [/rant rant rant]

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Postby Vaniver » Tue May 15, 2007 4:55 am UTC

Pfff, they didn't need quantum to figure that out, they used chemistry!

[/joke]
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Postby SpitValve » Tue May 15, 2007 5:06 am UTC

Vaniver wrote:Pfff, they didn't need quantum to figure that out, they used chemistry!

[/joke]


I like the [/joke] bit. It kinda implies that I was a little bit too scary in my lost post :D

I guess it's because I'm a condensed matter physicist at the moment that I believe that Quanum is so important. Because Quantum Physics makes Condensed Matter Physics work, and Condensed Matter Physics makes electronics work, and electonics makes everything work.

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Postby Solt » Tue May 15, 2007 7:39 am UTC

SpitValve wrote:
Quantum Mechanics? Relativity? Very few practical applications so far.


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Transistors use quantum mechanics. The very foundations of electronics are quantum mechanics. You need to know quantum to do band theory and you need band theory to know how devices like diodes and transistors and stuff really work.

Shut down your computer in shame. Because it runs on quantum.

Edit: Apologies for the rantiness, but quantum is just the way physics works... it's used in every bloody device... how could you say it has no applications? gah! [/rant rant rant]



I just learned more than I ever wanted to know about semiconductors in my materials science course, which I happen to have a final on in 12 odd hours.

There was definitely quantum physics involved in the understanding of how Silicon and n/p type materials worked, but the problem of inventing the transistor was overwhelmingly about thermodynamics. The group at Bell Labs that did it was specifically interested in reducing surface defects on their crystals- a thermodynamics problem. This is what allowed the Field Effect Transistor to be created. Thermo deals with doping, surfaces, interfaces, and the introduction of charge carriers into silicon to create semiconductors.

Maybe today we understand exactly how semiconductors work thanks to our understanding of quantum physics, but back then it was mostly thermodynamics that paved the way for the discoveries. The quantum interpretation didn't become clear for a while.
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Postby SpitValve » Tue May 15, 2007 8:23 am UTC

Even something like the difference between a semiconductor and a metal requires quantum theory...

Maybe originally they did it with thermo, but any modern approach to designing semiconductor devices will be heavily quantum based. Things like a Zener (sp?) diode only make sense due to quantum tunnelling and so on.

And if you want to properly predict properties of a material, you need to run a simulation that takes quantum effects into account - molecular dynamics (MD) can take you only so far before you need a more quantum simulation technique like density functional theory to tell you what's going on.

(Of course MD can be pretty useful sometimes, my work is doing simulations based on MD sims)

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Postby evilbeanfiend » Tue May 15, 2007 8:43 am UTC

SpitValve wrote:Even something like the difference between a semiconductor and a metal requires quantum theory...

Maybe originally they did it with thermo, but any modern approach to designing semiconductor devices will be heavily quantum based. Things like a Zener (sp?) diode only make sense due to quantum tunnelling and so on.

And if you want to properly predict properties of a material, you need to run a simulation that takes quantum effects into account - molecular dynamics (MD) can take you only so far before you need a more quantum simulation technique like density functional theory to tell you what's going on.

(Of course MD can be pretty useful sometimes, my work is doing simulations based on MD sims)


yep similar to lasers, to build a laser you just need classical optics (an etalon) and a lasing material (a plasma is probably easiest without qm) to explain how the lasing works or design new lasing material you will want QM.

that said i really don't think using QM for laser/semi/superconductors is that bad, in terms of a specific phenomena it just works. the mind bending part is when you try to consider the physical implications of what quantum mechanics means.
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necroforest
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Postby necroforest » Sat May 26, 2007 2:29 am UTC

LIST OF SUBJECTS, IN LOGICAL ORDER (not everything has to be done in this order, but this approximately indicates the logical coherence of the various subjects. Some notes are at a higher level than others)
* Languages



Aww, I was hoping that was Formal Languages :(


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