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Quantum Mechanics - Let's teach the people

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posted on Feb, 7 2006 @ 11:57 AM
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Anyone up for providing a good basic ground for Quantum Mechanics with me? I think it would be appreciated by the people on this board. Lemme know and we can U2U and come up with a lesson plan.

However, I really don't know what to do about the Schrodinger Equation. I don't want to have to each Partial Differential Equations and Separation of Variables, and I am not sure how to teach the rest of the stuff without calculus.

Lemme know if you have any ideas, anyone.




posted on Feb, 7 2006 @ 01:53 PM
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I'd suggest you start learning some linear algebra, if you do not already know.



posted on Feb, 7 2006 @ 07:07 PM
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You can do a "quick and dirty with a lot of stuff glossed over" version of quantum mechanics for the layman -- ala Wikipedia:
en.wikipedia.org...

But this will not give anyone the tools needed to fully understand it and its implications. To discuss it in depth, you need to be able to understand the math in papers such as this one:
www.aloj.us.es...(02)032108.pdf

And, frankly, while we could explain what the paper is about in English, you can't discuss the details until you understand the math.

[edit on 7-2-2006 by Byrd]



posted on Feb, 7 2006 @ 10:54 PM
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You will find that most people's knowledge of quantum mechanics here on ATS is limited to philosphical context. Discussions of quantum mechanics are not to be found here for the most part. More along the lines of the movie 'What the bleep' are the posts.

I think you will have a better chance at teaching non-tensorial relativity. There is a good book for this called 'Spacetime Physics' by Wheeler and Taylor.



posted on Feb, 7 2006 @ 11:18 PM
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How about this? I've had this idea of laying out the "player's"(theories, field of studies etc.) in this area much like a sports team. Who would be the star players, where are the goalpoasts etc. I guess you could call it a metaphorical framework.
I don't profess to understand the math's and my understanding (or lack) of Quantum Mechanics is pretty "intuitive" I guess you'd say, but I do like to try to keep up.
With a framework like the sports team scenario, it may enable the people who know this stuff to give the lay person something more than the philosophical views (e.g. What the Bleep. . .) and something to "barrack" for, which may keep them interested.
Just imagine, "Oh man, 12 Dimensional Hyperspace got it's a$$ kicked by xxx with a crushing yyy. . "


Keep in mind this is a conspiracy site and not advanced calculus101. I'd like to hear about the more contentious/controversial theories as well, without getting excessively bogged down in "Scientism". Can't wait. . .



posted on Feb, 8 2006 @ 11:54 AM
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That's not going to work on a metadata level, I'm afraid though it's interesting. In order to understand what's going on and to discuss whether something is possible, you need the in depth knowledge.

Furthermore, without the knowledge, your meta-identifications could be all wrong. Even with good meta-identifications, your conclusions (based on how you put them together) could be wrong... or absurd... or laughable.

Those who are interested in it NEED to get their hands dirty and start learning the math and the formulas. It's a fascinating field, but unless you learn the math of the situation, you're very limited in what you can accurately speak about.



posted on Feb, 9 2006 @ 07:19 AM
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Good points, Byrd. In the interest of eating an elephant (one bite at a time)
What would be a good first step to take?



posted on Feb, 11 2006 @ 03:31 PM
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There's no way one can teach quantum mechanics without calc 1-3, differential equations, and maybe even complex variables depending on your professor. QM is easier also if you know boundary value problems and even a course in probability and statistics helps out a bunch. I just can't see how someone can truly learn QM without knowing the math.



posted on Feb, 12 2006 @ 03:39 AM
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Originally posted by T_Jesus
There's no way one can teach quantum mechanics without calc 1-3, differential equations, and maybe even complex variables depending on your professor. QM is easier also if you know boundary value problems and even a course in probability and statistics helps out a bunch. I just can't see how someone can truly learn QM without knowing the math.


Yeah my quantum mechanics course absolutely requires Calc 1-3 and "requires" ordinary DE's and partial DE's. However, the book we use has some handy-dandy math chapters that give you a crash-course in certain math. I am actually taking PDE's at the same time, and I learned separation of variables in Quantum before my math class! There is some complex variable math taught. Not much theory - just "here's the equation. It's this way because we told you so." The calculus is more involved however, which is good.



How about this? I've had this idea of laying out the "player's"(theories, field of studies etc.) in this area much like a sports team. Who would be the star players, where are the goalpoasts etc."


I like that a lot. That gave me some good ideas - thank you. It would be good I think to talk about EM radiation in general, and then build on early quantum discoveries.

Explanation of variables and constants
Who's Who of Quantum Mechanics (the Scientists)
E = hv
Black Body Radiation
Rayleigh-Jean Law
Wein Displacement Law
Einstein's Quantum Explanation of the Photoelectric Effect
Balmer/Lyman/Paschen/Bracket series of the Hydrogen Atomic Spectrum
The Rydberg Forumula
De Broglie's lambda=plancks' constant / momentum
Bohr Hydrogen Atom
Heisenberg Uncertainty Principle

That sums up the first chapter in my book. The second chapter introduces wave equations in 1-D and 2-D and the mathematical principles of separation of variables. Chapter 3 is the Schrodinger Equation. Four and Five build on it from there.

It will be a lot of work, but translating this stuff into a more palatable form for a wider audience will help me learn it better principle-wise.



posted on Feb, 12 2006 @ 09:14 AM
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What QM book are you using? I used Griffiths...

You learned Sep of variables in QM before another math course? Ouch...your calc 2 prof must've sucked.



posted on Feb, 12 2006 @ 09:20 AM
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Originally posted by Ralph_The_Wonder_Llama
[I like that a lot. That gave me some good ideas - thank you. It would be good I think to talk about EM radiation in general, and then build on early quantum discoveries.

Explanation of variables and constants
Who's Who of Quantum Mechanics (the Scientists)
E = hv
Black Body Radiation
Rayleigh-Jean Law
Wein Displacement Law
Einstein's Quantum Explanation of the Photoelectric Effect
Balmer/Lyman/Paschen/Bracket series of the Hydrogen Atomic Spectrum
The Rydberg Forumula
De Broglie's lambda=plancks' constant / momentum
Bohr Hydrogen Atom
Heisenberg Uncertainty Principle

That sums up the first chapter in my book. The second chapter introduces wave equations in 1-D and 2-D and the mathematical principles of separation of variables. Chapter 3 is the Schrodinger Equation. Four and Five build on it from there.

It will be a lot of work, but translating this stuff into a more palatable form for a wider audience will help me learn it better principle-wise.


Heh. You could build a whole wiki out of it... but if you're game for it, I say "go for it!" My knowledge is limited; I've had calc but nothing beyond that and it's been an age since I looked at DEs (for those of you going "HUH?", DEs are not a type of delirium but are rather "differential equations" and 1-D and 2-D are "one dimensional and two dimensional")



posted on Feb, 12 2006 @ 07:02 PM
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To learn the mathematics behind quantum mechanics, partial differential equations are going to be really important. To learn those, you'll probably have to take the first three calculus courses. (at least in engineering, we covered it in three; the science department uses the same book and covers it in four) Some basic linear algebra and complex variables is also probably a good idea. The famous Schrodinger equation, for example, has a complex term in it, and many differential equations have solutions that have terms like e^ix or e^-ix or things of that nature. Some basic first year physics, like learning what a wave is, would also be a good thing to know.


What QM book are you using? I used Griffiths...


I haven't formally studied QM, but that is the book our physics department uses, too, and most of the students seem to find it quite useful.



posted on Feb, 12 2006 @ 08:42 PM
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I am really interested in the aspects and possibilites that Quantum Mechanics has, although I am NOT mathimatically inclined. I take it from these posts that someone who does not understand the intricacies of maths have not a hope in the world of even partially understanding this amazing field?

I know maths is the universal language, but could someone possibly translate it into English?


- Nazgarn



posted on Feb, 13 2006 @ 02:22 AM
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Originally posted by nazgarn
- Nazgarn


Exactly. Here is the Schrodinger equation, it apperas in my chem textbook as excessive enrichment material. It takes differential calculus to have any knowledge of what it means. I wish I could tell you, though I have no DE under my belt yet.



posted on Feb, 13 2006 @ 06:43 AM
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Griffiths' QM book is quite good, if you've had the math background. He does throw in alot of stuff that any person could read, but it's really impossible to understand QM without the math...well, I say that for any physics course really.



posted on Feb, 13 2006 @ 06:54 AM
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Theoretical mathematical bunkum.

Apparently QM has now shown that things can pop in and out of reality -hence pouring water on the fact that the creation of reality is nothing more than a particle going awry.

And folk believe it.

Talk about having no sense of what's real.


'Oh, yes, things just manifest from nothing, I'm still waiting for my brain to appear, blah blah.'



posted on Feb, 15 2006 @ 08:27 PM
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QM is the best tested theory mankind has ever come up with. The vast majority of the scientific community, or I should say any real scientist should know not to just believe what math tells you - it should also be tested. If not, it's all philosophy. I'd prefer to do physics



posted on Feb, 15 2006 @ 08:39 PM
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Originally posted by nazgarn
I am really interested in the aspects and possibilites that Quantum Mechanics has, although I am NOT mathimatically inclined. I take it from these posts that someone who does not understand the intricacies of maths have not a hope in the world of even partially understanding this amazing field?

I know maths is the universal language, but could someone possibly translate it into English?


ROFL!

Actually, there are some books that explain it in layman's terms and don't require you to know math. But the trap here is that they haven't told you everything (or even much of what goes on) and when you start to speculate or "what if" theorize, (as most people would like to do) or to "play" with the idea, your concepts are SO wrong as to be... well... silly.

My knowledge is this basic kind of knowledge -- but I also know people who know the math. I understand just how hollow and shallow my knowledge is.



posted on Feb, 16 2006 @ 10:07 AM
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I remember the first upper level physics course I took - electromagnetic theory. I got the first test back with a 49%, and was all bummed out thinking I was either going to fail the course or be forced to withdraw. Turned out that 49% was a B, lol.

Yea, it's like I've said many times on this board - if you don't understand the math in physics, then you don't understand physics.



posted on Feb, 16 2006 @ 11:18 AM
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I use a big fat red book "PHYSICAL CHEMISTRY: A Molecular Approach" by McQuarrie and Simon. Look it up on Amazon. I call it the Satanic Bible. In fact I made one of those book jackets out of a grocery bag and put a big pentagram on it and used the Greek font in Word to rewrite the title. I took it off after people started giving me wierd looks.

I once saw a bumper sticker that said "Honk if you passed Quantum Mechanics."


Originally posted by T_Jesus
What QM book are you using? I used Griffiths...

You learned Sep of variables in QM before another math course? Ouch...your calc 2 prof must've sucked.


Not this one -----> Int(u*dv) = u*v - Int(v*du)

That's the cake stuff you learn in Calc 2.

This other kind of Separation of Variable is something that you use to solve

d2u/dx2 = 1/v2 * d2u/d2t

Where u(x,t) = X(x)T(t)

Substituting gives:

d2X(x)T(t)/dx2 = 1/v2 * d2X(x)T(t)/dt2

= T(t) * d2X(x)/dx2 = X(x)/v2 * d2T(t)/dt2

Divide both sides by X(x)T(t)... equate both of the new product to each other and to K... (I'm skipping a bunch of stuff) rearrange each equation to get:

d2X(x)/dx2 - KX(x) = 0

d2T(t)/dt2 - KT(t) = 0

Using Ordinary Diff Eq's the first of the two equations goes to

Acos(sqrt(K)*x) + Bsin(sqrt(K)*x)

Use the boundary condition that u(0,t) = 0 and u(a,t) = 0

and bla bla bla

It goes on. And on. And that's only for 1-dimension. 2D and 3D are even bigger pains in the butt.

Anyway I'll have to hand-write all that stuff so that it actually looks okay, and then post the pictures.


[edit on 16-2-2006 by Ralph_The_Wonder_Llama]



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