Using the Schrodinger Equation to Find Particle Wave Functions

[RuroumiKenshin]

Originally posted by Einstiensqd
As for the statement that Quantum Physics is off limits to seventh graders, that is a mockery of what the children of today can learn! Heck, I'm only in sixth grade and I am reading The Secret Life of Quanta by M.Y. Han! So if anyone has the nerve to say phyisics is of limits off kids, you are officaly going to be posted as an idiot somewhere on this site where it is most embarresing to see it!

Really, cool! Greetings, fellow kid. I'm in 7th grade!

What if I start a thread on this...should be interesting...

 

[ahrkron]

Originally posted by Mulder
I'd be very very surprised if you had the mathematical background to be able to understand even the very basics.

I think we shouldn't transform this thread in one about the ability of seventh graders to understand the math of QM. It would be much more fruitful to try to explain the concepts behind it with as few math as possible.

Which, by the way, is an excellent way to see to what extent one understands the physics behind the equations.

 

[RuroumiKenshin]

I agree with ahrkron. It would be much more logical and productive.

 

[Mulder]

Of course, that post probably came out wrong. Its great that you're trying to learn about things long before you get to them in school . I'm sure I hadn't even heard of Quantum Mechanics when I was 13

 

[RuroumiKenshin]

I'm sorry Einstiensqd, but reading a pop paperback book on quantum physics is not the same as learning quantum physics. If you stick to it, you'll discover this soon enough on your own.

Then what's he supposed to do?? Books are the only wat kids like us can learn about things our schools will not teach us.

I will be taking a mechanics course(physics:motion) at a university. Would that be any good?

 

[eNtRopY]

Originally posted by Einstiensqd
As for the statement that Quantum Physics is off limits to seventh graders, that is a mockery of what the children of today can learn! Heck, I'm only in sixth grade and I am reading The Secret Life of Quanta by M.Y. Han! So if anyone has the nerve to say phyisics is of limits off kids, you are officaly going to be posted as an idiot somewhere on this site where it is most embarresing to see it!

Of course everyone here knows something about quantum physics, at least in the qualitative sense. With the popularization of quantum computing, quantum teleporation, photonics, semiconductors, and nanoscience, it would be difficult for anyone living in the western world to get away with not knowing anything about quantum physics.

At most universities, a two semester course sequence in quantum physics is taken in the senior year of the physics major. A two semester course sequence in quantum mechanics usually isn't taken until graduate school. Students doing their graduate work in theoretical physics may take four semesters of quantum mechanics.

Anyway, seventh graders haven't even taken a single class in calculus. Most physics majors will take three classes in general calculus, a class in differential calculus, a class in ordinary differential equations, a class in partial differential equations, a class in matrix algebra, and a class in probability before they begin taking quantum physics. So, I seriously think you should have more respect for the opinions of those you refer to as idiots.

By the way, I read the Secret Life of Quanta back in 1996. From what I remember of it, it's poorly written, there are little to no equations, and it basically just describes some very general concepts relating to solid state technology. For seventh graders, I would recommend http://ez2find.com/go.php3?site=book&go=1874166374 .

eNtRopY

 

[eNtRopY]

Originally posted by drag
What's hbar and k ?

hbar is Planck's constant. It is a constant which describes relationship of uncertainty between quantities in quantum mechanics. k is the wavevector, but in the special case I presented, we can think of it as just being a substitution variable for

k = (2mE / hbar^2)^1/2.

In other words, where ever you see k, replace it with (2mE / hbar^2)^1/2 in your mind. It makes the equation look a little cleaner.

eNtRopY

 

[eNtRopY]

Originally posted by chroot
Phenomenally good attempt, but I really don't think any real seventh grader would actually be able to follow even a quarter of that material -- especially when you introduce operator notation and begin performing derivatives. ;) One can gloss over details such as how to solve a differential equation, but one can't easily escape the detail what is a differential equation?. Still, I applaud your effort. I think your Intro would be better suited for second or third year undergraduates. Remember, these seventh graders are still learning what functions are.

Well thanks. This is good feedback. I'm actually thinking of developing two books. One would describe some advanced topics of physics to people with absolutely no mathematical background. I want to make it as simple as possible to understand. I'm thinking of calling it Kindergarten Physics.

The other would simply describe advanced physics topics with all the exhausting details. Basically, I would just take one of Tipler's books and include every last detail one would need to understand the book. I mean I would include derivations for all the math and explanations for all the physics used every step of the way. There would be a great deal of redundancy and the book would probably be 10 to 20 times longer than any other modern physics text, but I think there might be a market for something like this. I think I will call this book Modern Physics for Retards.

eNtRopY

 

[climbhi]

Originally posted by Einstiensqd
As for the statement that Quantum Physics is off limits to seventh graders, that is a mockery of what the children of today can learn! Heck, I'm only in sixth grade and I am reading The Secret Life of Quanta by M.Y. Han! So if anyone has the nerve to say phyisics is of limits off kids, you are officaly going to be posted as an idiot somewhere on this site where it is most embarresing to see it!

Who cares what you're reading, when I was a third grader I though my dad's "advanced astrodynamics" text looked neat and would make me look smart so I started reading it. But that's all I did was read the words on the pages, I didn't understand one single bit of it! In fact now as a college student I'll still occasionally go back and look at it and still have a hard time fully understanding it (partially because it teaches from an engineering standpoint whereas I'm used to a physics approach to things but...)
I don't think what the people on this forum are saying is "stay way the heck away from theoretical physics until you have enough math to be a PhD" but what they are saying is "realize that theoretical physics requires enormous amounts of mathematical sophistication which almost all seventh graders are incapable of understanding. If you want to dive into it just because you're fascinated by it and want to see what's on the frontier for you go for it, but realize that you will not actually be understanding it, and this might lead to some dangerous misconceptions that might be hard to overcome later on down the road when your grade is on the line!"
I still occasionally find myself peeking into graduate texts just so I can see what's on the horizon for me, just because I'm fascinated by it. And I'm not saying it's bad for seventh or sixth or first graders to do this also, but just realize that its way out on the horizon. I learned this the hard way reading through 500 pages of astrodynamics while I was still grappling to understand fractions, it just didn't work.

 

[climbhi]

CU Boulders physics department website also has some very good not mathematically oriented introductions to various topics in quantum physics. They are fun and illustrated and have really neat interactive applets to go along with everything which makes it really fun. I'll try to find a link for it.

 

[Mentat]

I understand that this has been a large detraction from the point of the thread, but I would like to point something out: You can pay thousands of dollars to go to a good school to learn advanced mathematics (and please note, I'm not putting this down) or you can check out books from the library and surf the net a little, and learn the same things.

This may sound wrong, but I have studied all of math, up to Calculus and Analytical Geometry, with books from the library. I have also seen the such complicated equations as those required for String Theory, on the internet. It is all available to people who look and try hard enough.

 

[Mentat]

I would also like to point out that those who have said that it's unlikely for a 7th grader to understand adavanced mathematics, you are correct. However, it is not impossible.

While one should never attempt to discuss complicated ideas, without the proper foundation, one is entitled to ask for a layman's explanation of any advanced concept. Einstein said that Physics should be shown as just pictures, and that mathematics were just to work out the details. I pretty much agree with him.

 

[climbhi]

Originally posted by Mentat
Einstein said that Physics should be shown as just pictures, and that mathematics were just to work out the details. I pretty much agree with him.

I agree with this too, but you've got to remember the details are very often the most important part. Also, let's say that I just bought a tremendously amazing computer, and I wanted to understand how it worked so I spend a lot of time having the very people who built the thing explain to me exactly how it works, all the way back to first principles and 1's and 0's and such. I would have a great conceptual understanding of computers, but it would be of no use to me until I learned how to use it, which can be a very complicated process these days (you should've seen my dad try and teach my grandma how to use her first computer, it was hilariously pathetic!). So in my little analogy, knowing how the computer works equals reading a brief history of time, or something else and getting a conceptual understanding, acutally knowing how to use the computer (the important part) equals knowing how to use lots of math.

 

[climbhi]

Originally posted by Mentat
I understand that this has been a large detraction from the point of the thread, but I would like to point something out: You can pay thousands of dollars to go to a good school to learn advanced mathematics (and please note, I'm not putting this down) or you can check out books from the library and surf the net a little, and learn the same things.

This may sound wrong, but I have studied all of math, up to Calculus and Analytical Geometry, with books from the library. I have also seen the such complicated equations as those required for String Theory, on the internet. It is all available to people who look and try hard enough.

I do think that there is something to be gained from learning something from an expert. I am a professional rock climber and have seen a few people who go out and read every single book there is on advanced climbing technique and think it will turn them into a great climber. In reality they just learn a bunch of vocubulary words and don't really become much better climbers. What you really need to proress in climbing is to find someone who is extremely good at it who likes to teach other people how to be good at it who will partner up with you and take you in the right direction. I think the same applies in math and physics education.

 

[Mentat]

climbhi, I know that the details are important - and am rather positive that Einstein did too. He was just saying that a physical concept should be expressable as a picture, so that anyone can understand/conceptualize it, and that the mathematics was the paint. IOW, the one that comes up with the idea, needs mathematics to paint the picture of the reality he/she is trying to describe. But this reality should be (in some way) "visual" - even to the layman.

 

[climbhi]

Originally posted by Mentat
climbhi, I know that the details are important - and am rather positive that Einstein did too. He was just saying that a physical concept should be expressable as a picture, so that anyone can understand/conceptualize it, and that the mathematics was the paint. IOW, the one that comes up with the idea, needs mathematics to paint the picture of the reality he/she is trying to describe. But this reality should be (in some way) "visual" - even to the layman.

Yes I agree with this

 

[eNtRopY]

So, MajinVegeta... if that is indeed your real name...
did my explanation help you at all, or did you find it confusing? I only ask because, as I've previously stated, I am planning on writing a pop-sci book someday.

eNtRopY

 

[RuroumiKenshin]

Entropy, I think what you wrote is BRILLIANT. I am 100% sure that it'll be a best seller. You made it very easy to visualize. From my own experience, kids who don't enjoy reading the dictionary like I do have hard time understanding some "long words", as they call'em. So my only suggestion is use smaller, more common words. I love it! I'll print it out, and have my friend read it (she's a kids as well).

No, my name is not MajinVegeta. MajinVegeta is the name if a Dragon Ball Z character.

 

[Stranger]

Well Majin I do understand your interest in quantum physics...I don't actually know about the function you asked for so I 'll explain about another equation that is easy to put in words...

[pard]^2 [psi]/ [pard]x^2 + [pard]^2 [psi]/ [pard]y^2 + [pard]^2 [psi]/ [pard]z^2 + 8 [pi]^2m/h^2 (E-U) [psi] = 0

m - mass of electron
E - total energy
U - potential energy

The equation indicates the variation of the value of wave function along x,y and z axes.
In a wave the amplitude is [psi]...as the electric field strength increases, the value of [psi] also increases and reaches its maximum which is indicated by the peak in the curve. Then the value of [psi] decreases. Above the x-axis it is -ve, at the x-axis it is 0 nad below it is -ve...Thus when the electric field strength is high, the intensity of light is high...[psi] denoted the intensity of the electromagnetic wave...the intensity of light is proportianal to the intensity of amplitude ( [psi]^2)...so [psi]^2 can be taken as the intensity of light or other electromagnetic radiation...In terms of photons, where intensity is high, it means that the density of photons is high...we may conclude that [psi]^2 indicates the density of photons in a certain space...
thats all I know about this equation...by the way...guess who I'm..