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: Schrodinger Equation

  1. Mar 20, 2003 #1
    I'm dong a presentation and I'm trying to explain how to use the Schrodinger Equation to find the wave function of a particle. And I have never done that before...I have a basic idea, but to be more accurate, I need you guys' help. Note that this is for a 7th grade class presentation (so if there are other equations involved, I would be glad to know them, but at the same time, I won't be able to use them if they're too complicated for 7th graders). Thanks, I need this by tomorrow.

    heres the equation:

    i h bar d/dt [psi](x,t)=H[psi](x,t)


    thanks in adavnce!
     
  2. jcsd
  3. Mar 20, 2003 #2

    chroot

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    I applaud your enthusiasm, but you're going about this all wrong. You asked what "slope" means in another thread, then lamented how you don't understand functions -- and then you come here and attempt to teach other people how to use the Schrodinger equation?!

    Here's the progression you need to follow:

    Step 1. Learn something (thoroughly).
    Step 2. Attempt to teach it.

    Right now you're clearly at Step 1. The Schrodinger equation uses complex numbers, calculus, operators, and functions -- all of which you haven't yet learned how to use. The entire subject of quantum mechanics is essentially off-limits for 7th graders, simply because QM requires a great deal of mathematical sophistication.

    In fact, you don't even have an understanding of what the equation does -- you do not use it to "find the wavefunction of a particle." The Schrodinger equation operates upon wavefunctions. It's essentially the dynamical equation that describes the behavior of a quantum mechanical system over time. You provide it a wavefunction, and it tells you how the wavefunction changes with time.

    - Warren
     
  4. Mar 20, 2003 #3

    arivero

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    Still, you can save the day by getting the "orbital shape" from the solution of the equation. This is, you get a solution for the time-independen part of phi. There are infinity of them, usually labeled with some set of integers. Well, you take one, call it f(x), it goies from the space, R3, to the complex. You take then its modulus square, say rho=|f|^2 = f^* f.

    Now, you define "chemical orbital" by supposing rho(x) to be a density over the whole space, then asking for the part of the space that contains a 90% of the total.

    That should be interesting enoug for a 7th grade presentation.
     
  5. Mar 20, 2003 #4

    Tom Mattson

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    For a 7th grader, I would say be as visual as possible. Even in Halliday and Resnick, they introduce QM by talking about standing waves on strings, culminating with the addage that I have taught to so many classes, Localization leads to quantization.

    Instead of presenting an equation that you do not really understand, why not try to do something like that^^^^?
     
  6. Mar 20, 2003 #5
    Yeah, I know its wierd. I am really good with math that some how involves physics. Without physics involved (usually), well....

    It IS NOT OFF LIMITS to 7th graders. I happen to be in 7th grade, and I am highly offended by this (i'm usually much more contained, but this sort of discrimination is my soft spot...). The only reason I picked the equation, was because it was the first thing that popped up in my head, and I couldn't think of anything else. If YOU have something else in mind, suggest it, then I'll see if I like your idea, and I may do it. Secondly, do ignore my age. It is utterly irrelavant. Again, theoretical physics is not off limits to anyone. I studied astronomy to chemistry when I was 6, 7,8 and later moved on to physics, little by little (and now that's all I ever think about. Not stupid rap music like most kids).


    I knew what the shcrodinger equation does, I always make the same mistake and I thank you for correcting me again(although, I would have corrected myself when I actually looked at it).
     
  7. Mar 20, 2003 #6
    Like what? ^^^^^?

    I sorta, kinda understand the equation. My question is, does the Hamilton's operator specify the evolution of the wave function?

    See, I'm outta ideas. I am SO boring!! (I was maybe thinking of doing a simple mechanics problem, though. I think that's my last resort.) What do you think, Tom?

    BTW, my teacher (thank god!) changed the due date to next Friday! So I've got tons of time! If you want to see the mechanics problem, I'll post it.
     
  8. Mar 20, 2003 #7
    is rho a constant? THANK YOU!!
     
  9. Mar 20, 2003 #8

    Tom Mattson

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    It is, in fact, off limits to 7th graders who are having trouble with algebra. I do not want to dampen your inquisitive spirit, but the discrimination is completely justified.

    I think he was not so much talking about your age as he was about your level of mathematical training. Majin, I am a PhD student in theoretical physics. I will have you know that theoretical physics was off limits to me until I had my first courses in advanced mathematics (ODE, PDE, Linear and Abstract Algebra, Vector and Tensor Analysis, etc..).

    It will be no different for you.

    Like what I said...

    "Even in Halliday and Resnick, they introduce QM by talking about standing waves on strings, culminating with the addage that I have taught to so many classes, Localization leads to quantization."

    Yes. The time evolution operator U(t,t0) is...

    U(t,t0)=exp(-iHt/hbar)

    Be my guest.

    It is time independent, but it is not a constant. It varies as a function of spatial coordinates.
     
  10. Mar 20, 2003 #9

    chroot

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    I am not trying to be offensive -- I was a kid once, too -- a bright one -- and probably had much the same attitude as yourself. You will eventually realize how little you know. As I've said, the more I learn, the more I realize I don't yet know. It's unfortunate that it takes something like 20 years of education to be able to comprehend theoretical physics, but it's entirely true. (By the way, quantum mechanics is not well categorized as "theoretical.")
    Well, which is it?
    Well said.

    - Warren
     
  11. Mar 20, 2003 #10
    Okay, never mind about posting the mechanics problem. I found it in one of my books, and there is a chapter on it! What parts should I type??!! I'll go ahead and do this one, it's simple enough.
     
  12. Mar 20, 2003 #11
    I believe what they're saying is you need to start from the very bottom and work your way up. Enthusiastic or not, you can't just skip ten years of material. Take it from me, I'd love to be jamming about theoretical physics with these guys but I realize I've got a lot of work to do before that can happen (slowly but surely working through a general physics textbook that's older than I am). One step at a time.
     
  13. Mar 20, 2003 #12

    chroot

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    I also feel the need to tell you that I am highly offended that a 7th grade kid who doesn't know functions is trying to tell me he knows theoretical physics. It's pretty much akin to telling a maestro that you could play his instrument as well as he in a day or two.

    - Warren
     
  14. Mar 21, 2003 #13
    Tom, you've mentioned Halliday and Resnik twice now. I'm just wondering what their signifigance is... they're the authors of my physics text for right now, and it sounds as if you're introducing them as the standard of physics texts, am I reading you right on this or what?
     
  15. Mar 21, 2003 #14
    Hey Tom, I'm undergrad in physics right now, planning to go to grad school, I've been trying to look a little ahead and plan my math courses, from what you have listed here it looks like I'm pretty much online.

    What I have is ODE & Linear Algebra, PDE, Complex Variables, and from here I'm not sure where to go. You mentioned Abstract Algebra, we have a class here called Modern Algebra, is this the same, and should I plan on trying to fit this in? Also this Vector and Tensor Analysis, in what class would I find this sort of math?

    Would a Foundations, or Intro to Analysis (I and II) be a good class to look into, how bout topology. The topology seems like it would be a good one, but that requires I take both semesters of analysis first which could be hard to fit in. Anything else that would be good, complex analysis, more advanced classes in diffirential eqn's, etc...

    Thanks!
     
  16. Mar 21, 2003 #15

    ahrkron

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    Majin,

    As other did, I really applaude your enthusiasm.

    I agree also with some when they say that you need to learn much more math, but

    Come on guys! she is not asking for the gory math details of how to expand H-atom states in sherical harmonics. She wants to make an intelligible presentation for 7th graders. I think that can be done if she asks enough questions and we look for simple analogies.
     
  17. Mar 21, 2003 #16

    ahrkron

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    Here's a start (I don't know how long the presentation should be... I'll assume 30 minutes; I also don't know how much math you can use or understand, so I will use the least I can... please don't get offended):

    Outline of the presentation:
    - The equation
    - Psi
    - "i hbar d/dt"
    - H
    - Putting it together
    - What is a "solution" for this?
    - What we need to learn

    Contents:

    - The equation: just show it.
    - Psi(position, time). It is a math object that tells you how likely it is to find a particle. The Psi for me would be like:

    Psi(in front of my computer, right now) = 100% (absolutely sure)
    Psi(in bed, tonight) = 30%
    Psi(at the office, 9 am) = 0%
    (plus a huge list of other position-time combinations)

    If you feel confortable with plots, you can show a plot with a gaussian, and show where it is likely to find the corresponding particle.

    - "i hbar d/dt"
    It is like a "magic wand" that transforms Psi into another function that has to do with how Psi changes.

    - H.
    Another "magic wand". It transforms Psi into a different Psi. Not any different Psi though. The precise recipe of the transformation is related to the energy of the particle.

    - Putting it together
    So, the equation says basically:

    The change in the probability of finding a particle here or there has to agree with what H does to the said probability

    - What is a "solution"?
    The two "magic wands" up there can do different things to Psi. "Solving" the equation means finding the family of Psis that give the same result when acted upon by "i hbar d/dt" or by H.

    - What we 7th graders need to learn.
    In order to really understand those "magic wands" (and the full eqn), we need to learn about: algebra, complex numbers, diff calculus, linear algebra, differrential equations and a ton of physics.
     
  18. Mar 21, 2003 #17
    abstract algebra is most likely the same class as modern algebra. if your scholl calls it one, and not the other, don t pay any mind.

    as far as usefulness for a physicist goes? well physicists use some very basic group theory, but mostly not what is taught in a math class. physicists use a lot of representation theory, and some math programs teach this, most that i have seen do not. i would recommend you take one semester of abstract algebra.

    tensor analysis is not taught in any math class. most mathematicians want this notion completely abolished. only physicists (and not mathematical physicists), use tensor analysis.

    nevertheless, tensor analysis is something most physicists need to know. you will probably have to learn that on your own, or else some beginning grad class in physics will teach it to you.

    analysis will be completely useless for physics. don t take that unless you think you want to also major in math.

    if topology requires analysis as a prereq (it did at my school), it is not because you need to know analysis to do topology, but rather only because topology requires a certain level of mathematical sophistification. if you think you have a great level of mathematical sophistification, then skip the analysis prereq. that is my advice.

    topology can be useful in certain aspects of physics, but analysis is not.
     
  19. Mar 21, 2003 #18

    chroot

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    lethe, what is proposed to replace tensor analysis??

    - Warren
     
  20. Mar 21, 2003 #19
    yeah...what ?
     
  21. Mar 21, 2003 #20
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