# : Schrodinger Equation

• RuroumiKenshin

#### RuroumiKenshin

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)

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

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.

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^^^^?

Originally posted by chroot
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

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).

Originally posted by Tom
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^^^^?

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.

Originally posted by arivero
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.

is rho a constant? THANK YOU!

Originally posted by MajinVegeta
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...).

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.

Secondly, do ignore my age. It is utterly irrelavant. Again, theoretical physics is not off limits to anyone.

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?

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."

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

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

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

If you want to see the mechanics problem, I'll post it.

Be my guest.

is rho a constant? THANK YOU!

It is time independent, but it is not a constant. It varies as a function of spatial coordinates.

Originally posted by MajinVegeta
It IS NOT OFF LIMITS to 7th graders.
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.")
I knew what the shcrodinger equation does
I sorta, kinda understand the equation.
Well, which is it?
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.
Well said.

- Warren

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.

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...)

...

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 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.

Originally posted by MajinVegeta
I happen to be in 7th grade, and I am highly offended by this
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

Originally posted by Tom

"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."

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?

Originally posted by Tom

... 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..).

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!

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.

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

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.

Originally posted by climbhi

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...

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.

lethe, what is proposed to replace tensor analysis??

- Warren

yeah...what ?

Greetings !
Originally posted by Entropia
...but here is my contribution to the thread:

Hmm... Hmm...
No offense, Entropia, but those equations are... nice.

Hey, what can I do ! I'm a guy, I see the important
things first...

from PF... I'll erase this - I promise ! )

"Does dice play God ?"

Live long and prosper.

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Originally posted by climbhi
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?

Yes, that is the most popular book for Physics I-II-III.

Originally posted by MajinVegeta
is rho a constant? THANK YOU!

Hi again Vegeta. rho(x), the density of probability, is a constant fuction for stationary states of a atom, this is tautological from the definition of "stationary" :)

Generally, we say that it is not constant, but "preserved". This is, the sum of the density across all the space remains constant. Of course, the peaks can move, just in this way you get a particle moving in space. In order to undestand this, one defines "current of probability", a quantity showing of rho(x) varies with time.

Originally posted by ahrkron
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.

Thank you. But what is the use of Planck's constant? Is it to measure the mass proportional to the energy level...? (I believe I have spent too much time memorizing the constants' numeral form, and not the definition)

hmm...how do I post the url for my presentation here?

Hmm... Schrodinger's Equation for 7th graders... Okay, let's do it!

First, let's have a look at the ol' Schrodinger equation:

H [psi] = E [psi].

It doesn't look so scary, does it?

Before we jump into solving for [psi], let's address the issue of what this equation actually represents anyway. In simplest terms, the Schrodinger equation is a probabilistic interpretation of the energy conservation law. For now, don't worry about what this means, let's take a closer look at the different parts of the equation.

The Schroinger wavefunction [psi] gives us information about the existence of an object in a system. By itself, it doesn't make much sense to us physically. But when we square the absolute value of this function we get a probability density function.

At this point, you might be asking yourself, what is a probability density function? To answer this question, I pose the following problem.

There is an electron sitting on top of a ruler. Just for fun, let's say the hand of God moves this electron around the ruler from time to time, but God is kind of anal retentive so he like place the electron exactly on top of integer markings... in other words, the 1 inch mark, the 2 inch mark, etc. Let's further suppose that God has told us that 1/16 of the time he puts the electron on top of the 4, 3/16 of the time he puts it on the 5, 1/2 of the time he puts it on the 6, 3/16 of the time he puts it on the 7, and 1/16 of the time he puts it on the 8. Now, I ask you to calculate the average the position of the electron along the ruler. I'm sure you readily see that answer is 6, but to calculate this statistic rigorously, maybe you would write something on paper that looks like this:

(1/16)*4 + (3/16)*5 + (1/2)*6 + (3/16)*7 + (1/16)*8 = 6

Notice the fractional factor in front of each term. These numbers actually describe a probability density function. Let's call this density function P and say that it is a function of the distance x measured along the ruler in units of inches:

P(x < 4) = 0,
P(x = 4) = 1/16,
P(x = 5) = 3/16,
P(x = 6) = 1/2,
P(x = 7) = 3/16,
P(x = 8) = 1/16,
P(x > 8) = 0.

Remember what we said before. The square of the absolute value of the wavefunction [psi] gives us a probability density function. Symbolically, this means:

P(x) = (Abs[[psi](x)])^2.

There are two important characteristics to notice about our function P(x). The first, as we're already mentioned, is that we can find the average distance along the ruler where the electron exists by multiplying each distance point by that points corresponding probability P(x) and summing these products.

Average[x] = Sum x * P(x).

In this sense, we can think of the value x as being it's own operator. When you want to find the average value of a quantity, multiply the operator by the probability density and some over all points. Here are some examples of common physical values and their corresponding quantum mechanical operators:

x --> x, x = distance;
p --> -i hbar d/dx (in one dimension), p = momentum; and
E --> i hbar d/dt, E = energy.

Don't worry about what these operators really mean right now.

The second important characteristic of P(x) is the fact that it is normalized (remember this key word). When we say it is normalized, we mean that if we sum P(x) for all values of x we get unity.

Sum P(x) = Sum (Abs[[psi](x)])^2 = 1

Let's get back to describing the Schrodinger equation. The factor H in this equation is called the Hamiltonian. It is also an operator. To really understand where the Hamiltonian comes from, you need to understand variational calculus. But to understand it's function, you don't need to know jack sh:t! I jest... you need to some sh:t... but just a little. Actually, the Hamiltonian describes the allocation of the energy in the system. In other words it is the kinetic energy plus the potential energy.

At this point, let's recap and fill in as much information about Schrodinger's equation that we have thus far established.

H [psi] = E [psi], where
H = T + V,
T = the kinetic energy of the system,
V = the potential energy of the system,
E = the total energy of the system, and
[psi] = a wavefunction which gives information about the existence of the object in our system.

Now, here comes the part you've been waiting for. We're going to solve the Schrodinger equation for the case of an unbound electron flying through the void of space! Does that sound exciting or what?

First, let's get rid of the time dependency that shows up in the energy operator.

E --> i hbar d/dt

This term only applies to cases where total energy of the system is changing. There's no external force being applied to our electron; so, we're dealing a closed system, and we can allow E to be a constant. This assumption leaves us with:

(T + V) [psi] = E [psi].

Of course, we have already stated that this electron is unbound. Therefore, we can set the potential energy to zero... leaving us with:

T [psi] = E [psi].

As we've stated before, T is the kinetic energy term. Maybe you've heard in your science class that classically kinetic energy is equal to:

T = 1/2 mv^2, where
m = mass, and
v = velocity.

Perhaps, you've also heard that classically, momentum is:

p = mv.

Well, putting these two equations together, we get:

T = p^2 / 2m.

In quantum mechanics, we must use the momentum operator for p, so:

T = (hbar^2 / 2m) * d^2/dx^2.

Our equation is now:

(d^2 [psi] /dx^2) + k^2 * [psi] = 0, where
k = (2mE / hbar^2)^1/2.

This expression is a second order differential equation. You probably won't really learn how to solve these equations until high school, but you can easily find the solution to this form of equation by simply referencing the CRC Handbook for Physics and Chemistry. The solution will give you:

[psi](x) = A*Exp[+ i k * x] + B*Exp[- i k * x].

There are two terms in this equation. The first represents a wave traveling in the positive x direction. The second represents a wave traveling in the negative x direction. We stated before that our electron is flying through space; so, let's just arbitrarily say that our electron is moving in the positive direction, and let's get rid of the second term.

[psi](x) = A*Exp[i k * x]

Now, all we have to do is solve for A. We can do this by normalizing the wavefunction.

Sum (Abs[[psi](x)])^2 = 1

In this case, we have to sum over a continuum of points. Therefore, we must actually integrate our probability density over all of space:

Integral (Abs[[psi](x)])^2 = 1.

Fortunately though, we have a shortcut because the squared absolute value of [psi](x) is:

Abs[[psi](x)]^2 = (A*Exp[+i k * x]) * (A*Exp[-i k*x]) = A^2.

So we only have to integrate over one:

Integral (A^2) = (A^2) * Integrate[1] = 2pi * A^2 = 1.

Solving for A, we get:

A = (2pi)^(-1/2).

Putting A back into our solution for [psi], we have:

[psi](x) = (2pi)^(-1/2) * Exp[i k * x], where
k = (2mE / hbar^2)^1/2.

eNtRopY

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Originally posted by MajinVegeta
Thank you. But what is the use of Planck's constant? Is it to measure the mass proportional to the energy level...? (I believe I have spent too much time memorizing the constants' numeral form, and not the definition)

That would be a very long topic by itself. You can think of it as a "conversion factor" from uncertainties in time to uncertainties in enrgy (or you can use position and momentum, or spin component in two orthogonal directions,...).

Or you can think of it as a way of counting quanta given the energy of a system.

Hey!

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!

Greetings !

eNtRopY, I lost you after :
Originally posted by eNtRopY
In quantum mechanics, we must use the momentum operator for p, so:
What's hbar and k ?

"Does dice play God ?"

Live long and prosper.

Hmm... Schrödinger's Equation for 7th graders... Okay, let’s do it!
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.
Heck, I'm only in sixth grade and I am reading The Secret Life of Quanta by M.Y. Han!
This is probably the most unfortunate result of the popular press. It's excellent that the public is so interested in scientific topics, but far too many talented physicists are just pandering to the NY Time bestseller list by publishing books that they know full well do not teach anyone anything. Even more unfortunate is that many people read these book and actually think they're being educated -- then they stand around in cocktails parties, discussing "the latest work of Hawking and Kaku," and think they're cosmologists.

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.

I am rather dismayed at how you and MajinVegeta both totally disrespect the opinion of real, practicing physicists like Tom and I.

- Warren

Unrelated question: chroot, is Kaku actually a top physicist on the forefront or is he just "pandering to the NY Time bestseller list"? Or a mixture?

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!
I'd be very very surprised if you had the mathematical background to be able to understand even the very basics.

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...

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.