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Physics experts - Please help me describe the wave function to my students!

Hulk

Hulk

Diamond Member
I am a high school Physics teacher and always have difficulty giving my students a qualitative description of the wave function. I know it really can't be described except by mathematics but I do think there must be a way to give them something they can sink their teeth into. Somethign that will lead to further discussion.

Of course when talking about the square of the function it's easy enough to talk about the probably of a particle being located at a certain position in space/time. But what about the wave function (psi) itself? How do scientists use it?

The explanation I have been using is something like this. Please realize that my background is Mechanical Engineering and not extremely well versed in Quantum Mechanics myself.


1. Describe qualitatively what the Schrodinger wave equation tells us.
(The wave equation tells us what feature of the electron or other particle is actually "waving." For all types of waves some field quantity is varying in time. For waves on strings its the transverse displacement of the string that is waving, or varying its position with time, for sound waves it?s the differential pressure, and for electromagnetic waves it?s the electric and magnetic fields. For matter waves the wave function, psi, which is also a field quantity, is what is waving. To describe a problem involving matter the wave function must be known as a function of space (position) and time. Psi(r,t) where r is a position vector.

Is this really bad? Hopefully I haven't mangled the physics too much.
 


<< Please help me describe the wave function to my students! >>



Holding arm/wrist/hand rigid and upright, move the limb from side to side in a short, rapid motion, approximately 2-3&quot; of travel in both directions. 😛
 
I didn't understand your explanation at all, but I just started taking physics, my teacher is probably much worse than you (I can almost guarantee it), and I'm very tired. I'd offer help, but I haven't learned it myself. Don't worry, if you don't explain it well, we always can just read the book before the test.
 
When I was in high school (last year) doing an advanced physics program, I did not have to learn some of the terminology that you are using there. Even in university, we're doing physical waves (simple harmonic motion and such) right now, and we don't have to use some of that terminology.

The most obvious way to explain a wave is simply by drawing a sinusoidal wave (mentioning its the same sine and cosine waves from their math class) on a coordinate axis with distance or time on the x-axis and height or something on the y-axis. If they don't understand / can't visualize a sinusoidal wave, I'm pretty sure stuff about position vectors and Schrodinger's equations will confuse them.

Just start at the beginning and work from there. A nice explanation of transverse vs. longitudinal waves. Explain using a transverse wave that there is a &quot;particle&quot; speed up and down as well as a wave speed left and right (yes, I know that I'm simplifying the situation). Explain that for a longitudinal wave that the particle speed/displacement occurs in the same direction as that in which the wave travels (the propagation direction).

If they are just beginning, start solely with physical examples and transverse waves (waves on a string). It's the best for visualization. Unless they are already familiar with waves, they can't really get too much into electromagnetic waves or sound or light (although light can be simplified).

When you say that &quot;differential pressure&quot; is varying for sound waves, I doubt many students would understand. I also doubt they understand enough about electric and magnetic fields to understand how electromagnetic waves work. The string probably works the best.

Sorry for my rambling here. I will say though that I commend your efforts on trying to teach your students even better--striving for excellence. There really should be more teachers who are willing to take the time and effort to make the class easier to understand and more enjoyable. Some teachers are boring, talking over the heads of students and don't care. Again, I commend your efforts.
 
I guess the problem is the wave function can't be physically interpreted in a simple manner. Also, it cannot be verified experimentally (although psi^2 can).

I just want to get across the point that for a string of an instrument say, the string is &quot;waving&quot; back and forth and the quantity waving is the displacement (position) of the string.

Although we can't really visualize the wave function, IT is the thing that is waving or varying in time. The variation of the wave function, psi itself is the &quot;waving thing.&quot;

Hopefully one of the physics gurus around here can help me out...
 
Yahoo, I can finally put my optics degree to work. Seriously, is this for a regular physics class or an AP class? There are many ways to describe the wave. You can use Shrodingers(sp?) equation or you can use Born's statitical interpretation. I think both of these might be a little much for highschool. The problem is that the classical wave is a little different from the quantum wave. The classical is real easy to explain and the quantum is still a pain in my ass. If want a really deep explanantion than I can give you one. Just ask.
 
Jeez man they're just highschool kids, I had highschool physics, did pretty well and it wasn't generally considered to be an easy class btw, and I'm a bit confused 🙂 Think you might be getting a bit more advanced than what they need to know?
 
Yes, it's an AP class.

I just want to do more than my teacher did. That was basically write psi on the board and say &quot;yeah, that's the solution.&quot;

I think it's an important topic. We wouldn't have computer, lasers, and a lot of other conviences we take for granted without the Schrodinger's wave equation.

I don't want them to derive the equation for the ground state of He or anything. Just to have a &quot;feel&quot; for its significance.
 
I think that you are going to have to do this by using mostly commen sense. You can't explain it by deriving it because I think everyone would get lost. All you can really say about the wave equation is that it a solution to the time dependent Schrodinger equation. The wave equation tells all sorts of things about the particle. Where its at, the speed, and so on. good examples would be the string on a musics instrument and stuff like that. I'm sorry if this sounds confusing but I am trying not to go into the quantum side of it. You know, things like the particles position is not known the instant before and after but is known only when it is measured. It would be nice to descsribe to the students everything about the wave equation but I had a class just on it. It would be really hard to do without the math or calculus. My teacher in high school always had a lot of demos that kept us interested. Good luck in your explanantion.
 
Hmm.. I don't remember AP Physic going into Quantum Machanic at all.. I think you might be going a bit far. But hey, I just finished HS, dont' listen to me!


I think the problem you're facing is that the majority of your students don't have any clue as to what Quantum Physics or Particle Physics is. Since it's an AP class, it should be taught while using some Calculus. At least that's the way in my HS, we don't have a Phys. AP and a Calc AP class seperately, only exist as a bundle Calc/Phys AP.

I'm and odd ball in that a few years ago I was really into this quantum theory stuff, but I'd bet 99.99% of your students probably doesn't read up on Steven Hawkings as a Hobby. I think the first thing you have to do is to get the &quot;theory&quot; part into their mind first. Quantum Theory is relatively far fetch from everyday reality, and even more for those who had learned classical physics all their lives. Basically, you gotta get them into the mind set that in the Quantum level, nature works differently, and lay out several &quot;ground rules&quot; to them.

How do you want to explain it to them? Like as in Pure math or Pure Theory? I don't think AP level have enough math to solve or sufficently understand the Schrodinger wave equation from the math point of view. Wave particle physics is hard to explain, I guess you just have to tell them that any measurement is only accurate at that moment of time at that point in space. And basically when any particle goes from point A to point B, it will semitaniously take ALL possible route to get there. Your students will freak hehe.

Bottom line, if you're just looking to explain the math, I don't think your students are ready for it, 1st year calculus is just not enough to understand those function. Try a more theorlitical approuch, and spike up their interest in this and get a discussion going first... Then you might have something.
 
If you want a physical demonstration, my teacher placed a slinky sideways on the floor and moved it side to side so that we could see the displacement of the slinky from where it originally lied. Then he explained how the peaks and troughs were amplitude, etc. I don't know if that's what you're looking for, but it might give you an idea.

-Tom
 
Use the special teacher super powers: find a video on it and show it to the class.

Either that, or ramble on about your personal life. Another secret teacher super power that many teachers have used in my classes.
 
what is the wave function itself? which one you refering to?
PSi? how come i never heard of that?

i have done a fair bit of physics in high school and now in engineering

could the use of Simple harmonic motion explain the wave effect of particle?
 
wave function? as in Sin wave??

A very easy visual aid would be to use a rope. Move it on one end to simulate a sin wave.

As practical example of sin wave, get a electronic scope, and show them what an AC wave looks like. Tells them that this is what's coming out of the plug at home.

BTW,
Your explanation is too complicated for HS students. I took AP Physics, I had two physics class in college, and I think that language you use is still too high.
 
Hehe, I taught a class on quantum wave theory. Of course it was a graduate level course 😉.

As others have already said, stick to the classical wave problems if you want to talk about waves. Quantum waves can't really be explained in anything other than mathematics, and you would probably lose most of the class if you got into that. And there are very few good examples to demonstrate quantum waves. A HS class is definitely not the place to get into it. Hell, 1/4 of my class failed and they all had degrees in physics 😱.

If you just want the class to learn a little about QT (quantum theory) just give them some highlights. Nothing about QT makes any sense without looking at the mathematics, and I believe that is probably way over their heads. Hell, some of it is over my head, and I got my PhD doing QT research.
 


<< Please realize that my background is Mechanical Engineering and not extremely well versed in Quantum Mechanics myself. >>



then why are you trying to explain the Schrodinger wave equation to HS students?

you teaching quantum mechanics?
 
My physics teacher never took physics in HS and took Astrophysics in College, yet she's capable of being hired to teach this stuff to us.
 
In my opinion, there's just no way that high schoolers will be able to grasp the material you're trying to teach them. As the others have observed, the math background is just not there, they would need to know integrals at the very least, to comprehend the wave fcn. (integrating over all space, normalization, etc.). BTW, isn't Psi and the Schrodinger eqn. and all that good stuff the concern of physical chemistry? That stuff was difficult enough for me as a junior in college!
 
bring a demo of a pendulum or a spring or something that oscillates. Explain its like a wave function if you plot the displacement over time. They'll get it.
 
vertical axis shows the distance between the bike rider's foot and the ground; horizontal axis shows the distance the bike has traveled. to me, that's a wave.

yes, i'm not a scientist 🙂
 
It'd be hard ... and no matter how good your explaination is, only a few would understand it.
Heck, read back to some previous comments in this thread ... they don't even know what you're trying to do. Describing it like a physical wave isn't going to help, only to confuse. In fact, I would avoid mentioning it all together just not to get them mix up in their head.
 
Mday-

I believe you may have misunderstood what I am saying.

I am not a expert at Quantum Theory but I believe I do have enough background to give a brief introduction to Quantum Mechanics and I would like that introduction to include the Schrodinger wave function.

All I was asking of the forum was some opinions on how to approach it, how far to go, etc...

I don't need to be insulted. I was only trying to establish that I don't proclaim myself an expert. Unlike many science teachers I like to be well versed in something before I teach it. I feel I must be prepared to answer questions/engage in discussions well beyond the current material if need be to spur student interest.

I don't want to get all insecure on you but I have had a bit of math and science in college.
5 semster of calculus (including partial differential equations)
4 semesters of physics
2 semesters thermodynamics
statics
dynamics
vibrations and controls
design of thermal systems
finite element analysis
mechanics of materials
heat transfer
aerodynamics
aircraft structures
elementary ciruit analysis
applied numerical methods for digital computation
fluid mechanics

and many others.

I do believe I am qualified to teach high school physics. Thank you.
 
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