$k$ is the wavenumber: $2\pi/\lambda$. By 'lesser planck constant', do you mean 'reduced planck constant'? In that case the symbol is $\hbar$ \hbar. Also, that's not the schrodinger equation, just a particular solution given some function $u(x)$ for potential, which seems to be constant here.

Yes, I meant reduced instead of lesser. And I have no experience in LaTeX, I just created this equation in the Grapher Application that came with my Mac. I am sort of confused with the u(x)...

I fixed it for you. Anyways, LaTeX (rather MathJax) is down at the moment. $U(x)$ is the potential energy function. Also written as $V(x)$. Could you provide a link to where you got that equation from? Its not the schrodinger equation, rather a specific solution of it. Kind of like how you get a specific solution for $y$ in $x+y=11$ when you substitute a value for $x$. The specific solution is not the whole equation....

Just out of interest, how much Quantum mechanics do you know? It's better to stay away from the schrodinger equation till you know enough calculus as well as general physics. If you want to graph some solutions of it, I would suggest showing electron orbital graphs or something. Also, how are you connecting QM to Theory and Logic?

@Manishearth, I know, it is a very large challenge for me, but in my school I have a math teacher who used to teach calc, so I have resources there. And as for the logic, the whole purpose is to prove that it is possible under certain conditions that a cat can be dead and alive at the same time.

So this is more of the wave function graph-equation, right?

@CodeAdmiral Are you sure you have researched schrodinger's cat thoroughly? IIRC it's jo longer really accepted as something that could actually occur. And I don't see how you would prove it without some deeper QM...

@Manishearth I am just starting out this project, so I am still building my understanding. That being said, I need something that I can use when presenting to kids who aren't as "gifted" (so to speak) to tie the theory and the proof behind it to where they can understand.

@CodeAdmiral That's not enough calc except for the simplest wavefunction (box potential well). Solving a partial differential equation is way above school level (theses are written on certain PDEs).. Oh, I didn't quite understand your second comment? Are you asking if there are more such wavefunctions? Definitely, there are infinite. Out of which quite a few have been analysed.

@Manishearth I got the equation-thing from hyperphysics.phy-astr.gsu.edu/hbase/quantum/scheq.html#c2 And also, is this more of an equation I would graph?

@CodeAdmiral The issue is that the copenhagen interpretation is somewhat outdated. I would say it's best to use the cat as an anecdotal example. Don't try to prove anything,

@Manishearth So you are saying find a more recent interpretation to use as the base of my project... Right?

If you want to explain QM to peers, you may want to have a peek at the "why shouldn't they be close" section of this answer: physics.stackexchange.com/questions/20962/… . I've explained wave-particle duality and what a QM wave is in terms that students can understand.

@CodeAdmiral: A more recent interpretation would be even worse. I'm saying that you should be aware of the complexity of the situation. It's outdated, hard to prove, and you'll end up confusing your peers. Instead, just explain to them what a superposition is, first use a normal example, then use the cat.

@Manishearth Wow, that is one heck of an answer! Thank you so much! I think this will greatly help me.

If you can't talk in chat, let me know via a comment.

(there's a rep requirement i think)

I think I can talk in chat...

Yep! I can, and I think it is twenty, but it doesn't seem to be a problem.

I guess that's because I created the room

Here are some atomic orbitals: falstad.com/qmatom

they're wavefunctions as well

And the rounded-d is a partial derivative, correct?

Yep

it's called 'del' or 'partial'

Yeah, I have a live resource that explained that to me.

To explain QM, I'd say you start of with the history

First explain the debate between particles and waves--how Young's experiment proved that they were unequivocally waves

And how the pholoelectric effect proved how they were unequivocally particles

(they=light here)

Which meant everyone was o_0

Finally, they suggested that all light is both photons and waves

BOTH being the keyword

So I start with the cathode rays and the work of Faraday, and move from there?

Maybe not cathode rays..

I'd say start directly with Young's expmt

You know what it is?

(Wikipedia will confuse you, don't go there)

Not exactly... In the papers I have printed out I have not come across Young's Experiment...

Consider a setup where you have a screen

Parallel to that there's a cardboard wall

In the wall you have a slit

You mean the doucle-slit experiment?

yep

You know it?

(and how to explain it using ripples of water?)

Well, I saw it in one of my articles. And I should be able to explain it fairly well.

Great!

(Oh, in response to your comment: physics.stackexchange.com/questions/22322/… , I meant thatyou should take a nonliving object. Maybe a simple flashlight that's on or off)

Alright

So, now explain how (using ripples), a YDSE can be explained through wave nature

but not particle nature

because particle-light would give two spots on the screen

Also tell them about the photoelectric effect

Yeah, or kind of like the paradox of if a tree falls in the woods, does it make noise if falls, sort of, right?

Nothing too confusing yet.. First simple, easy-to-wrap-head-around example. THen the confusing cat/tree ones

Now, once you have established that everyone (in the past) was confused about light, explain that this, in conjunction with other things, made them believe that light was BOTH

Meaning both particles and waves, right?

Now you can inch towards the copenhagen interpretation

Yep

EM waves but also photons

Now explain to them a modified YDSE (YDSE=young's double slit expmt)

And how the wavefunction collapses in the event of measurement (meaning the Copenhagen)

where photons are sent one by one into the slits

Yes, but not yet

In this case, we STILL get a fringe pattern

even though there is no other photon to interfere with.

Fringe pattern... oh boy, haven't heard that yet...

Only one photon between the slits&screen at any one moment

Oh, fringe pattern is the alternating bands in the YDSE

Okay, gotcha.

Now, the confused people were even MORE confused

What can the photon interfere with?

It was soon established that it interferes with ITSELF

Which is absurdish

How?

It turns out that effectively HALF a photon goes through each slit

Wait, half a photon?

But, one can argue that a photon is a quantised packet..

How does that work?

Exactly

This is where copenhagen starts worming in

It turns out that a photon is a wave, right?

BEcause if a photon wasn't a wave, it could not split into two and go through a slit!, right?

Well, it turns out that the wave is a probability wave

Meaning...

This means that the value of the wave at each point is related to the probability

That is key, isn't it?

Of finding it there

Yep... I'll explain a bit as i go on.. A lot of this is explained in the linked answer

Alright, gotcha. I will print that out and read it during our boring one-hour reading time UGGGHHHHH

You may have to stitch together the pieces(this chat+that answer) to make your lecture comprehensive

Note:the other parts of the answer are irrelevent. Only the section I mentioned is relevant

Alright.. So we have shakily established that a photon wave is related ti the probability

Yeah, and judging by my audience, I will have to put a lot into stitching it together. Thank God I have until May

So, if it has a half-half probability of going through either slit, there is effectively half a photon in each slit.

And that goes back to the cat being dead and alive!

This is also key: when something is in such a superposition, it exists in BOTH STATES AT ONCE

Yep

But don't give that yet

Exactly what I am trying to say in this project.

Since your audience will still be confused

Now would be the time to explain the linked answer

Actually not yet

So... I need what piece before the linked answer?

One more experiment: a YDSE, but this time set up so that we know which slit a photon went through (complicated mechanism, dont worry about it)

Now, in this experiment, the fringes disappear and we get a simple two-spot pattern.

Basically log which slit the photon went through?

Actually it would be better to explain the linked answer before this

And the wave function collapses!

Awesome.

I feel proud of myself now... :D

That SHOULD be enough to move onto more complicated examples at this point, right?

They should be able to automatically figure out what happens themselves if you explain the YDSE, one-photon YDSE, linked answer, and then detectorYDSE in that order

They'll feel proud as well:D

Yep. Now you can first put a flashlight with an on/off button in the cat box (without the cat) so that its on if the decay occored and off if it didnt

Don't assume anything with my audience, i will have left half (if not more) in the dust.

Well, those who are listening..

Once you explain that the flashlight was both on and off at the same time, move on to the cat

You can give the tree as a Zen example as well

So when the flashlight is on, the cat is dead. And vice versa, right?

In your example

Not really

Two separate experiments.. Going directily to the cat can confuse them

First set up box with atom and gieger counter

Put the flashlight inside, attached to the gieger counter

Thats experiment 1

So the light goes on if there is decay, right?

Now replace the flashlight with the hydrocyanic acid-hammer-cat thingamajig

Yippy! Cat killing device!

Yep.. You can make it go the other way if you want. Makes no diff

GOtcha

You may also enjoy this:

Suspense!

abstrusegoose.com/6 and abstrusegoose.com/7

(not suspense, i was finding the links :p)

And this: abstrusegoose.com/74

The wierd pointy symbols are called kets. Basically |A> (ket A) denites state A

*denotes

The 1/sqrt2 is there because the kets act like perpendicular vectors on addition, and they must add up to a vector of length one

Aah, if i think of anything I'll just post it here.. Or maybe ill email you... Keep me posted on your progress on the project! (ill send you a blank email)

Bye then :)

Bye :)