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I am an eighth grader in need of some guidance in my school project on Quantum Mechanics, Theory, and Logic. I am attempting the create a graph of the Schrödinger Equation given the needed variables. To do this, I need to know what all of the variables mean and stand for.

For starters, I get to the point of:

$$\Psi \left( x,t \right)=\frac{-\hbar}{2m}\left( i\frac{p}{\hbar} \right)\left( Ae^{ikx-i\omega t} \right)$$

Where $\hbar$ is the reduced Planck constant. And my guess is that $k$ is kinetic energy of the particle, $m$ is the mass, $p$ is the potential energy, and $\omega$ is the frequency.

What are the other variables?

Also, am I right so far?

AccidentalFourierTransform
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fr00ty_l00ps
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    $k$ 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. – Manishearth Mar 13 '12 at 14:40
  • 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)... – fr00ty_l00ps Mar 13 '12 at 14:44
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    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.... – Manishearth Mar 13 '12 at 15:22
  • 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 Mar 13 '12 at 15:25
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    CodeAdmiral: That is a real challenge to have a school project on QM, Theory and Logic. Maybe you can explain a bit want you want to achieve, simply plotting the given equation will look basically like a wave: $f(x)=a*sin(x)$. As Manishearth already pointed out that is not the Schrödinger Equation. – Alexander Mar 13 '12 at 20:17
  • @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. – fr00ty_l00ps Mar 14 '12 at 13:37
  • So this is more of the wave function graph-equation, right? – fr00ty_l00ps Mar 14 '12 at 13:38
  • @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 Mar 14 '12 at 13:41
  • @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. – fr00ty_l00ps Mar 14 '12 at 13:44
  • @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 Mar 14 '12 at 13:45
  • @Manishearth I got the equation-thing from http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/scheq.html#c2 And also, is this more of an equation I would graph? – fr00ty_l00ps Mar 14 '12 at 13:45
  • @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 Mar 14 '12 at 13:46
  • @Manishearth So you are saying find a more recent interpretation to use as the base of my project... Right? – fr00ty_l00ps Mar 14 '12 at 13:48
  • 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: http://physics.stackexchange.com/questions/20962/do-particles-and-anti-particles-attract-each-other/20972#20972 . I've explained wave-particle duality and what a QM wave is in terms that students can understand. – Manishearth Mar 14 '12 at 13:49
  • @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 Mar 14 '12 at 13:52
  • @Manishearth Wow, that is one heck of an answer! Thank you so much! I think this will greatly help me. – fr00ty_l00ps Mar 14 '12 at 13:53
  • let us continue this discussion in chat – Manishearth Mar 14 '12 at 13:53
  • Umm.. I don't see the equation you used above anywhere. You do know that $\partial$ is a weird sort of derivative, don't you? The solution they've given is for a free particle anyways. A rather uninteresting one IMO. – Manishearth Mar 14 '12 at 13:55
  • @Manishearth sounds like a plan. And a normal example would be like the quantum-tunneling used by USB drives, and other devices that use flash memory, to thoroughly erase their data, right? – fr00ty_l00ps Mar 14 '12 at 13:56

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This is just a placeholder answer so that this (answered) question does not go into our unanswered backlog and get bumped up every now and then by this obnoxious fellow known as Community ♦. Please accept this answer.

The equation you've given is not the Schrödinger equation, rather, it is most probably a specific solution of it.

  • $k=2\pi/\lambda$ is the (angular) wavenumber, where $\lambda$ is the wavelength
  • $\omega$ is (angular) frequency
  • $p$ is probably momentum. In the Schrödinger equation, potential energy is usually represented with $U(x)$ or $V(x)$
  • $m$ is the mass of the particle
  • $A$ is the amplitude of the wave. This itself may be a function of $x$
  • $i=\sqrt{-1}$
  • $t$ is time
  • $\Psi$ is the wavefunction

http://chat.stackexchange.com/transcript/2778 has a full transcript of a discussion which lead to the resolution of the dilemma.

Community
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Manishearth
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