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?

  • 1
    $\begingroup$ $k$ 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. $\endgroup$ – Manishearth Mar 13 '12 at 14:40
  • $\begingroup$ 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)... $\endgroup$ – fr00ty_l00ps Mar 13 '12 at 14:44
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    $\begingroup$ 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.... $\endgroup$ – Manishearth Mar 13 '12 at 15:22
  • $\begingroup$ 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? $\endgroup$ – Manishearth Mar 13 '12 at 15:25
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    $\begingroup$ 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. $\endgroup$ – Alexander Mar 13 '12 at 20:17

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.


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