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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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1 Answers1

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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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