Shrodinger Equation [ENDORSED]

[Alysia Garcia 1B]

For the equation Hψ (n,m,ml)=Eψ (n,m,ml), what exactly does n,m,ml represent and how are they applied to the equation?

[Marisol Sanchez - 1E]

For the Schrodinger equation, I think the setup is actually Ψ(x,y,z) = energyΨ(x,y,z) or HΨ = EΨ. The values x,y,z are referred to as a position when I wrote about it in my notes from lecture so I am assuming the three values determine a location for the wave function. The letters you used are for the quantum numbers of electrons which is a separate concept to my knowledge. In case you did mean this, n = principle quantum number and determines the energy and size (shell), ml = magnetic quantum number and levels the different orbitals of a subshell (orientation), l = angular quantum number and describes the shape, and ms = spin magnetic quantum number and determines if the electron spins up or down.

[Chem_Mod]

Alysia, your equation is the more accurate representation. For the Schroedinger equation, you can derive different functions (which correspond to the different orbitals) based on the quantum numbers you listed. Each of these functions is a solution to the Schroedinger equation with different quantum parameters. For the explanation of numbers, see this post:
viewtopic.php?f=20&t=31153&p=98732&hilit=&sid=874e1856cd012f5fa5273b40b2b53ea5#p98732