sarsoo/stem
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
40f5eca82e
stem/Quantum/Orbitals.md
andy 64276f270d vault backup: 2023-05-23 17:05:48 
Affected files:
.obsidian/graph.json
.obsidian/workspace-mobile.json
.obsidian/workspace.json
STEM/AI/Literature.md
STEM/AI/Neural Networks/MLP.md
STEM/AI/Properties.md
STEM/Quantum/Orbitals.md
STEM/Quantum/Schrödinger.md
STEM/Quantum/Wave Function.md
STEM/Signal Proc/Convolution.md
STEM/Signal Proc/Image/Image Processing.md
STEM/img/hydrogen-electron-density.png
STEM/img/hydrogen-wave-function.png
STEM/img/orbitals-radius.png
STEM/img/radial-equations.png
STEM/img/radius-electron-density-wf.png
STEM/img/wave-function-nodes.png
STEM/img/wave-function-polar-segment.png
STEM/img/wave-function-polar.png
2023-05-23 17:05:48 +01:00

887 B
Raw Blame History

Wave Function

Quantum Numbers

n

Principal quantum number

  • 1, 2, 3...
  • Electron shell, electron energy and size of orbital
l

Orbital Angualar Momentum Number

  • 0-(n-1)
  • Shape of the orbital
    • 0 = s
    • 1 = p
    • 2 = d
m

Z-component / Magentic of l

  • -l to +l
  • Orientation of orbital

!wave-function-polar-segment.png

Filling

  1. Aufbau
    • Start lowest in energy
  2. Pauli's Exclusion
    • Max two electrons per orbital
    • No two electrons can have same n, l, m, s tuple
  3. Hund's Rule of Maximum Multiplicity
    • Orbitals with same energy filled one at a time
    • Degenerate

!orbitals-radius.png !wave-function-nodes.png

Radial

!radial-equations.png

  • Z = Atomic number
  • Bohr radius
    • a_0=\frac \hbar {\alpha mc}
  • Normalisation
    • \int_0^\infty r^2R_{nl}^*R_{nl}dr=1

!radius-electron-density-wf.png