Wavefunctions illustrated: Bloch functions for a 2-D square lattice

00:18 Bloch functions for 2-D square lattice
02:15 8 x 8 square lattice, with lattice spacing a
02:53 Wavefunction for kx=0 and ky=0 using 1s orbitals as the periodic functions
03:55 Simplified sketch of the orbital phase relationships (all in phase, so all bonding)
04:22 Wavefunction for kx=1 and ky=0
04:53 Simplified sketch of the orbital phase relationships (if same color as neighbor, then bonding; otherwise, antibonding)
05:38 Wavefunction for kx=0 and ky=1
06:08 Simplified sketch of the orbital phase relationships
06:37 Wavefunction for kx=1 and ky=1
07:10 Wavefunction for kx=1 and ky=1, 3-D view
07:38 Simplified sketch of the orbital phase relationships
08:07 Wavefunction for kx=2 and ky=0
08:37 Simplified sketch of the orbital phase relationships
09:09 Wavefunction for kx=2 and ky=0
09:39 Simplified sketch of the orbital phase relationships
10:07 Wavefunction for kx=2 and ky=2
10:41 Simplified sketch of the orbital phase relationships
11:08 Wavefunction for kx=4 and ky=4
11:38 Wavefunction for kx=4 and ky=4, 3-D view
12:07 Simplified sketch of the orbital phase relationships (note all antibonding)

The eigenfunctions for the Hamiltonian of the 1s orbitals of the 64 atoms arranged on an 8 x 8 lattice are displayed using Microsoft Excel (R). Additionally, quick sketches of the phase relationships are demonstrated.

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