Unformatted text preview: is called a band .
4β
“s” band Tightbinding (LCAO) Band Theory
Tight LCAO Wavefunction
Wavefunction Energy for LCAO Bands
Energy Energy for LCAO Bands
Energy Reduced Hamiltonian Matrix: Reduced Overlap Matrix: Reduced Overlap Matrix for 1D Lattice
Reduced
Single orbital, single atom basis Reduced Hamiltonian Matrix for 1D Lattice
Reduced
Single orbital, single atom basis Energy Band for 1D Lattice
Energy
Single orbital, single atom basis LCAO Wavefunction for 1D Lattice
LCAO
Single orbital, single atom basis LCAO Wavefunction for 1D Lattice
LCAO
Single orbital, single atom basis k=0 k≠0
k=π/a
k = 2πp /( Na ) LCAO Wavefunction for 1D Lattice
LCAO
Single orbital, single atom basis lowest energy (fewest nodes) remember H2 ? H2
highest energy (most nodes) Bloch’s Theorem
Bloch’s Translation of wavefunction by a lattice constant… …yields the original wavefunction multiplied by a phase factor Consistent that the probability density is equal at each lattice site Wavefunction Normalization
Normalization
Using periodic boundary conditione for a crystal
with N lattice sites between boundaries… Counting Number of States in a Band
Counting Combining periodic boundary condition… …with Bloch’s theorem… …yields a discrete set of kvectors Within the 1st Brillouin Zone there are N states or 2N electrons Tightbinding and Lattice Wave Formalism
Tight
Electrons (LCAO) Lattice Waves...
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 Spring '03
 TerryOrlando
 Electron, 1d lattice, LCAO Wavefunction

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