2 - WIEN 2k

Dirac equation: H D and Ψ are 4-dimensionalΨ is a four-component single-particle wave function that describes spin-1/2particles.spin upspin downH D⎛ψ1 ⎞ ⎛ψ1 ⎞⎜ ⎟ ⎜ ⎟⎜ψ2 ⎟ ⎜ψ2 ⎟⎜ ⎟ = εψ ⎜ ⎟3ψ3⎜ ⎟ ⎜ ⎟⎝ψ4 ⎠ ⎝ψ4 ⎠In case of electrons:Largecomponents (Φ)Smallcomponents (χ)⎛Φ⎞ψ = ⎜ ⎟⎝ χ ⎠factor∝ 1/(m ec 2 )Φ and χ are time-independent two-component spinors describing the spatialand spin-1/2 degrees of freedomLeads to a set of coupled equations for Φ and χ:cc( ) (2σ p χ = ε −V− m c )φ⋅ r( ) (2σ p φ = ε −V+ m c )χ⋅ ree