2 - WIEN 2k

One electron radial Schrödinger equationHARTREE ATOMIC UNITSINTERNATIONAL UNITS⎡ 1 2H SΨ = ⎢−∇⎣ 2V= −⎤+ V ⎥ Ψ = εΨ⎦ZrHIn a sphericallysymmetric potentialΨ= RSΨ( r) Y ( θ,ϕ)n, l,m n,l l,m=⎡⎢−⎣V2h2me∇22Ze= −4πε r⎤+ V ⎥ Ψ = εΨ⎦022 1 ∂ ⎛ 2 ∂ ⎞ 1 ∂ ⎡ ∂ ⎤ 1 ⎛ ∂∇ = ⎜r⎟ +( ) +( ) ⎢sin θ ⎥⎜222 22r ∂r⎝ ∂r⎠ r sin θ ∂θ⎣ ∂θ⎦ r sin⎞( θ ) ⎟ ⎝ ∂ϕ⎠Atomic units:ħ = m e = e = 11/(4 πε 0 ) = 1c = 1/ α ≈ 137 au