Assume that the hamiltonian matrix elements between

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Unformatted text preview: u ( x ) . Assume that these functions satisfy: ∞ ∫ dx ϕ ( x )ϕ ( x ) = δ * u v u ,v , −∞ with δ u ,v the Kronecker delta function. Assume that the Hamiltonian matrix elements between these states can be written: ∞ H uv = ˆ ∫ dx ϕ ( x ) H ϕ ( x ) = E δ * u −∞ v o u ,v − V (δ u ,v+1 + δ u ,v−1 ) , with Eo the atomic energy and −V the average potential energy, both assumed constant. We will write the solution to this cha...
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