Hydrogen molecule. Intensity is proportional to ∫ |Ψ(r)|2dz.
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Hydrogen molecule

Hydrogen 1s wave function is
    Ψ1s(r) ~ 2 e -r.
Valence bond theory proposes that covalent bonds form when the atomic orbitals of two atoms overlap
    Ψ1s(r + a) + Ψ1s(r - a)
Sigma (σ) bonds arise from the 'end-on' overlap between adjacent orbitals. This leads to a region of high electron density along the inter-nuclear axis, which bond positively charged nuclei. Unbonding orbital
    Ψ1s(r + a) - Ψ1s(r - a)
has low inter-nuclear electron density.

bonding orbital

unbonding orbital
The combined, overlapping orbitals, contain a total of two electrons with opposed spins.
Valence bond theory     updated 8 Apr 2012