= Atomic orbital
{title2=$\phi_{n\ell m}(\mathbf r)$}
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An atomic orbital is a one-<Electron> spatial <wavefunction> used to describe an <Electron>'s state in a <chemical atom>. For a one-electron <hydrogen atom>, orbitals can be exact <energy eigenstates>; descriptions of many-electron atoms instead use an orbital approximation. A normalized atomic orbital has $\int|\phi|^2\,d^3\mathbf r=1$, and the <Born rule> gives the position <probability density> $|\phi|^2$. It is a function extending through space, not a prescribed classical orbit. https://openstax.org/books/chemistry-2e/pages/6-3-development-of-quantum-theory[Flowers et al., Chemistry 2e, 6.3: atomic orbitals and the wavefunction description]{ref}
The <linear combination of atomic orbitals> combines these single-centre functions to approximate a <molecular orbital>. The <orbital overlap> measures their <inner product>, and their relative <quantum phase> controls the <interference> shown in <molecular orbital theory>.
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