A classic topic in physics!

The quantum mechanics of one- and two-electron atoms is a fundamental area of study in atomic physics. Here's a comprehensive guide to get you started:

Hψ = Eψ

H = -ℏ²/2m ∇² - Ze²/r

where H is the Hamiltonian operator, ψ is the wave function, and E is the total energy.

where a_0 is the Bohr radius.

where r₁ and r₂ are the distances between the electrons and the nucleus, and r₁₂ is the distance between the two electrons.

The Hamiltonian for a one-electron atom is:

The Hamiltonian for a two-electron atom is:

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