The Hamiltonian for a two-electron atom is:
where ℏ is the reduced Planck constant, m is the electron mass, e is the elementary charge, and r is the distance between the electron and the nucleus. quantum mechanics of one- and two-electron atoms pdf
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 two-electron atom is: where
The one-electron atom, also known as the hydrogen-like atom, consists of a single electron orbiting a nucleus with atomic number Z. The time-independent Schrödinger equation for this system is: m is the electron mass
Hψ = Eψ
The two-electron atom, also known as the helium-like atom, consists of two electrons orbiting a nucleus with atomic number Z. The time-independent Schrödinger equation for this system is: