Quantum Mechanics · Chapter 22

Identical particles

Two electrons cannot be told apart even in principle, and quantum mechanics takes that literally. The exchange operator, bosons and fermions, symmetric and antisymmetric states, the Pauli principle and Slater determinants, exchange effects, the helium atom, the shell structure of many-electron atoms and the self-consistent field of Hartree and Fock.

P^_{12} ψ = \pm ψ

[a^_{i}, a^_{j}^{†}] = δ_{ij}

{c^_{i}, c^_{j}^{†}} = δ_{ij}

ψ_{\pm} = \frac{ϕ _{a} ϕ _{b} \pm ϕ _{b} ϕ _{a}}{2}

Lessons

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07Many-electron atomsAn atom with many electrons is described first by a central field: each electron moves in the spherically symmetric average of the nucleus and all the others, the full charge $Ze$ close to the nucleus and a single charge far out.Read lesson →

08The Hartree–Fock ideaThe central field of the last lesson was a guess; Hartree turned it into a calculation.Read lesson →

09Chapter practiceBring the chapter together: the exchange operator, bosons and fermions, symmetric and antisymmetric states, Slater determinants and the Pauli principle, exchange energies, the helium atom, many-electron atoms and the self-consistent field. No worked example sits above the answers.Read lesson →

Mapping the lesson.

Identical particles

Build the foundation