Concept

Exclusion principle — where it appears

The rule that no two identical fermions occupy the same quantum state, which gives matter its volume and the periodic table its shape. It is not a force and does no work, and yet it produces a pressure that holds up a white dwarf and keeps atoms from collapsing into one another.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

No two in the same state, and why matter has volume

Nothing in the energy levels of an atom says how many electrons may occupy each one. The answer is one per state, it is not derived from any force, and it is the reason a table holds a cup up.

quantum · Exclusion

One well, two wells, and the band they become. The energy levels of a chain of identical wells, for 1, 2, 3, 6, 12, 40 of them, with an on-site energy of -4 eV and a coupling of -0.9 eV between neighbours. One well has one level. Two split it into two, 1.80 eV apart. By 40 the levels have filled a band 3.59 eV wide, which is closing on the limit of four times the coupling, 3.60 eV — and no further widening happens however many more wells are added. The count of levels grows with the number of wells; the width of the band does not.

What happens when the wells get close

Two atoms brought together split one level into two. A thousand split it into a thousand, packed into a band whose width stops growing after the third. Whether that band is full or half full is the whole difference between a wire and a window.

quantum · Bands

Named alongside it

The objects these essays reach for when they reach for this one.

Energy levels Quantisation Atomic structure Band gap Band structure The Boltzmann factor Conductivity Degeneracy pressure Normal modes Periodic table Spin Zero-point energy

All concepts