Fermions & Bosons

Fermions & bosons in a 1D infinite well

Simulation

Challenges

Spatial wave function

ψ_space(x₁, x₂) = ψ_n(x₁) ψ_m(x₂)

No symmetry under exchange x₁ ↔ x₂

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Spatial probability density

| ψ(x₁, x₂) |²

Spatial wave function ψ_space

Product wave function Symmetric under exchange Antisymmetric under exchange

Indistinguishable particles with spin

Indistinguishable
fermions

Indistinguishable
bosons

Exchange symmetry of the spatial and spin parts:

ψ_tot

ψ_space

ψ_spin

anti-
symmetric

symmetric

anti-
symmetric

symmetric

The text on start-up appears here.

Energy controls

System energy: ... E₁

E₁

E₂ = 4E₁

E₃ = 9E₁

E₄ = 16E₁