A particle confined to a box with infinite walls (V = 0 inside, ∞ outside). Switch between one particle in 1D, one particle in 2D, two non-interacting particles in 1D, and two interacting particles in 1D (screened Coulomb, solved numerically). The 2D and two-free-particle cases share the same product wavefunction (x,y ↔ x₁,x₂); turning on interaction breaks that factorization and produces correlation. Lengths are in units of the box length L (= 1), energies in units of h²/8mL².
ψn(x) — amplitude (n−1 interior nodes)
|ψn(x)|² — probability density
ψ — signed (nodal lines)
|ψ|² — probability density
3D surface — drag to rotate
particle 1: |φn₁(x₁)|² (where it is found, dashed)
particle 2: marginal |φn₂(x₂)|² and conditional P(x₂|x₁)