Few-body physics — the quantum / classical dynamics of systems of 2-5 particles, distinguished from both many-body physics (statistical-mechanical limit) and few-level problems (internal structure abstracted). Foundational mathematical…
few-body-physics
Pair count: C(n,2) = n·(n-1)/2
In an n-particle system, the number of distinct unordered pairs is the binomial coefficient C(n,2) = n·(n-1)/2 — the leading…
Efimov geometric scaling: E_{n+1}/E_n = exp(-2π/s_0)
Efimov (1970) discovered an infinite geometric tower of three-body bound states in the unitary limit (two-body scattering length a → ±∞,…
Jacobi 3-body reduced mass: μ_{12,3} = (m1+m2)·m3/(m1+m2+m3)
Jacobi coordinates decompose an n-body center-of-mass-frame into (n-1) independent coordinates. For three particles: ρ = r_2 - r_1…
Pair count at n=3: C(3,2) = 3
Sympy-exact witness of the smallest non-trivial three-body pair count. Setup: C(n,2) = n·(n-1)/2 as a symbolic one-parameter expression. …
Efimov ratio anchor: E_{n+1}/E_n(s_0=1) = exp(-2π)
Sympy-exact witness of the Efimov geometric-scaling canonical anchor at s_0 = 1. Setup: E_{n+1}/E_n = exp(-2π/s_0). Identity: at the s_0…
Jacobi equal-mass: μ_{12,3}/m (m_i=m) = 2/3
Sympy-exact witness of the identical-mass Jacobi 3-body reduced-mass ratio. Setup: μ_{12,3} = (m_1+m_2)·m_3/(m_1+m_2+m_3) as a…