For a free charm quark (mass m_c) start with the Dirac equation: (iγ^μ∂_μ − m_c)ψ = 0. Use plane-wave ψ(x)=u(p)e^{−ip·x} ⇒ (γ·p − m_c)u(p)=0. In the Dirac basis the positive‑energy spinors are
u_s(p)=√(E+m_c) [ χ_s ; (σ·p)/(E+m_c) χ_s ],
with χ_s the 2‑spinor and normalization ūu=2m_c. For bound states (charmonium) use NR Schrödinger with the Cornell V(r)=−4/3 α_s/r + σr or Bethe–Salpeter for relativistic treatment.
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