An introduction to the quark model

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Few-charge systems History of the quark model Mesons Baryons Multiquarks and other exotics Outlook Radial equation Assume a simple V (r) without spin dependence, and let Ψ = uℓ(r) r ℓz Yℓ (ˆr) × spin × colour , Thus for u = uℓ(r) (no dependence upon ℓz) −u ′′ (r) + ℓ(ℓ + 1) r 2 u(r) + m V (r) u(r) = m E u(r) , with boundary conditions u(0) = u(∞) = 0 Exactly solvable in a few cases Coulomb, see section on atoms HO, reduces to −u ′′ (r) + ℓ(ℓ + 1) u(r)/r 2 + r 2 u(r) = ɛ u(r) , with ɛ = 3 + 4 (n − 1) + 2 ℓ = 3 + 2 N Linear for ℓ = 0 JMR Quark Model
Few-charge systems History of the quark model Mesons Baryons Multiquarks and other exotics Outlook Linear potential for ℓ = 0 very similar to the Airy equation −u ′′ (r) + r u(r) = ɛ u(r) , −y ′′ (x) + x y(x) = 0 Aix 0.4 0.2 6 4 2 2 4 0.2 0.4 ɛ = −zero of the Airy function = −an vn(r) = Ai(r + an)/ Ai ′ (an) . JMR Quark Model x
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An introduction to the quark model

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