An introduction to the quark model

Few-charge systems History of the quark model Mesons Baryons Multiquarks and other exotics Outlook
The harmonic oscillator (HO)
V =
2 K
3
H(m, m, m) = p2 x
m + p2 y
2
r12 + r 2 23 + r 2
31
m + K (x 2 + y 2 ) ,
K
E = (6 + 4 nx + 2ℓx + 4 ny + 2 ℓy)
m
N = 2 nx + ℓx + 2 ny + ℓy)
Levels named after the multiplicity and ℓ P ,
For instance [56, 0 + ] for the ground state with 8 spin 1/2 and 10
spin 3/2, i.e., 2 × 8 + 4 × 10 = 56 states. [56, 0 + ] ′ for Roper.
The first orbital excitation is [70, 1 − ],
the first state with a full antisymmetric orbital wave function is
[20, 1 + ].
JMR Quark Model