Can someone explain to me how a particle can exist in [tex]\Psi[/tex](l=0, s= 3/2).
Well, QM's pretty tricky. It's hard to believe any of it actually works. Maybe you're wondering how they know the spin is 3/2.
The 3⁄2 spin means that all the three quarks inside a Δ particle have their spin axis pointing in the same direction, unlike the nearly identical proton and neutron (called "nucleons") in which the intrinsic spin of one of the three constituent quarks is always opposite the spin of the other two. This difference in spin alignment is the only quantum number distinction between the Δ+ and Δ0 and ordinary nucleons, whose spin is 1⁄2.
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