According to wave mechanics, the ground state angular momentum is equal to
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That is, the energy associated with rotation is zero, so that the ground state energy is limited to the radial motion. ... We say that the ground state (e.g. of the hydrogen atom) is in an "eigenstate" of the angular momentum operator L^2 with eigenvalue l(l+1) = 0 - this is what is referred to when we say "l=0".
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None of that is the square of the orbital angular momentum that is 0(zero) (quantam mechanically) in the S-state. The orbital angular momentum itself has strong fluctuations and it is zero only on average. If you want to imagine the S-state classically, then think that electron is orbiting around the nucleus, but this orbiting does not have
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