Science

Gamma is over 40 Hz. Associated with intense information processing and calculation. The gamma paper listed in the OP surprised me. Gamma and beta are reduced by meditation. Often present in stressed-out states.

Beta is 12 to 40 Hz. Associated with focus and problem solving in conventional ways (conventional for the individual). Increased by caffeine and stimulants.

Alpha is about 8 to 12 Hz. Associated with serenity, creativity, non-directed thinking, and dreaming (wake or sleep).

Theta is about 4 to 8 Hz. Associated with hynogogic states: drowsiness, creativity thinking outside of the box, solving problems "in our sleep" in the light phases of sleep especially at the edges. Famous example is Kekule drowsing in front of a fireplace and coming up with the ring structure fundamental to many organic molecules (model modified with modern evidence).

Delta is about 0 to 4 Hz. Associated with deep sleep (no dreams). I think this is the slow waves the OP excerpt referred to.