QQ - whats your plan postflop?

[RolloRolf]

The easiest way to play this hand is bet/fold i think, but I'm not sure this is the best line as i don't see any worse hands calling or any better hands folding. If he has the Ad, then he will also have hit the king, as I don't think this villan would call preflop with AQ or AJ.

Is this just betting for information then? Could a check ever be justified? Could villan ever bet JJ if checked to him, or check AK (with the Ad) thinking he's way ahead and trying to get value from QQ/JJ?