Neither of Gödel's two incompleteness theorems apply to quantum mechanics.

The two theorems apply to logical systems which prove facts about the natural numbers. While this is an incredibly broad class of things, it doesn't include physical theories like quantum mechanics.

Guess I Dunning Kruegered, when I thought physics is based on mathematics and logical systems, to which a theory (itself having been proven) aught apply.

Physics isn’t based on mathematics and logical systems, it’s based on measurements that the mathematics are chosen to fit