Specifically, the Schroedinger quote actually is:
You surely must understand, Bohr, that the whole idea of quantum jumps necessarily leads to nonsense... If we are going to have to put up with these damn quantum jumps, I am sorry that I ever had anything to do with quantum theory.
This is from his discussions with Bohr and Heisenberg and the argument over matrix mechanics versus wave mechanics. Schroedinger wins the argument with his wave mechanics but loses the fight in Copenhagen the next year over the interpretation of them. Of course the modern handling of quanta has "evolved".
I am not math-proficient but have read a lot about quantum mechanics, enough to know that from the human and macroscopic perspectives it is intensely weird in its implications. But to the extent that I must rely on others for the math, my necessarily deficient understanding must also rely on those whose intelligence, honesty and authority I trust based, I suppose, on context, consistency, their ability to explain and the examples they provide.
Penrose is excellent but his math is exceedingly tedious which, I surmise, is to allow other mathematicians to contest it. This enhances his credibility. I also like Walker. He focuses on the right issue, which is the mechanics of the continuous resolution of infinite probabilities into one hard reality, a deep and true mystery, a paradox, from our perspective. And he breaks ground with his facts and speculations as to how brain function employs quantum mechanics to yield consciousness.
That very few if any really understand quantum mechanics is thus to be expected. It doesn't square at all with our daily reality and something quite mysterious is going on, especially if one tries to impose Materialistic suppositions upon it.