Why do we say that classical physics is a lot different from quantum physics? The laws that determine the macroscopic world should be derivable from quantum laws. So in a way the Newtonian or classical laws are basically quantum laws( maybe a bit approximated) So why differentiate between macroscopic and microscopic world?
We don't (except by mistake). We say that quantum physics is different from classical physics :) All dogs may be animals but not all animals are dogs. All classical physics is a consequence of quantum - but not all quantum physics can be described classically. Technically - classical physics is what QM does on average ... so the math is different.