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What does it mean to use the momentum operator over wavefunction? What does it give? I am guessing it doesn't give momentum since momentum can never be a function of space.

How to calculate kinetic energy, given the wavefunction?

My professor once told me "the difference between classical mechanics and quantum mechanics is that classical variables are operators in QM" i just wish to know what does that mean?

I am abit confused, and i referred many books, but i didnt find anything that explains these things simply, its still first time to do QM for me.

Thank you