Quantum mechanics was a class taught at Starfleet Academy.
Spock lead his year in the field along with eight other disciplines. (EV comic: "Flesh of My Flesh")
Sinnit Arvid studied quantum mechanics at the University of Mississippi. (DS9 - The Lives of Dax short story: "Old Souls")
Nilani Kahn once told her husband Torias Dax that she wanted to study quantum mechanics, something which Torias was not interested in. (DS9 episode: "Rejoined")
Nikolas Kyprios was taught quantum mechanics at the Academy by Professor Tarleggia. (DS9 novel: Saratoga)