The speaker says quantum-mechanical calculations are expensive because wave functions involve an exponentially large Hilbert space, and the problem becomes especially difficult as system size increases.

“density functional theory is probably the most commonly used simulation method for materials it kind of comes from Kohn-Hohenberg theorem and Kohn got a Nobel Prize for this when he realized that sure quantum mechanics is very expensive because”

“you basically have this exponential Hilbert space for every wave function.”

“So you have to solve this like very difficult problem,”

“especially as the system size grows.”