How important to physics (and science) is quantum mechanics?
Quantum Mechanics is the field that deals with the some of the tiniest particles in this Universe. Atoms, Electrons, Neutron, Proton and even Quarks!
Some of the most popular theories from some of the most popular scientists like Albert Einstein and Max Planck relies on Quantum Mechanics.
The Photoelectric Effect, String Theory, Radioactive materials, the things we know today on nano-scopic level, these all work on the principles of Quantum Mechanics.
So now you know how important is Quantum Mechanics to Science!