I was reading quantum field theory and came across second quantization. There the wave function was quantized to field operators. The field operator is expressed as a sum of the product of creation/annihilation operator(that depends on time) and wave function satisfying Schrodinger's equation. In the beginning of quantum mechanics we quantized observables to operators and operated them on the wave function that contains all the information about the system under consideration. In QFT, upon what do operate the field operator?