The time-dependent Schrödinger equation (TDSE) is a first-order time derivative because it ensures that wave functions remain complex, which is essential for accurately describing quantum states. This first-order requirement is linked to Noether's theorem, where energy conservation arises from time invariance. If the TDSE were a second-order time derivative, it could lead to non-physical solutions, such as instabilities or negative probabilities. The necessity for complex wave functions allows for interference and superposition, fundamental aspects of quantum mechanics. Understanding these principles is crucial for grasping the foundational postulates of quantum theory.