Conceptual

Quantum Dynamics: The Second Postulate and Schrödinger's Equation in Quantum Mechanics

The Second Postulate of Quantum Mechanics dictates that the time evolution of a closed quantum system is governed by a unitary transformation operating on its state space. This principle establishes that continuous temporal changes are described rigorously by the Schrödinger equation, where the rate of change of the state vector is linearly dependent on the Hamiltonian operator and Planck's constant $\hbar$. Consequently, this postulate serves as the fundamental dynamical law within quantum mechanics, linking abstract unitary operators to physical time evolution through a specific differential relationship.