A quantum state is a mathematical representation of a physical system that encapsulates all observable properties, differing from classical states which are defined by specific points in phase space. In quantum mechanics, states are represented as vectors in Hilbert space, with the evolution of the system's state determined by the theory's equations over time. The discussion also touches on concepts like Bose-Einstein Condensate and the Pauli Exclusion Principle, which relate to the behavior of particles at quantum levels. The distinction between a vector and a unit ray in quantum states is noted, although this detail may be too advanced for beginners. Understanding these foundational concepts is essential for grasping the complexities of quantum mechanics.
