In quantum mechanics, a pure state represents a system with a precise and complete description, characterized by a single wave function or state vector in a Hilbert space. It contrasts with mixed states, which represent statistical mixtures of different possible states and lack complete information about the system's properties.

Pure State

Quantum mechanics is a fundamental theory in physics that describes the physical properties of nature at the smallest scales, such as atoms and subatomic particles. It introduces concepts like wave-particle duality, uncertainty principle, and quantum entanglement, which challenge classical intuitions about the behavior of matter and energy.

quantum mechanics

pure state

Precise description

complete description

The wave function is a fundamental concept in quantum mechanics that describes the quantum state of a system, encoding information about the probability amplitudes of a particle's position, momentum, and other physical properties. It is typically represented as a complex-valued function, and its squared magnitude gives the probability density of finding a particle in a particular state or location.

wave function

A state vector is a mathematical representation of a physical system's state in a given space, encapsulating all the information necessary to describe the system at a particular time. It is fundamental in quantum mechanics and control theory, where it is used to predict future states and analyze system behavior.

state vector

Hilbert Space is a complete inner product space that generalizes the notion of Euclidean space, providing the framework for quantum mechanics and many areas of functional analysis. Its structure allows for the rigorous treatment of infinite-dimensional spaces, making it essential for understanding wave functions and operators in quantum theory.

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