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Quantum state is the state of a quantum mechanical system given by a vector in the underlying Hilbert space.

Snippet from Wikipedia: Quantum state

In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system represented by the state. Knowledge of the quantum state, and the rules for the system's evolution in time, exhausts all that can be known about a quantum system.

Quantum states may be defined differently for different kinds of systems or problems. Two broad categories are

• wave functions describing quantum systems using position or momentum variables and
• the more abstract vector quantum states.

Historical, educational, and application-focused problems typically feature wave functions; modern professional physics uses the abstract vector states. In both categories, quantum states divide into pure versus mixed states, or into coherent states and incoherent states. Categories with special properties include stationary states for time independence and quantum vacuum states in quantum field theory.

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