In quantum mechanics, a pure state vector represents the complete quantum state of a quantum system. It describes the state of a system with certainty, meaning that measurements of all observable quantities associated with that system will yield definite values.
Mathematically, a pure state vector is represented by a unit vector in a complex vector space called a Hilbert space. The Hilbert space corresponds to the space of all possible states the system can occupy. The pure state vector, denoted as |ψ⟩, represents the quantum state of the system.
The state vector |ψ⟩ contains information about the probabilities of obtaining different measurement outcomes when performing measurements on the system. The probabilities are calculated by taking the inner product (also known as the scalar product or the dot product) of the state vector with the corresponding measurement operator.
One important characteristic of pure state vectors is that they evolve deterministically under the Schrödinger equation, which describes the time evolution of quantum systems. This means that if the initial state of a system is known as a pure state, its future state can be predicted precisely using the Schrödinger equation.
Pure states play a fundamental role in quantum mechanics, and they form the basis for understanding various concepts such as superposition, entanglement, and quantum computations.