Quantum state
A quantum state is the mathematical object that encodes everything the theory can use to predict measurement probabilities. In Susskind’s presentation, a pure state is a vector in a complex vector space, written as a ket such as |Ψ⟩.
Plain-language picture
A classical state is like a complete inventory: positions, momenta, and other properties that determine what will happen. A quantum state is not that kind of inventory. It does not assign definite values to every possible measurement. Instead, it tells you how to compute probabilities once you specify the measurement.
Basis expansion
In a basis {|j⟩}, the state can be written:
|Ψ⟩ = Σ_j α_j |j⟩
α_j = ⟨j|Ψ⟩The coefficients are amplitudes. The probabilities are |α_j|².
What “complete” means
Complete does not mean classically deterministic. It means that no additional accessible data are part of the quantum state description. Given the state and the observable, the theory gives the full probability distribution allowed by quantum mechanics.
Common pitfalls
- Do not ask what all measurement values were “before” measurement as though the state must contain a hidden classical table.
- Do not identify the state with one specific column vector independent of basis.
- Do not confuse a pure state with a classical probability distribution.