In this section the postulates of quantum mechanics are described in terms of the state vector. This formalism works for an isolated physical system. Postulate 1: States of physical systems are represented by vectors The state of a physical system is described by a state vector |ψ that belongs to a complex Hilbert space. The superposition principle holds, meaning that if |φ1 , |φ2 ,..., |φn are kets belonging to the Hilbert space, the linear combination |χ = α1 |φ1 + α2 |φ2 +···+ αn |φn is also a valid state that belongs to the Hilbert space. States are normalized to conform to the Born probability interpretation, meaning ψ |ψ = 1 If a state is formed from a superposition of other states, normalization implies that the squares of the expansion coefficients must add up to 1: χ |χ = |α1| 2 + |α2| 2 +···+ |αn| 2 = 1
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