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Quantum state

The quantum state vector |ψ is an abstract symbol that stands for a physical state. In this way the laws of quantum mechanics can be written as algebraic equations.



States are expressed as numbers in a vector space. These numbers refer to the probabilities of the possible outcomes of a measurement on the system. The so-called amplitudes are complex numbers that indicate how likely each measuring outcome is.


Example 1

A photon can be polarized horizontally or vertically. Until the polarization is measured, the photon is in a superposition of these two states, and we write this as

|ψ⟩ = α |H⟩ + β |V

where α and β are complex probability amplitudes. The chance that you measure a photon in state |H is |α|2 and that you measure state |V is |β|2, because

|α|2 + |β|2 = 1


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