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Probability amplitude

In quantum mechanics the probability amplitude is used to indicate the chance that you will find a system in a particular state. It is usually written as

|ψ|2

 


Explanation

It does not say that a system has a certain state. You must perform a measurement in order to determine a state, and this can be done in several ways, that may produce different results.

 


Example 1

A qubit can be expressed as a linear combination of the two basic states

|ψ⟩ = α |0⟩ + β |1⟩

where α and β are complex probability amplitudes. The chance that you measure a qubit in the state |0⟩ is |α|2 and that you measure state |1⟩ is |β|2, because

|α|2 + |β|2 = 1

 


Example 2

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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