Probability Amplitude

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Probability Amplitude

A probability amplitude is a complex number which multiplies a certain part of a quantum state vector (called an eigenvector). A typical quantum state may be seen as the sum of several eigenvectors -one for each possible measurement outcome- multiplied by their respective amplitudes. For example, an electron which could have 2 possible energy values will have a state described by:

\left | State \right \rangle = A_{1} \left | E_{1} \right \rangle + A_{2} \left | E_{2} \right \rangle

The number multiplying E1 is the probability amplitude for E1. The amplitude is such that, when squared (actually, since it’s a complex number, multiplied by its complex conjugate), it gives us the probability of obtaining E1 when measuring the electron’s energy. Because amplitudes’ squares can be interpreted as probabilities, in any quantum system it must happen that the sum of all their squares equal to one (since, in physics, probabilities are not expressed in percentages, but in fractions of 1).

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