Probability Amplitude - A Basic Example

A Basic Example

Take a quantum system that can be in two possible states: for example, the polarisation of a photon. When the polarisation is measured, it could be horizontal, labelled as state, or vertical, state . Until its polarisation is measured the photon can be in a superposition of both these states, so its wavefunction, would be written:

The probability amplitudes of states and are α and β respectively. When the photon's polarisation is measured, it has probability of being horizontally polarised, and probability of being vertically polarised.

Therefore, a photon with wavefunction whose polarisation was measured would have a probability of 1/3 to be horizontally polarised, and a probability of 2/3 to be vertically polarised.