Superposition

Superposition is a principle in physics describing how linear systems respond to multiple causes. In mathematics, it asserts that a state or signal can be expressed as a linear combination of basis components, and that the system’s total response is the sum of the responses to each component.

In classical wave physics, this means that overlapping waves add their displacements at every point in space. The result can show constructive or destructive interference, depending on the relative phases of the waves.

In quantum mechanics, superposition states that a system may exist in a linear combination of basis states, described by a wavefunction with complex amplitudes. The probabilities of outcomes are given by the squared magnitudes of these amplitudes. When a measurement occurs, the system collapses to a definite state. Superposition underpins interference phenomena and enables quantum computation, where qubits can encode both 0 and 1 simultaneously in a probabilistic sense.

The principle applies most directly to linear, non-dissipative systems such as many optical, acoustic, and electrical problems. Real-world effects such as decoherence and nonlinearity can limit or modify superposition, making the total response deviate from a simple sum over time or configurations.