# nLab superposition

Contents

This page is concerned with the general superposition of solutions of linear differential equations. For the special case of quantum superposition see there.

# Contents

## Idea

The solutions to linear equations and linear differential equations may be linearly combined to produce further solutions. Such linear combinations, in particular the sums of two solutions, is also called superposition of solutions, in particular if it concerns solutions to wave equations.

## Examples

### Classical waves

If two waves are described by a linear wave equation, then the superposition of the two waves exist and the amplitude of the superposition of the two waves is the sum of the amplitudes of the two waves.

### Quantum states

In quantum physics, quantum states in the form of wavefunctions are solutions to linear differential equations such as the Schrödinger equation, Dirac equation, Klein-Gordon equation, Tomonaga-Schwinger equation, etc. Their superposition is also known as quantum superposition, a concept that is at the heart of peculiar features of quantum physics, notably in the context of entanglement.