Somebody already asked this question ([here](https://www.reddit.com/r/explainlikeimfive/comments/26uzgu/eli5_quantum_mechanics_superpositions/)), but I did not really understand the explanation, and the post was archived so I can’t ask for a more detailed explanation.
In: Physics
Superposition is an attribute of physical systems described by linear equations.
A linear equation has the property that if x and y are solutions of the equation, and a and b are two arbitrary constants, then a*x+b*y is also a solution to the equation.
If a physical system is described by a linear equation, then physical states correspond to solutions of that equation. For example x and y might be two different electron spins or two different propagating waves. Superposition means that a*x+b*y is also a possible state of the physical system.
Superposition can be found in classical or quantum physics, usually in the context of waves. For example in classical electromagnetism superposition means that some light waveform propagating through space can be described as a sum of a combination of plane waves.
In quantum mechanics superposition is particularly important because states are described by waves functions that are solutions to the Schrodinger equation. A sum of different wavefunctions can be a state of the system.
The principle of superposition it’s important because there is usually some set of solutions that don’t overlap with each other, called an orthogonal basis. For vibrations of a strong tied at two ends they are the normal modes. For a quantum system they are the energy eigenstates. In any case, knowing about an orthogonal basis means operations on a superposition of those states is easy to work with because you can apply the operations to each basis state without affecting the other states.
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