For any particular quantum system, the principle of quantum superposition states the existence of certain relations amongst states, respectively pure with respect to particular distinct quantum state analysers. It is a fundamental principle of quantum mechanics.
Mathematically, it refers to a property of pure state solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of pure state solutions to a particular equation will also be a pure state solution of it. Such solutions are often made to be orthogonal (i.e. the vectors are at right-angles to each other), such as the energy levels of an electron. In other words, the overlap of the states is nullified, and the expectation value of an operator is the expectation value of the operator in the individual states, multiplied by the fraction of the superposition state that is "in" that state (see also eigenstates). Such resolution into orthogonal components is the basis of what is known as "quantum measurement", a concept that is characteristic of quantum physics, inexplicable in classical physics.