Superposition

CORE DEFINITION

In quantum mechanics, the superposition principle states that if a quantum system can be in any of several distinct quantum states, then any normalized linear combination of these states is also a possible quantum state of the system. This linear combination is called a "superposition state." If the constituent states are mutually orthogonal, the probability of the system being in any particular state is the squared absolute value of the corresponding coefficient. The superposition principle is an application of the linear superposition principle from mathematics to quantum mechanics. Mathematically, it is a property of solutions to the Schrödinger equation: since the equation is linear, any linear combination of solutions is also a solution. These solutions forming the linear combination (the "superposition state") are often set to be mutually orthogonal (called "basis states"), such as the electron energy levels of a hydrogen atom. In other words, these basis states do not overlap with each other. Thus, the expectation value of any observable measured on the superposition state is the sum, over all basis states, of the expectation value measured on each basis state multiplied by the probability that the superposition state is in that basis state.