Quantum superposition
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Quantum superposition is the application of superposition principle to quantum mechanics. The superposition principle is addition of the amplitudes of waves from interference. In quantum mechanics it is the amplitudes of wavefunctions, or state vectors, that add. It occurs when an object simultaneously "possesses" two or more values for an observable quantity (e.g. the position or energy of a particle).
More specifically, in quantum mechanics, any observable quantity corresponds to an eigenstate of a Hermitian linear operator. The linear combination of two or more eigenstates results in quantum superposition of two or more values of the quantity. If the quantity is measured, the projection postulate states that the state will be randomly collapsed onto one of the values in the superposition (with a probability proportional to the amplitude of that eigenstate in the linear combination).
The question naturally arose as to why "real" (macroscopic, Newtonian) objects and events do not seem to display quantum mechanical features such as superposition. In 1935, Erwin Schrödinger devised a well-known thought experiment, now known as Schrödinger's cat, which highlighted the dissonance between quantum mechanics and Newtonian physics.
In fact, quantum superposition does result in many directly observable effects, such as interference peaks from an electron wave in a double-slit experiment.
If two observables correspond to non-commuting operators, they obey an uncertainty principle and a distinct state of one observable corresponds to a superposition of many states for the other observable.