Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular, theoretically possible states (or, configuration of its properties) simultaneously; but, when measured or observed, it gives a result corresponding to only one of the possible configurations (as described in interpretation of quantum mechanics).
Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions to a particular equation will also be a 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. By doing so the overlap energy of the states is nullified, and the expectation value of an operator (any superposition state) is the expectation value of the operator in the individual states, multiplied by the fraction of the superposition state that is "in" that state.
An example of a directly observable effect of superposition is interference peaks from an electron wave in a double-slit experiment. Another example is a pure quantum logical qubit state, as used in quantum information processing, which is a linear superposition of the "basis states" and .
Read more about Quantum Superposition: Concept, Experiments and Applications, Formal Interpretation
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