Quantum superposition refers to the quantum mechanical property of a particle to occupy all of its possible quantum states simultaneously. Due to this property, to completely describe a particle one must include a description of every possible state and the probability of the particle being in that state.^{[citation needed]} Since the Schrödinger equation is linear, a solution that takes into account all possible states will be a Linear combination of the solutions for each individual state.^{[clarification needed]} This mathematical property of linear equations is known as the superposition principle.
An example of a directly observable effect of superposition is interference peaks from an electron wave in a doubleslit experiment.
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The Superposition principle of quantum mechanics
The principle of superposition states that if the world can be in any configuration, any possible arrangement of particles or fields, and if the world could also be in another configuration, then the world can also be in a state which is a superposition of the two, where the amount of each configuration that is in the superposition is specified by a complex number.
Examples
For an equation describing a physical phenomenon, the superposition principle states that a linear combination of solutions to an equation is also a solution. When this is true then the equation is linear and said to obey the superposition principle. Thus if functions f_{1}, f_{2}, and f_{3} solve the linear equation ψ, then ψ=c_{1}f_{1}+c_{2}f_{2}+c_{3}f_{3} would also be a solution where each c is a coefficient. For example, the electrical field due to a distribution of charged particles can be described by the vector sum of the contributions of the individual particles.
Similarly, probability theory states that the probability of an event can be described by a linear combination of the probabilities of certain specific other events (see Mathematical treatment). For example, the probability of flipping two coins (coin A and coin B) and having at least one turn face up can be expressed as the sum of the probabilities for three specific events A heads with B tails, A heads with B heads, and A tails with B heads. In this case the probability could be expressed as:
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