View source for Superposition (quantum mechanics)

== Introduction ==

Superposition in [[Quantum Mechanics|quantum mechanics]] is a fundamental principle that holds that any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. This principle is at the heart of quantum mechanics and differentiates it from classical mechanics.

[[Image:Detail-27890.jpg|thumb|center|Photograph of a wave interference pattern, demonstrating the concept of superposition.|class=only_on_mobile]]
[[Image:Detail-27891.jpg|thumb|center|Photograph of a wave interference pattern, demonstrating the concept of superposition.|class=only_on_desktop]]

== Concept and Definition ==

The term "superposition" comes from the mathematical concept of superposition functions. In quantum mechanics, it refers to the quantum state of a system with multiple potential outcomes. The principle of superposition asserts that if a physical system may be in one of many configurations—arrangements of particles or fields—then the most general state is a combination of all of these possibilities, where the amount in each configuration is specified by a complex number.

For example, if there are two configurations labelled by 0 and 1, the most general state would be c0|0⟩ + c1|1⟩, where the ci are complex numbers. In this sense, the system is in a "superposition" of states. This concept is a direct result of the [[Wave-Particle Duality|wave-particle duality]] of quantum particles.

== Mathematical Formulation ==

The principle of superposition can be mathematically formulated using the language of [[Hilbert Spaces|Hilbert spaces]] and [[Linear Algebra|linear algebra]]. A quantum state, in the abstract formalism of quantum mechanics, is a ray in a Hilbert space over the complex numbers. The principle of superposition states that any linear combination of states is also a state. 

[[Image:Detail-27892.jpg|thumb|center|Photograph of a chalkboard with complex mathematical equations representing the principle of superposition in quantum mechanics.|class=only_on_mobile]]
[[Image:Detail-27893.jpg|thumb|center|Photograph of a chalkboard with complex mathematical equations representing the principle of superposition in quantum mechanics.|class=only_on_desktop]]

This is a direct consequence of the fact that the Hilbert space of quantum mechanics is a linear space, meaning that it is closed under addition and scalar multiplication. The coefficients in the linear combination are complex numbers, which allows for interference effects when the superposition is collapsed, as in the [[Double-Slit Experiment|double-slit experiment]].

== Superposition and Measurement ==

One of the most intriguing aspects of superposition in quantum mechanics is its relationship with measurement. According to the [[Copenhagen Interpretation|Copenhagen interpretation]] of quantum mechanics, measurement causes a superposed state to collapse to one of the states in the superposition. This is known as the "collapse of the wavefunction".

The outcome of the measurement is probabilistic, with the probability of obtaining each possible result given by the square of the absolute value of the coefficient of the corresponding state in the superposition. This is known as the [[Born Rule|Born rule]].

[[Image:Detail-27894.jpg|thumb|center|Photograph of a scientific apparatus used in quantum mechanics experiments, representing the concept of measurement in superposition.|class=only_on_mobile]]
[[Image:Detail-27895.jpg|thumb|center|Photograph of a scientific apparatus used in quantum mechanics experiments, representing the concept of measurement in superposition.|class=only_on_desktop]]

== Quantum Superposition in Quantum Computing ==

Quantum superposition is a key principle in [[Quantum Computing|quantum computing]]. In classical computing, a bit is a fundamental unit of information that can exist in two states, 0 or 1. In quantum computing, however, we use quantum bits or "qubits", which can exist in a superposition of states.

This means that a qubit can represent a 0, a 1, or any quantum superposition of those two qubit states. This property is what allows quantum computers to work on a large number of computations simultaneously, giving them potential for great computational power.

[[Image:Detail-27896.jpg|thumb|center|Photograph of a quantum computer, representing the application of superposition in quantum computing.|class=only_on_mobile]]
[[Image:Detail-27897.jpg|thumb|center|Photograph of a quantum computer, representing the application of superposition in quantum computing.|class=only_on_desktop]]

== Interpretations and Philosophical Implications ==

The principle of superposition and its implications for the nature of reality have been the subject of much philosophical debate. Different interpretations of quantum mechanics, such as the Copenhagen interpretation, the [[Many-Worlds Interpretation|many-worlds interpretation]], and the [[De Broglie-Bohm Theory|de Broglie-Bohm theory]], offer different views on what the principle of superposition means for the nature of reality.

[[Image:Detail-27898.jpg|thumb|center|Photograph of a philosophical text on quantum mechanics, representing the philosophical implications of superposition.|class=only_on_mobile]]
[[Image:Detail-27899.jpg|thumb|center|Photograph of a philosophical text on quantum mechanics, representing the philosophical implications of superposition.|class=only_on_desktop]]

== See Also ==

* [[Quantum Entanglement]]
* [[Quantum State]]
* [[Quantum Field Theory]]
* [[Quantum Mechanics]]

[[Category:Quantum Mechanics]]
[[Category:Physics]]
[[Category:Quantum Computing]]