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'''Quantum superposition principle''' states that if a quantum system can be in one of two or more states, then any linear combination of those states is also a valid quantum state.<ref>[https://phys.libretexts.org/Workbench/Quantum_Mechanics_and_Quantum_Computation_%28Vazorani%29/01%3A_Introduction/1.03%3A_The_Superposition_Principle The Superposition Principle – Physics LibreTexts]</ref>
'''Quantum superposition principle''' states that if a quantum system can be in one of two or more states, then any linear combination of those states is also a valid quantum state.<ref>[https://phys.libretexts.org/Workbench/Quantum_Mechanics_and_Quantum_Computation_%28Vazorani%29/01%3A_Introduction/1.03%3A_The_Superposition_Principle The Superposition Principle – Physics LibreTexts]</ref>
[[File:Quantum_superposition_light.svg|thumb|400px|Superposition of two quantum states forming a new state as a linear combination of wavefunctions.]]
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[[File:Quantum_superposition_light.svg|thumb|280px|Quantum Superposition principle.]]
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== Mathematical formulation ==
== Mathematical formulation ==

Revision as of 14:00, 17 May 2026


← Back to Wavefunctions and modes Book I


Quantum superposition principle states that if a quantum system can be in one of two or more states, then any linear combination of those states is also a valid quantum state.[1]

Quantum Superposition principle.

Mathematical formulation

If ψ1 and ψ2 are valid wavefunctions, then any linear combination

ψ=c1ψ1+c2ψ2

is also a valid wavefunction, where:

  • c1 and c2 are complex coefficients

For a normalized two-state system,

|c1|2+|c2|2=1.[2]

Physical interpretation

Superposition means that a system is described by a combination of possible states rather than a single definite classical state. In standard quantum mechanics, measurement is associated with probabilistic outcomes and state reduction.[3]

Interference effects

Superposition gives rise to interference phenomena:

  • Constructive interference — amplitudes reinforce
  • Destructive interference — amplitudes cancel

This is observed in wave and quantum experiments such as interference and wave-packet formation.[4]

Basis states and Hilbert space

Quantum states form a vector space (Hilbert space):

  • States can be expressed in different bases
  • Superposition depends on the chosen basis
  • Eigenstates form a complete set

This vector-space structure is part of the standard postulates of quantum mechanics.[5]

Applications

Superposition is central to modern quantum technologies:

  • Quantum computing
  • Quantum interference devices
  • Atomic and optical physics

Britannica’s overview of quantum computing explicitly describes qubits as using superposition to hold multiple possible values at once.[6]

See also

Table of contents (217 articles)

Index

Full contents

References

  1. ↑ The Superposition Principle – Physics LibreTexts
  2. ↑ The Postulates of Quantum Mechanics – Physics LibreTexts
  3. ↑ Quantum Mechanics – Stanford Encyclopedia of Philosophy
  4. ↑ Principle of superposition – Britannica
  5. ↑ The Postulates of Quantum Mechanics – Physics LibreTexts
  6. ↑ How Do Quantum Computers Work? – Britannica
Author: Harold Foppele


Source attribution: Quantum Superposition principle

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