Born rule in quantum mechanics
E75605
The Born rule in quantum mechanics is the fundamental postulate that connects a system’s wavefunction to experimentally observed probabilities by stating that measurement outcomes occur with probabilities given by the squared magnitude of the wavefunction’s amplitudes.
Aliases (4)
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
postulate of quantum mechanics
→
probability rule → |
| alsoKnownAs |
Born statistical interpretation
→
Born’s rule → |
| appliesTo |
positive operator-valued measures
→
projective measurements → quantum measurement outcomes → |
| assumes |
normalized wavefunction
→
|
| concerns |
outcome statistics of repeated measurements
→
|
| connects |
Hilbert space formalism to experimental statistics
→
|
| domain |
Hilbert space of quantum states
→
|
| field |
quantum mechanics
→
|
| formalExpression |
P(a) = ⟨ψ|Π_a|ψ⟩ where Π_a is the projector onto the eigenspace of outcome a
→
P(i) = |c_i|^2 for a state |ψ⟩ = Σ_i c_i |i⟩ → |
| implies |
interference patterns in double-slit experiments
→
probabilities depend on relative phases of amplitudes → total probability equals one → |
| isAssumedIn |
standard quantum theory
→
|
| isAssumedRatherThanDerivedIn |
standard textbook formulations
→
|
| isCompatibleWith |
unitary time evolution between measurements
→
|
| isDebatedIn |
interpretations of quantum mechanics
→
|
| isDerivedInSomeApproachesFrom |
decision-theoretic axioms
→
envariance arguments → symmetry principles → typicality arguments → |
| isEssentialFor |
empirical predictions of quantum mechanics
→
|
| isFoundationFor |
Bayesian approaches to quantum probabilities
→
Born measure on projective Hilbert space → frequentist interpretation of quantum probabilities → quantum decision theory → |
| isPostulateIn |
Copenhagen interpretation of quantum mechanics
→
|
| isUsedIn |
Born approximation in scattering
→
particle physics experiments → quantum computing → quantum information theory → quantum optics → quantum state tomography → quantum statistical mechanics → scattering theory → spectroscopy → |
| namedAfter |
Max Born
→
|
| relates |
measurement probabilities
→
wavefunction → |
| requires |
complex-valued wavefunction or state vector
→
|
| role |
gives operational meaning to the wavefunction
→
links quantum states to observable probabilities → |
| statesThat |
the probability of obtaining a measurement outcome is given by the squared modulus of the corresponding amplitude in the wavefunction
→
|
| usesQuantity |
probability amplitude
→
squared magnitude of the wavefunction → |
| yearProposed |
1926
→
|
Referenced by (5)
| Subject (surface form when different) | Predicate |
|---|---|
|
Born rule
("Born’s rule")
→
|
alsoKnownAs |
|
Copenhagen interpretation of quantum mechanics
("Born rule")
→
|
coreConcept |
|
Copenhagen interpretation of quantum mechanics
("Born's probabilistic interpretation")
→
|
influencedBy |
|
Max Born
→
|
knownFor |
|
von Neumann measurement scheme
("Born rule for outcome probabilities")
→
|
postulates |