Disambiguation evidence for Born rule in quantum mechanics via surface form
"Born rule"
As subject (50)
Triples where this entity appears as subject under the
label "Born rule".
| Predicate | Object |
|---|---|
| alsoKnownAs | Born statistical interpretation ⓘ |
| alsoKnownAs |
Born rule in quantum mechanics
ⓘ
surface form:
Born’s rule
|
| appliesTo | positive operator-valued measures ⓘ |
| appliesTo | projective measurements ⓘ |
| appliesTo | 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 ⓘ |
| formalExpression | P(i) = |c_i|^2 for a state |ψ⟩ = Σ_i c_i |i⟩ ⓘ |
| implies | interference patterns in double-slit experiments ⓘ |
| implies | probabilities depend on relative phases of amplitudes ⓘ |
| implies | total probability equals one ⓘ |
| instanceOf | postulate of quantum mechanics ⓘ |
| instanceOf | probability rule ⓘ |
| isAssumedIn | standard quantum theory ⓘ |
| isAssumedRatherThanDerivedIn | standard textbook formulations ⓘ |
| isCompatibleWith | unitary time evolution between measurements ⓘ |
| isDebatedIn | interpretations of quantum mechanics ⓘ |
| isDerivedInSomeApproachesFrom | decision-theoretic axioms ⓘ |
| isDerivedInSomeApproachesFrom | envariance arguments ⓘ |
| isDerivedInSomeApproachesFrom | symmetry principles ⓘ |
| isDerivedInSomeApproachesFrom | typicality arguments ⓘ |
| isEssentialFor | empirical predictions of quantum mechanics ⓘ |
| isFoundationFor | Bayesian approaches to quantum probabilities ⓘ |
| isFoundationFor | Born measure on projective Hilbert space ⓘ |
| isFoundationFor | frequentist interpretation of quantum probabilities ⓘ |
| isFoundationFor | quantum decision theory ⓘ |
| isPostulateIn | Copenhagen interpretation of quantum mechanics ⓘ |
| isUsedIn | Born approximation in scattering ⓘ |
| isUsedIn | particle physics experiments ⓘ |
| isUsedIn | quantum computing ⓘ |
| isUsedIn | quantum information theory ⓘ |
| isUsedIn | quantum optics ⓘ |
| isUsedIn | quantum state tomography ⓘ |
| isUsedIn | quantum statistical mechanics ⓘ |
| isUsedIn | scattering theory ⓘ |
| isUsedIn | spectroscopy ⓘ |
| namedAfter | Max Born ⓘ |
| relates | measurement probabilities ⓘ |
| relates | wavefunction ⓘ |
| requires | complex-valued wavefunction or state vector ⓘ |
| role | gives operational meaning to the wavefunction ⓘ |
| role | 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 ⓘ |
| usesQuantity | squared magnitude of the wavefunction ⓘ |
| yearProposed | 1926 ⓘ |
As object (1)
Triples where some other subject referred to this entity
as "Born rule".
Copenhagen interpretation of quantum mechanics
→
coreConcept
→
"Born rule"
ⓘ
↳ resolves to Born rule in quantum mechanics