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.
All labels observed (7)
| Label | Occurrences |
|---|---|
| Born rule | 4 |
| Born rule for outcome probabilities | 1 |
| Born rule for probabilities | 1 |
| Born rule for transition probabilities | 1 |
| Born rule in quantum mechanics canonical | 1 |
| Born's probabilistic interpretation | 1 |
| Born’s rule | 1 |
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
postulate of quantum mechanics
ⓘ
probability rule ⓘ |
| alsoKnownAs |
Born statistical interpretation
ⓘ
Born rule in quantum mechanics ⓘ
surface form:
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 (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Born rule
this entity surface form:
Born's probabilistic interpretation
subject surface form:
Born rule
this entity surface form:
Born’s rule
this entity surface form:
Born rule for outcome probabilities
this entity surface form:
Born rule for transition probabilities
this entity surface form:
Born rule for probabilities
this entity surface form:
Born rule
this entity surface form:
Born rule
this entity surface form:
Born rule