Schrödinger picture
E508534
The Schrödinger picture is a formulation of quantum mechanics in which states evolve in time according to the Schrödinger equation while observables remain fixed.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
formulation of quantum mechanics
ⓘ
representation in quantum mechanics ⓘ |
| appliesTo |
non-relativistic quantum mechanics
ⓘ
quantum field theory ⓘ |
| assumes |
Born rule for probabilities
NERFINISHED
ⓘ
Hilbert space structure of quantum states ⓘ linearity of quantum evolution ⓘ |
| contrastedWith | Heisenberg picture where operators carry time dependence ⓘ |
| differsFrom |
Heisenberg picture by distribution of time dependence
ⓘ
interaction picture by treatment of free and interaction parts of Hamiltonian ⓘ |
| energyEigenstatesSatisfy | H|Eₙ⟩ = Eₙ|Eₙ⟩ ⓘ |
| equivalentTo |
Heisenberg picture
ⓘ
interaction picture ⓘ path integral formulation under suitable conditions ⓘ |
| formalismUses |
kets |ψ(t)⟩ for states
ⓘ
time-independent operators  for observables ⓘ |
| hasAdvantage |
convenient for solving time-dependent potentials
ⓘ
intuitive wavefunction description in configuration space ⓘ natural connection to classical limit via wave packets ⓘ |
| hasCharacteristic |
observables are time-independent in the Heisenberg sense
ⓘ
operators representing observables are fixed in time ⓘ states evolve in time ⓘ time dependence carried by state vectors ⓘ |
| hasCoreConcept |
Hamiltonian operator
NERFINISHED
ⓘ
state vector in Hilbert space ⓘ wavefunction ⓘ |
| hasGeneralization | Schrödinger picture in quantum field theory NERFINISHED ⓘ |
| hasHistoricalContext |
developed in the 1920s
ⓘ
introduced after matrix mechanics of Heisenberg ⓘ |
| hasInterpretation | wavefunction as probability amplitude ⓘ |
| hasMeasurementPostulate | projection postulate on eigenstates of observables ⓘ |
| isUsedIn |
atomic physics
ⓘ
condensed matter physics ⓘ quantum chemistry ⓘ quantum information theory NERFINISHED ⓘ |
| namedAfter | Erwin Schrödinger NERFINISHED ⓘ |
| probabilityDensityGivenBy | |ψ(x,t)|² in position representation ⓘ |
| relatedConcept |
Dirac bra–ket notation
NERFINISHED
ⓘ
Schrödinger equation NERFINISHED ⓘ state vector formalism ⓘ wave mechanics ⓘ |
| timeEvolutionOfEnergyEigenstate | |Eₙ(t)⟩ = e^{−iEₙt/ħ}|Eₙ(0)⟩ ⓘ |
| timeEvolutionOfStatesGivenBy | unitary time-evolution operator ⓘ |
| timeEvolutionOperator | U(t,t₀) = exp[-(i/ħ)H(t−t₀)] for time-independent H ⓘ |
| usesEquation |
iħ ∂|ψ(t)⟩/∂t = H|ψ(t)⟩
ⓘ
time-dependent Schrödinger equation ⓘ |
| usesMathematicalStructure |
complex Hilbert space
ⓘ
self-adjoint operators for observables ⓘ unitary operators for time evolution ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.