EBK quantization
E814349
EBK quantization is a semiclassical method that generalizes the old Bohr–Sommerfeld quantization rules by incorporating phase corrections from classical turning points and caustics to approximate quantum energy levels in integrable systems.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
quantization rule
ⓘ
semiclassical quantization method ⓘ |
| abbreviation | EBK ⓘ |
| appliesTo |
classically integrable systems
ⓘ
integrable Hamiltonian systems ⓘ |
| approximates | eigenvalues of the Schrödinger equation ⓘ |
| assumes |
existence of invariant tori in phase space
ⓘ
separability in action–angle coordinates ⓘ |
| basedOn |
action–angle variables
ⓘ
classical mechanics ⓘ |
| captures |
boundary condition phase shifts
ⓘ
topological phase information ⓘ |
| category | asymptotic method in physics ⓘ |
| developedInContextOf | old quantum theory ⓘ |
| field |
mathematical physics
ⓘ
quantum mechanics ⓘ semiclassical analysis ⓘ |
| framework | Hamiltonian mechanics ⓘ |
| fullName | Einstein–Brillouin–Keller quantization NERFINISHED ⓘ |
| generalizes | Bohr–Sommerfeld quantization NERFINISHED ⓘ |
| hasQuantizationCondition | ∮ p_i dq_i = 2πħ (n_i + μ_i/4) ⓘ |
| historicalPrecursorOf | modern semiclassical quantization schemes ⓘ |
| improvesAccuracyComparedTo | Bohr–Sommerfeld quantization NERFINISHED ⓘ |
| incorporates |
Maslov index
NERFINISHED
ⓘ
phase corrections from caustics ⓘ phase corrections from classical turning points ⓘ |
| namedAfter |
Albert Einstein
NERFINISHED
ⓘ
Josef Maria Jauch (Keller’s collaborator contextually, but main name is Keller) NERFINISHED ⓘ Joseph B. Keller NERFINISHED ⓘ Léon Brillouin NERFINISHED ⓘ |
| notWellSuitedFor | classically chaotic systems ⓘ |
| refines | old quantum theory ⓘ |
| relatedTo |
WKB approximation
NERFINISHED
ⓘ
action quantization ⓘ semiclassical approximation ⓘ |
| relatesQuantumNumbersTo | topology of classical phase space GENERATED ⓘ |
| reliesOn | invariant tori quantization ⓘ |
| requires |
integrability of the classical system
ⓘ
knowledge of classical trajectories ⓘ |
| usedFor |
approximation of quantum energy levels
ⓘ
semiclassical spectrum calculation ⓘ |
| usedIn |
atomic physics
ⓘ
molecular spectroscopy ⓘ quantum billiards ⓘ semiclassical analysis of bound states ⓘ |
| usesQuantity |
Planck constant ħ
NERFINISHED
ⓘ
classical action integral ⓘ |
| validInLimit | ħ → 0 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.