Rayleigh–Schrödinger perturbation theory
E5100
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
All labels observed (3)
How this entity was disambiguated
This entity first appeared as the object of triple T58721 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: Rayleigh–Schrödinger perturbation theory Context triple: [Feynman–Hellmann theorem, relatedTo, Rayleigh–Schrödinger perturbation theory]
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A.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
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B.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
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C.
The Nature of the Chemical Bond
The Nature of the Chemical Bond is a landmark chemistry book by Linus Pauling that systematically explains chemical bonding using quantum mechanics and became one of the most influential scientific texts of the 20th century.
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D.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
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E.
Einstein coefficients
Einstein coefficients are parameters in quantum theory that quantify the probabilities of absorption, spontaneous emission, and stimulated emission of radiation by atoms or molecules.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Rayleigh–Schrödinger perturbation theory Target entity description: Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
A.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
-
B.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
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C.
On a Heuristic Point of View Concerning the Production and Transformation of Light
"On a Heuristic Point of View Concerning the Production and Transformation of Light" is Albert Einstein’s 1905 paper that introduced the concept of light quanta (photons), laying the foundation for quantum theory and explaining the photoelectric effect.
-
D.
The Nature of the Chemical Bond
The Nature of the Chemical Bond is a landmark chemistry book by Linus Pauling that systematically explains chemical bonding using quantum mechanics and became one of the most influential scientific texts of the 20th century.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
method in quantum mechanics
ⓘ
perturbation theory ⓘ |
| appliesTo |
bound states
ⓘ
time-independent quantum systems ⓘ |
| approximationType | systematic series expansion ⓘ |
| assumes | exactly solvable unperturbed Hamiltonian ⓘ |
| computes |
energy corrections
ⓘ
wavefunction corrections ⓘ |
| contrastedWith | time-dependent perturbation theory ⓘ |
| developedInContextOf | early quantum mechanics ⓘ |
| domain | non-relativistic quantum mechanics ⓘ |
| expandsIn | power series in perturbation parameter ⓘ |
| failsWhen |
energy levels are nearly degenerate without proper treatment
ⓘ
perturbation is not small ⓘ |
| field | quantum mechanics ⓘ |
| generalizes | classical Rayleigh perturbation theory ⓘ |
| hasVariant |
Rayleigh–Schrödinger perturbation theory
self-linksurface differs
ⓘ
surface form:
degenerate Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory self-linksurface differs ⓘ
surface form:
non-degenerate Rayleigh–Schrödinger perturbation theory
|
| includes |
first-order energy correction
ⓘ
higher-order corrections ⓘ second-order energy correction ⓘ |
| influenced |
many-body perturbation theory
ⓘ
quantum chemistry methods ⓘ |
| isToolFor | approximate solutions of Schrödinger equation ⓘ |
| mathematicalForm | power series in coupling constant ⓘ |
| namedAfter |
Erwin Schrödinger
ⓘ
Lord Rayleigh ⓘ |
| relatedTo |
Brillouin–Wigner perturbation theory
ⓘ
time-independent perturbation theory ⓘ |
| requires |
non-degenerate spectrum for simplest form
ⓘ
small perturbation compared to level spacings ⓘ |
| teaches | systematic correction to idealized models ⓘ |
| treats | interaction as small perturbation ⓘ |
| usedFor |
Stark effect
ⓘ
Zeeman effect ⓘ atomic spectra calculations ⓘ molecular energy level calculations ⓘ solid-state band structure approximations ⓘ |
| usedIn |
graduate quantum mechanics courses
ⓘ
undergraduate quantum mechanics courses ⓘ |
| usesConcept |
Hamiltonian operator
ⓘ
eigenstates ⓘ eigenvalues ⓘ orthonormal basis of unperturbed eigenstates ⓘ projection onto unperturbed states ⓘ |
| validWhen | perturbation series converges or is asymptotically useful ⓘ |
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Subject: Rayleigh–Schrödinger perturbation theory Description of subject: Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.