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In quantum physics, energy level splitting or a split in an energy level of a quantum system occurs when a perturbation changes the system. The perturbation changes the corresponding Hamiltonian and the outcome is change in eigenvalues; several distinct energy levels emerge in place of the former degenerate (multi-state) level. This may occur because of external fields, quantum tunnelling between states, or other effects. The term is most commonly used in reference to the electron configuration in atoms or molecules. will be: |0⟩: the E0 + ε level, and|1⟩: the E0 − ε level,

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rdfs:label	Energy level splitting (en)
rdfs:comment	In quantum physics, energy level splitting or a split in an energy level of a quantum system occurs when a perturbation changes the system. The perturbation changes the corresponding Hamiltonian and the outcome is change in eigenvalues; several distinct energy levels emerge in place of the former degenerate (multi-state) level. This may occur because of external fields, quantum tunnelling between states, or other effects. The term is most commonly used in reference to the electron configuration in atoms or molecules. will be: \|0⟩: the E0 + ε level, and\|1⟩: the E0 − ε level, (en)
foaf:depiction
dcterms:subject	Quantum mechanics
Wikipage page ID	1615196 (xsd:integer)
Wikipage revision ID	1121196463 (xsd:integer)
Link from a Wikipage to another Wikipage	Quantum state Qubit Electric charge Electron configuration Energy level Molecule Perturbation theory (quantum mechanics) Nitrogen inversion Quantum physics Quantum mechanics Quantum tunnelling Electric field Magnetic field Delocalized electron Hamiltonian (quantum mechanics) Identity matrix Perturbation theory Quantum superposition Stark effect Larmor precession dbr:Ammonia Diagonal matrix Resonance (chemistry) Atom Atomic physics Jahn–Teller effect Zeeman effect Spin-½ Spin (physics) Field (physics) Maser Physical chemistry Eigenvalues Pauli matrix
Link from a Wikipage to an external page	https://feynmanlectures.caltech.edu/III_toc.html
sameAs	Energy level splitting Energy level splitting Energy level splitting
dbp:wikiPageUsesTemplate	dbt:Rangle dbt:Math dbt:More_citations_needed dbt:Harvnb
thumbnail	wiki-commons:Special:FilePath/Breit-rabi-Zeeman.png?width=300
has abstract	In quantum physics, energy level splitting or a split in an energy level of a quantum system occurs when a perturbation changes the system. The perturbation changes the corresponding Hamiltonian and the outcome is change in eigenvalues; several distinct energy levels emerge in place of the former degenerate (multi-state) level. This may occur because of external fields, quantum tunnelling between states, or other effects. The term is most commonly used in reference to the electron configuration in atoms or molecules. The simplest case of level splitting is a quantum system with two states whose unperturbed Hamiltonian is a diagonal operator: Ĥ0 = E0 I, where I is the 2 × 2 identity matrix. Eigenstates and eigenvalues (energy levels) of a perturbed Hamiltonian will be: \|0⟩: the E0 + ε level, and\|1⟩: the E0 − ε level, so this degenerate E0 eigenvalue splits in two whenever ε ≠ 0. Though, if a perturbed Hamiltonian is not diagonal for this quantum states basis {\|0⟩, \|1⟩} , then Hamiltonian's eigenstates are linear combinations of these two states. For a physical implementation such as a charged spin-½ particle in an external magnetic field, the z-axis of the coordinate system is required to be collinear with the magnetic field to obtain a Hamiltonian in the form above (the σ3 Pauli matrix corresponds to z-axis). These basis states, referred to as spin-up and spin-down, are hence eigenvectors of the perturbed Hamiltonian, so this level splitting is both easy to demonstrate mathematically and intuitively evident. But in cases where the choice of state basis is not determined by a coordinate system, and the perturbed Hamiltonian is not diagonal, a level splitting may appear counter-intuitive, as in examples from chemistry below. (en)
prov:wasDerivedFrom	wikipedia-en:Energy_level_splitting?oldid=1121196463&ns=0
page length (characters) of wiki page	3785 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Energy_level_splitting
is Link from a Wikipage to another Wikipage of	Principal quantum number Index of energy articles Index of physics articles (E) Pyramidal inversion Iron oxide nanoparticle Irreducible representation Lauren Rohwer Azimuthal quantum number
is foaf:primaryTopic of	wikipedia-en:Energy_level_splitting

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