3 syllables: ei, gen, state. Stress on ei.
EYE-guhn-stayt
/ˈaɪɡənˌsteɪt/
eigenstate is pronounced EYE-guhn-stayt (/ˈaɪɡənˌsteɪt/). It has three syllables (ei-gen-state), with the stress on "ei". Eigenstate refers to a quantum system’s state that is an eigenvector of an observable, typically the Hamiltonian, with a definite value (eigenvalue) for that observable. In quantum mechanics, systems described by eigenstates have well-defined properties, such as energy, momentum, or spin, and form a complete basis for the system’s state space. The term combines the mathematical concept of an eigenvector with physical state description.
Eigenstate refers to a quantum system’s state that is an eigenvector of an observable, typically the Hamiltonian, with a definite value (eigenvalue) for that observable. In quantum mechanics, systems described by eigenstates have well-defined properties, such as energy, momentum, or spin, and form a complete basis for the system’s state space. The term combines the mathematical concept of an eigenvector with physical state description.
"The particle’s energy is found in the eigenstate of the Hamiltonian corresponding to that energy level."
"In the measurement, the system collapses from a superposition to a particular eigenstate with a definite eigenvalue."
"Eigenstates form the eigenbasis, allowing us to expand any state as a sum of these basis states."
IPA: ˈaɪɡənˌsteɪt. Break it as EIG-en-state: stress on the first syllable. Start with the /aɪ/ diphthong as in “eye,” then /ɡ/ with a hard stop, then /ən/ as a schwa + n, and finally /steɪt/ with /eɪ/ as in “state.” Keep the /ɡ/ well articulatorily released and avoid letting the second syllable slur into the first.
Common errors: (1) Slurring ei to become /iː/ like “sea,” making /ˈiːɡənˌsteɪt/. (2) Misplacing stress, saying /ˈiːɡənˌsteɪt/ or /ˈeɪɡənˌsteɪt/. (3) Weak /t/ at the end or nasalizing the /n/ before the final stop. Corrections: emphasize /aɪ/ in the first syllable, keep /ɡ/ clipped but not swallowed, ensure a clear final /t/. Practicing with minimal pairs can help: eye-gen-state vs eager-state is not a true pair but can highlight misplacement of vowels.
US/UK/AU share /ˈaɪɡənˌsteɪt/ baseline. US often has a tighter /ɡ/ and crisper /t/, with rhotic linking less pronounced in connected speech. UK may show slightly more rounded /ɡə/ blend in the second syllable and a subtle non-rhotic tendency in rapid speech, though scientific register often preserves clear /r/ in careful speech. AU typically mirrors US vowel quality but may feature broader vowels and a more pronounced final /t/ in some speakers. In all, primary stress remains on first syllable; the /eɪ/ in /steɪt/ remains stable.
Two main challenges: the initial diphthong /aɪ/ combined with a hard /ɡ/ can create a momentary blip if the tongue doesn’t rise quickly enough; and the /ən/ sequence before /steɪt/ requires a light, neutral schwa followed by a distinct /n/. The stacked stress pattern (ˈaɪɡənˌsteɪt) can feel awkward if you’re not pausing between syllables. Practicing with deliberate, slow production helps anchor accurate mouth positions and timing.
The most specific feature is the clear, two-part stress pattern: primary stress on the first syllable and secondary emphasis on the final content word element. Unlike many English compounds, eigenstate maintains a crisp separation between /ˈaɪɡən/ and /ˌsteɪt/, ensuring the /ɡ/ is released and the /eɪ/ in /steɪt/ remains a distinct vowel. Your mouth should move from a rounded, open front position for /aɪ/ to a closed, tense /steɪt/.
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The term eigenstate comes from the German word eigen, meaning 'own' or 'proper' and used in mathematics in the context of eigenobjects. In linear algebra, an eigenvector v of a linear operator A satisfies Av = λv, where λ is the eigenvalue. The word eigen, borrowed into English in the 19th century, entered quantum mechanics early in the field’s development, around the 1920s, as physicists borrowed linear-algebra terminology to describe observable properties with definite values. The first known uses occur in mathematical literature to denote eigenvectors and eigenvalues, later adopted by quantum theorists to describe states with fixed measurable quantities. The compound eigenstate was popularized as the formal state associated with a particular eigenvalue of an observable, especially energy (Hamiltonian). The concept became central to the postulates of quantum mechanics, where a system in an eigenstate of an operator yields a deterministic measurement outcome for that operator, in contrast to a superposition. Over time, “eigenstate” has broadened beyond energy to include momentum, spin, and other observables, but the core meaning remains: a state with a definite value for the measured quantity. In modern usage, eigenstate is standard in both mathematical physics and quantum chemistry, often used in discussions of eigenbasis, spectral decomposition, and state preparation. The term’s pronunciation has remained stable, with the initial “ei” sounding like the long a in “eye,” and “state” as in ordinary English.
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