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feat(QuantumMechanics): Begin spectral theory of symmetric operators#1194

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jstoobysmith merged 9 commits into
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gloges:symmetric
Jun 17, 2026
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feat(QuantumMechanics): Begin spectral theory of symmetric operators#1194
jstoobysmith merged 9 commits into
leanprover-community:masterfrom
gloges:symmetric

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@gloges

@gloges gloges commented Jun 17, 2026

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Begins the spectral theory for symmetric operators with some results on the regularity domain and numerical range.

  • Adds some general results for behavior under negation / scalar multiplication.
  • Defines realNumericalRange which is the numerical range of a symmetric operator as a subset of ℝ rather than of ℂ, allowing for the notion of upper/lower bounds.
  • Proves that the regularity domain contains all complex numbers with nonzero imaginary part as well as (-∞,m) or (m,∞) when m is a lower/upper bound on the numerical range.
  • Adds a characterization of when the regularity domain is connected.

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gloges commented Jun 17, 2026

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t-quantum-mechanics

@github-actions github-actions Bot added the t-quantum-mechanics Quantum mechanics label Jun 17, 2026
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Thank you for this PR, which will now be reviewed.
If submitting to ./Physlib or ./QuantumInfo, please
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Looks good to me. Approved - will merge shortly.

@jstoobysmith jstoobysmith added the ready-to-merge This PR is approved and will be merged shortly label Jun 17, 2026
@jstoobysmith jstoobysmith merged commit f9448b0 into leanprover-community:master Jun 17, 2026
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@gloges gloges deleted the symmetric branch June 17, 2026 07:39
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ready-to-merge This PR is approved and will be merged shortly t-quantum-mechanics Quantum mechanics

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2 participants