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feat(QuantumMechanics): basic properties/defs for HarmonicOscillator#1442

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jstoobysmith merged 9 commits into
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Jul 19, 2026
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feat(QuantumMechanics): basic properties/defs for HarmonicOscillator#1442
jstoobysmith merged 9 commits into
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gloges:qho

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@gloges gloges commented Jul 19, 2026

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The harmonic oscillator should probably serve as the model example of a well-developed, well-documented quantum mechanical system -- this PR lays the groundwork.

  • Adds @[simp] tags to the hbar lemmas (requires a fix to the 1d QHO).
  • Defines the HarmonicOscillator structure containing data for the mass and natural frequencies (all positive).
  • Defines the characteristic lengths $$ξ_i = \sqrt{ℏ / m \omega_i}$$ and introduces some lemmas to take care of inverses and squares (to help with the sqrt).
  • Defines a property IsIsotropic for when all natural frequencies are equal. When this property holds the potential is spherically symmetric: eigenfunctions can be written neatly in terms of spherical harmonics and the spectrum is highly degenerate.
  • Defines kinetic, potential and Hamiltonian operators. Some of their important properties (e.g. (ess.) self-adjointness) depend on improving the definition of derivative operators (this is currently being developed).
  • Creates HarmonicOscillator/LadderOperator.lean with a rough TODO list.

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Thank you for this PR, which will now be reviewed. If submitting to ./Physlib or ./QuantumInfo, please see our review guidelines if you are not familiar with the process. You should expect a back and forth with a reviewer before your PR is merged. See also that link for how to add appropriate labels to your PR. The PR will also go through a number of automated checks. You can learn more about these here, including how to run them locally.

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@github-actions github-actions Bot added the t-quantum-mechanics Quantum mechanics label Jul 19, 2026

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Looks good - approved.

@jstoobysmith jstoobysmith added the ready-to-merge This PR is approved and will be merged shortly label Jul 19, 2026
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jstoobysmith merged commit e02ba31 into leanprover-community:master Jul 19, 2026
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gloges deleted the qho branch July 19, 2026 12:16
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