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Merged
gloges merged 1 commit into from
Jul 21, 2026
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refactor(QuantumMechanics): rename SelfAdjoint to Symmetric #1449

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4 changes: 2 additions & 2 deletions Physlib/QuantumMechanics/Operators/OneDimension/Momentum.lean
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Expand Up @@ -117,11 +117,11 @@ lemma planeWaveFunctional_generalized_eigenvector_momentumOperatorUnbounded (k :

/-!

## The momentum operator is self adjoint
## The momentum operator is symmetric

-/

lemma momentumOperatorUnbounded_isSelfAdjoint : momentumOperatorUnbounded.IsSelfAdjoint := by
lemma momentumOperatorUnbounded_isSymmetric : momentumOperatorUnbounded.IsSymmetric := by
intro ψ1 ψ2
have hint : ∀ f g : 𝓢(ℝ, ℂ),
MeasureTheory.Integrable (fun x => star (f x) * g x) MeasureTheory.volume :=
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6 changes: 3 additions & 3 deletions Physlib/QuantumMechanics/Operators/OneDimension/Parity.lean
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Expand Up @@ -93,14 +93,14 @@ lemma parityOperatorSchwartz_parityOperatorSchwartz (ψ : 𝓢(ℝ, ℂ)) :

/-!

## Parity operator is self adjoint
## Parity operator is symmetric

-/

open InnerProductSpace

lemma parityOperatorUnbounded_isSelfAdjoint :
parityOperatorUnbounded.IsSelfAdjoint := by
lemma parityOperatorUnbounded_isSymmetric :
parityOperatorUnbounded.IsSymmetric := by
intro ψ1 ψ2
dsimp [parityOperatorUnbounded]
rw [schwartzIncl_inner, schwartzIncl_inner]
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6 changes: 3 additions & 3 deletions Physlib/QuantumMechanics/Operators/OneDimension/Position.lean
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Expand Up @@ -93,12 +93,12 @@ lemma positionStates_generalized_eigenvector_positionOperatorUnbounded (x : ℝ)

/-!

## Position operator is self adjoint
## Position operator is symmetric

-/

lemma positionOperatorUnbounded_isSelfAdjoint :
positionOperatorUnbounded.IsSelfAdjoint := by
lemma positionOperatorUnbounded_isSymmetric :
positionOperatorUnbounded.IsSymmetric := by
intro ψ1 ψ2
dsimp [positionOperatorUnbounded]
rw [schwartzIncl_inner, schwartzIncl_inner]
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8 changes: 6 additions & 2 deletions Physlib/QuantumMechanics/Operators/OneDimension/Unbounded.lean
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Expand Up @@ -62,8 +62,12 @@ lemma isGeneralizedEigenvector_ofSelfCLM_iff {Op : S →L[ℂ] S}

open InnerProductSpace

/-- The condition on an unbounded operator to be self-adjoint. -/
def IsSelfAdjoint : Prop :=
/-- The condition for an unbounded operator to be *symmetric* (equivalently, formally
self-adjoint): `⟪U ψ1, ι ψ2⟫ = ⟪ι ψ1, U ψ2⟫` for all `ψ1 ψ2`. This is the Hermitian
pairing on the underlying space `S`; on its own it does **not** imply genuine
self-adjointness (`A† = A`, including equality of domains), which for an unbounded
operator on a proper dense core is strictly stronger. -/
def IsSymmetric : Prop :=
∀ ψ1 ψ2 : S, ⟪U ψ1, ι ψ2⟫_ℂ = ⟪ι ψ1, U ψ2⟫_ℂ

end UnboundedOperator
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