Eigenfunction square integrable
QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_square_integrable
Plain-language statement
The eigenfunctions are square integrable.
Exact Lean statement
@[fun_prop]
lemma eigenfunction_square_integrable (n : ℕ) :
MeasureTheory.Integrable (fun x => ‖Q.eigenfunction n x‖ ^ 2)Formal artifact
Lean source
@[fun_prop]lemma eigenfunction_square_integrable (n : ℕ) : MeasureTheory.Integrable (fun x => ‖Q.eigenfunction n x‖ ^ 2) := by have h0 (x : ℝ) : Real.exp (- x ^ 2 / Q.ξ^2) = Real.exp (- (1 /Q.ξ^2) * x ^ 2) := by simp only [neg_mul, Real.exp_eq_exp] ring conv => enter [1, x] rw [eigenfunction_point_norm_sq] rw [physHermite_pow, h0] enter [2, 1, 1, 1] rw [← one_div_mul_eq_div] apply MeasureTheory.Integrable.const_mul apply guassian_integrable_polynomial_cons simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/QuantumMechanics/HarmonicOscillator/OneDimension/Eigenfunction.lean:122-137
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