Eigenfunction integrable
QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_integrable
Plain-language statement
The eigenfunctions are integrable.
Exact Lean statement
@[fun_prop] lemma eigenfunction_integrable (n : ℕ) : Integrable (Q.eigenfunction n)
Formal artifact
Lean source
@[fun_prop]lemma eigenfunction_integrable (n : ℕ) : Integrable (Q.eigenfunction n) := by rw [eigenfunction_eq] apply Integrable.const_mul apply Integrable.ofReal change Integrable (fun x => physHermite n (x / Q.ξ) * Real.exp (- x^2 / (2 * Q.ξ^2))) have h1 : (fun x => physHermite n (x / Q.ξ) * Real.exp (- x^2 / (2 * Q.ξ^2))) = (fun x => physHermite n (1/Q.ξ * x) * Real.exp (- (1 / (2 * Q.ξ^2)) * x ^ 2)) := by funext x ring_nf rw [h1] apply guassian_integrable_polynomial_cons simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/QuantumMechanics/HarmonicOscillator/OneDimension/Eigenfunction.lean:71-83
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