DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

feat: Notes for harmonic oscillator

Browse source
This commit is contained in:
jstoobysmith 2025-02-26 11:03:29 +00:00
parent dad988f880
commit c21ce36eb1
9 changed files with 229 additions and 19 deletions
Download patch file Download diff file Expand all files Collapse all files

49
scripts/MetaPrograms/notes.lean
View file

@ -290,10 +290,57 @@ def perturbationTheory : Note where
.name ``FieldSpecification.FieldOpAlgebra.wicks_theorem_normal_order .complete
]
def harmonicOscillator : Note where
title := "The Quantum Harmonic Oscillator in Lean 4"
curators := ["Joseph Tooby-Smith"]
parts := [
.h1 "Introduction",
.p "The quantum harmonic oscillator is one of the foundational examples
of a 1d quantum mechanical system. It is perhaps the first example that
many undergraduate students encounter when learning quantum mechanics.",
.p "
This note shall present the digitilisation (or formalization) of the
quantum harmonic oscillator into the theorem prover Lean 4. This is part of a larger
project called PhysLean. Note not every definition and theorem is given here.",
.h1 "Hilbert Space",
.name ``QuantumMechanics.OneDimension.HilbertSpace .complete,
.name ``QuantumMechanics.OneDimension.HilbertSpace.MemHS .complete,
.name ``QuantumMechanics.OneDimension.HilbertSpace.memHS_iff .complete,
.name ``QuantumMechanics.OneDimension.HilbertSpace.mk .complete,
.h1 "The Schrodinger Operator",
.name ``QuantumMechanics.OneDimension.HarmonicOscillator .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.schrodingerOperator .complete,
.h1 "The eigenfunctions of the Schrodinger Operator",
.name ``PhysLean.physHermite .complete,
.name ``PhysLean.physHermiteFun .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction .complete,
.h2 "Properties of the eigenfunctions",
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_integrable .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_conj .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_aeStronglyMeasurable .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_square_integrable .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_memHS .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_differentiableAt .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_orthonormal .complete,
.h1 "The time-independent Schrodinger Equation",
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenValue .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.schrodingerOperator_eigenfunction
.complete,
.h1 "Completeness",
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.orthogonal_power_of_mem_orthogonal .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.orthogonal_exp_of_mem_orthogonal .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.fourierIntegral_zero_of_mem_orthogonal .complete,
.name ``QuantumMechanics.OneDimension.HarmonicOscillator.eigenfunction_completeness .complete,
]
unsafe def main (_ : List String) : IO UInt32 := do
initSearchPath (← findSysroot)
let ymlString ← CoreM.withImportModules #[`PhysLean] (perturbationTheory.toYML).run'
let fileOut : System.FilePath := {toString := "./docs/_data/perturbationTheory.yml"}
IO.println (s!"YML file made.")
IO.println (s!"YML file made for perturbation theory.")
IO.FS.writeFile fileOut ymlString
let ymlString2 ← CoreM.withImportModules #[`PhysLean] (harmonicOscillator.toYML).run'
let fileOut2 : System.FilePath := {toString := "./docs/_data/harmonicOscillator.yml"}
IO.println (s!"YML file made for harmonic oscillator.")
IO.FS.writeFile fileOut2 ymlString2
pure 0