Package evaluation to test TwoBody on Julia 1.14.0-DEV.2802 (918269a29b*) started at 2026-08-28T02:09:07.670 ################################################################################ # Set-up # Installing PkgEval dependencies (TestEnv)... Activating project at `~/.julia/environments/v1.14` Set-up completed after 14.73s ################################################################################ # Installation # Installing TwoBody... Resolving package versions... Installed TwoBody ─ v0.0.12 Updating `~/.julia/environments/v1.14/Project.toml` [a92d7657] + TwoBody v0.0.12 Updating `~/.julia/environments/v1.14/Manifest.toml` [47edcb42] + ADTypes v1.24.0 [621f4979] + AbstractFFTs v1.5.0 [79e6a3ab] + Adapt v4.7.0 [66dad0bd] + AliasTables v1.1.3 [ec485272] + ArnoldiMethod v0.4.0 [4fba245c] + ArrayInterface v7.30.0 [a9b6321e] + Atomix v1.1.3 [ab4f0b2a] + BFloat16s v0.6.1 [c3b6d118] + BitIntegers v0.3.7 [2a0fbf3d] + CPUSummary v0.2.7 [082447d4] + ChainRules v1.73.0 [d360d2e6] + ChainRulesCore v1.26.1 [bbf7d656] + CommonSubexpressions v0.3.1 [f70d9fcc] + CommonWorldInvalidations v1.2.0 [34da2185] + Compat v4.18.1 [2569d6c7] + ConcreteStructs v0.2.8 [187b0558] + ConstructionBase v1.6.0 [adafc99b] + CpuId v0.3.1 [9a962f9c] + DataAPI v1.16.0 [864edb3b] + DataStructures v0.19.6 [e2d170a0] + DataValueInterfaces v1.0.0 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.16.0 [a0c0ee7d] + DifferentiationInterface v0.7.21 [8d63f2c5] + DispatchDoctor v0.4.28 [ffbed154] + DocStringExtensions v0.9.5 [da5c29d0] + EllipsisNotation v1.12.0 [4e289a0a] + EnumX v1.0.7 [f151be2c] + EnzymeCore v0.8.21 [21656369] + ExpressionExplorer v1.1.5 [9aa1b823] + FastClosures v0.3.2 [1a297f60] + FillArrays v1.17.0 [6a86dc24] + FiniteDiff v2.33.0 [a7a66f33] + FiniteDifferenceMatrices v0.1.0 [f6369f11] + ForwardDiff v1.4.5 [d9f16b24] + Functors v0.5.3 [46192b85] + GPUArraysCore v0.2.0 [076d061b] + HashArrayMappedTries v0.2.0 [7869d1d1] + IRTools v0.4.20 [615f187c] + IfElse v0.1.1 [87f1ea11] + InterpolativeQTT v0.1.3 [92d709cd] + IrrationalConstants v0.2.6 [42fd0dbc] + IterativeSolvers v0.9.4 [82899510] + IteratorInterfaceExtensions v1.0.0 [692b3bcd] + JLLWrappers v1.8.0 [63c18a36] + KernelAbstractions v0.9.42 [0b1a1467] + KrylovKit v0.10.4 [8ac3fa9e] + LRUCache v1.6.2 ⌃ [d3d80556] + LineSearches v7.5.1 [7a12625a] + LinearMaps v3.11.4 [2ab3a3ac] + LogExpFunctions v1.0.1 [b2108857] + Lux v1.31.4 [bb33d45b] + LuxCore v1.5.3 [82251201] + LuxLib v1.15.9 [7e8f7934] + MLDataDevices v1.17.10 [1914dd2f] + MacroTools v0.5.16 [4cc553b9] + Maxvol v1.0.0 [e1d29d7a] + Missings v1.2.0 ⌅ [d41bc354] + NLSolversBase v7.10.0 [872c559c] + NNlib v0.9.44 [77ba4419] + NaNMath v1.1.4 ⌅ [429524aa] + Optim v1.13.3 [3bd65402] + Optimisers v0.4.9 [bac558e1] + OrderedCollections v2.0.1 [65ce6f38] + PackageExtensionCompat v1.0.2 [85a6dd25] + PositiveFactorizations v0.2.4 [aea7be01] + PrecompileTools v1.3.4 [21216c6a] + Preferences v1.5.2 [92933f4c] + ProgressMeter v1.11.0 [43287f4e] + PtrArrays v1.4.0 [1fd47b50] + QuadGK v2.11.3 [a3311ec8] + ReactantCore v0.1.21 [c1ae055f] + RealDot v0.1.0 [3cdcf5f2] + RecipesBase v1.3.4 [189a3867] + Reexport v1.2.2 [ae029012] + Requires v1.3.1 [431bcebd] + SciMLPublic v1.3.0 [7e506255] + ScopedValues v1.6.2 [efcf1570] + Setfield v1.1.2 [a2af1166] + SortingAlgorithms v1.2.3 [dc90abb0] + SparseInverseSubset v0.1.3 [276daf66] + SpecialFunctions v2.9.0 [aedffcd0] + Static v1.4.6 [90137ffa] + StaticArrays v1.9.19 [1e83bf80] + StaticArraysCore v1.4.4 [10745b16] + Statistics v1.11.1 [82ae8749] + StatsAPI v1.8.0 [2913bbd2] + StatsBase v0.34.13 [5e0ebb24] + Strided v2.6.4 [4db3bf67] + StridedViews v0.5.2 [09ab397b] + StructArrays v0.7.3 [2b7f82d5] + Subscripts v0.1.3 [3783bdb8] + TableTraits v1.0.1 [bd369af6] + Tables v1.14.0 [b261b2ec] + TensorCrossInterpolation v0.9.19 [6aa20fa7] + TensorOperations v5.8.0 [304e70ee] + TensorTrainNumerics v1.1.4 [9d95972d] + TupleTools v1.6.0 [a92d7657] + TwoBody v0.0.12 [013be700] + UnsafeAtomics v0.3.2 [409d34a3] + VectorInterface v0.6.0 [d49dbf32] + WeightInitializers v1.3.4 [e88e6eb3] + Zygote v0.7.12 [700de1a5] + ZygoteRules v0.2.8 [efe28fd5] + OpenSpecFun_jll v0.5.6+0 [56f22d72] + Artifacts v1.11.0 [2a0f44e3] + Base64 v1.11.0 [ade2ca70] + Dates v1.11.0 [8ba89e20] + Distributed v1.11.0 [9fa8497b] + Future v1.11.0 [b77e0a4c] + InteractiveUtils v1.11.0 [ac6e5ff7] + JuliaSyntaxHighlighting v1.13.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.14.0 [56ddb016] + Logging v1.11.0 [d6f4376e] + Markdown v1.11.0 [de0858da] + Printf v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v1.13.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.13.0 [f489334b] + StyledStrings v1.13.0 [4607b0f0] + SuiteSparse [fa267f1f] + TOML v1.0.3 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.5.7+0 [4536629a] + OpenBLAS_jll v0.3.34+0 [05823500] + OpenLibm_jll v0.8.7+0 [bea87d4a] + SuiteSparse_jll v7.10.1+0 [8e850b90] + libblastrampoline_jll v5.15.0+0 Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m` Installation completed after 6.25s ################################################################################ # Precompilation # Precompiling PkgEval dependencies... Precompiling package dependencies... Precompiling project... 2.1 s ✓ InterpolativeQTT ┌ Warning: Replacing docs for `Antique.laguerre_polynomial :: Union{}` in module `Antique` └ @ Base.Docs docs/Docs.jl:253 2.1 s ✓ Antique 5.4 s ✓ TensorTrainNumerics → TensorTrainNumericsInterpolativeQTTExt 15.1 s ✓ TwoBody 4 dependencies successfully precompiled in 26 seconds. 199 already precompiled. 1 dependency had output during precompilation: ┌ Antique │ ┌ Warning: Replacing docs for `Antique.laguerre_polynomial :: Union{}` in module `Antique` │ └ @ Base.Docs docs/Docs.jl:253 └ Precompilation completed after 54.88s ################################################################################ # Testing # Testing TwoBody Status `/tmp/jl_NiAM91/Project.toml` [be6e5d0e] Antique v0.15.0 [f6369f11] ForwardDiff v1.4.5 [b2108857] Lux v1.31.4 [3bd65402] Optimisers v0.4.9 [1fd47b50] QuadGK v2.11.3 [276daf66] SpecialFunctions v2.9.0 [a92d7657] TwoBody v0.0.12 [de0858da] Printf v1.11.0 [9a3f8284] Random v1.11.0 [8dfed614] Test v1.11.0 Status `/tmp/jl_NiAM91/Manifest.toml` [47edcb42] ADTypes v1.24.0 [621f4979] AbstractFFTs v1.5.0 [79e6a3ab] Adapt v4.7.0 [66dad0bd] AliasTables v1.1.3 [be6e5d0e] Antique v0.15.0 [ec485272] ArnoldiMethod v0.4.0 [4fba245c] ArrayInterface v7.30.0 [a9b6321e] Atomix v1.1.3 [ab4f0b2a] BFloat16s v0.6.1 [c3b6d118] BitIntegers v0.3.7 [2a0fbf3d] CPUSummary v0.2.7 [082447d4] ChainRules v1.73.0 [d360d2e6] ChainRulesCore v1.26.1 [bbf7d656] CommonSubexpressions v0.3.1 [f70d9fcc] CommonWorldInvalidations v1.2.0 [34da2185] Compat v4.18.1 [2569d6c7] ConcreteStructs v0.2.8 [187b0558] ConstructionBase v1.6.0 [adafc99b] CpuId v0.3.1 [9a962f9c] DataAPI v1.16.0 [864edb3b] DataStructures v0.19.6 [e2d170a0] DataValueInterfaces v1.0.0 [163ba53b] DiffResults v1.1.0 [b552c78f] DiffRules v1.16.0 [a0c0ee7d] DifferentiationInterface v0.7.21 [8d63f2c5] DispatchDoctor v0.4.28 [ffbed154] DocStringExtensions v0.9.5 [da5c29d0] EllipsisNotation v1.12.0 [4e289a0a] EnumX v1.0.7 [f151be2c] EnzymeCore v0.8.21 [21656369] ExpressionExplorer v1.1.5 [9aa1b823] FastClosures v0.3.2 [1a297f60] FillArrays v1.17.0 [6a86dc24] FiniteDiff v2.33.0 [a7a66f33] FiniteDifferenceMatrices v0.1.0 [f6369f11] ForwardDiff v1.4.5 [d9f16b24] Functors v0.5.3 [46192b85] GPUArraysCore v0.2.0 [076d061b] HashArrayMappedTries v0.2.0 [7869d1d1] IRTools v0.4.20 [615f187c] IfElse v0.1.1 [87f1ea11] InterpolativeQTT v0.1.3 [92d709cd] IrrationalConstants v0.2.6 [42fd0dbc] IterativeSolvers v0.9.4 [82899510] IteratorInterfaceExtensions v1.0.0 [692b3bcd] JLLWrappers v1.8.0 [63c18a36] KernelAbstractions v0.9.42 [0b1a1467] KrylovKit v0.10.4 [8ac3fa9e] LRUCache v1.6.2 ⌃ [d3d80556] LineSearches v7.5.1 [7a12625a] LinearMaps v3.11.4 [2ab3a3ac] LogExpFunctions v1.0.1 [b2108857] Lux v1.31.4 [bb33d45b] LuxCore v1.5.3 [82251201] LuxLib v1.15.9 [7e8f7934] MLDataDevices v1.17.10 [1914dd2f] MacroTools v0.5.16 [4cc553b9] Maxvol v1.0.0 [e1d29d7a] Missings v1.2.0 ⌅ [d41bc354] NLSolversBase v7.10.0 [872c559c] NNlib v0.9.44 [77ba4419] NaNMath v1.1.4 ⌅ [429524aa] Optim v1.13.3 [3bd65402] Optimisers v0.4.9 [bac558e1] OrderedCollections v2.0.1 [65ce6f38] PackageExtensionCompat v1.0.2 [85a6dd25] PositiveFactorizations v0.2.4 [aea7be01] PrecompileTools v1.3.4 [21216c6a] Preferences v1.5.2 [92933f4c] ProgressMeter v1.11.0 [43287f4e] PtrArrays v1.4.0 [1fd47b50] QuadGK v2.11.3 [a3311ec8] ReactantCore v0.1.21 [c1ae055f] RealDot v0.1.0 [3cdcf5f2] RecipesBase v1.3.4 [189a3867] Reexport v1.2.2 [ae029012] Requires v1.3.1 [431bcebd] SciMLPublic v1.3.0 [7e506255] ScopedValues v1.6.2 [efcf1570] Setfield v1.1.2 [a2af1166] SortingAlgorithms v1.2.3 [dc90abb0] SparseInverseSubset v0.1.3 [276daf66] SpecialFunctions v2.9.0 [aedffcd0] Static v1.4.6 [90137ffa] StaticArrays v1.9.19 [1e83bf80] StaticArraysCore v1.4.4 [10745b16] Statistics v1.11.1 [82ae8749] StatsAPI v1.8.0 [2913bbd2] StatsBase v0.34.13 [5e0ebb24] Strided v2.6.4 [4db3bf67] StridedViews v0.5.2 [09ab397b] StructArrays v0.7.3 [2b7f82d5] Subscripts v0.1.3 [3783bdb8] TableTraits v1.0.1 [bd369af6] Tables v1.14.0 [b261b2ec] TensorCrossInterpolation v0.9.19 [6aa20fa7] TensorOperations v5.8.0 [304e70ee] TensorTrainNumerics v1.1.4 [9d95972d] TupleTools v1.6.0 [a92d7657] TwoBody v0.0.12 [013be700] UnsafeAtomics v0.3.2 [409d34a3] VectorInterface v0.6.0 [d49dbf32] WeightInitializers v1.3.4 [e88e6eb3] Zygote v0.7.12 [700de1a5] ZygoteRules v0.2.8 [efe28fd5] OpenSpecFun_jll v0.5.6+0 [56f22d72] Artifacts v1.11.0 [2a0f44e3] Base64 v1.11.0 [ade2ca70] Dates v1.11.0 [8ba89e20] Distributed v1.11.0 [9fa8497b] Future v1.11.0 [b77e0a4c] InteractiveUtils v1.11.0 [ac6e5ff7] JuliaSyntaxHighlighting v1.13.0 [8f399da3] Libdl v1.11.0 [37e2e46d] LinearAlgebra v1.14.0 [56ddb016] Logging v1.11.0 [d6f4376e] Markdown v1.11.0 [de0858da] Printf v1.11.0 [9a3f8284] Random v1.11.0 [ea8e919c] SHA v1.13.0 [9e88b42a] Serialization v1.11.0 [6462fe0b] Sockets v1.11.0 [2f01184e] SparseArrays v1.13.0 [f489334b] StyledStrings v1.13.0 [4607b0f0] SuiteSparse [fa267f1f] TOML v1.0.3 [8dfed614] Test v1.11.0 [cf7118a7] UUIDs v1.11.0 [4ec0a83e] Unicode v1.11.0 [e66e0078] CompilerSupportLibraries_jll v1.5.7+0 [4536629a] OpenBLAS_jll v0.3.34+0 [05823500] OpenLibm_jll v0.8.7+0 [bea87d4a] SuiteSparse_jll v7.10.1+0 [8e850b90] libblastrampoline_jll v5.15.0+0 Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. Testing Running tests... φ(SGB,r) = exp(-a*r^2) a r numerical analytical 13.01 0.00 1.000000000 1.000000000 ✔ 13.01 0.10 0.878027557 0.878027557 ✔ 13.01 0.20 0.594336751 0.594336751 ✔ 13.01 0.50 0.038699349 0.038699349 ✔ 13.01 1.00 0.000002243 0.000002243 ✔ 13.01 2.00 0.000000000 0.000000000 ✔ 13.01 5.00 0.000000000 0.000000000 ✔ 13.01 10.00 0.000000000 0.000000000 ✔ 1.96 0.00 1.000000000 1.000000000 ✔ 1.96 0.10 0.980570445 0.980570445 ✔ 1.96 0.20 0.924517629 0.924517629 ✔ 1.96 0.50 0.612308064 0.612308064 ✔ 1.96 1.00 0.140565880 0.140565880 ✔ 1.96 2.00 0.000390409 0.000390409 ✔ 1.96 5.00 0.000000000 0.000000000 ✔ 1.96 10.00 0.000000000 0.000000000 ✔ 0.44 0.00 1.000000000 1.000000000 ✔ 0.44 0.10 0.995564576 0.995564576 ✔ 0.44 0.20 0.982375992 0.982375992 ✔ 0.44 0.50 0.894820401 0.894820401 ✔ 0.44 1.00 0.641126175 0.641126175 ✔ 0.44 2.00 0.168956161 0.168956161 ✔ 0.44 5.00 0.000014914 0.000014914 ✔ 0.44 10.00 0.000000000 0.000000000 ✔ 0.12 0.00 1.000000000 1.000000000 ✔ 0.12 0.10 0.998781251 0.998781251 ✔ 0.12 0.20 0.995133910 0.995133910 ✔ 0.12 0.50 0.969972751 0.969972751 ✔ 0.12 1.00 0.885193335 0.885193335 ✔ 0.12 2.00 0.613977621 0.613977621 ✔ 0.12 5.00 0.047419108 0.047419108 ✔ 0.12 10.00 0.000005056 0.000005056 ✔ φ(r) = exp(-ar²) φ(k) = exp(-k²/4a) / (2a)^(3/2) φ(k) = 1/√2π³ ∫ φ(r) eⁱᵏʳ r²sin(θ)drdθdφ a k θk φk numerical analytical 13.01 0.00 0.0 0.0 0.007536206 0.007536206 ✔ 13.01 0.00 0.0 1.0 0.007536206 0.007536206 ✔ 13.01 0.00 0.5 0.0 0.007536206 0.007536206 ✔ 13.01 0.00 0.5 1.0 0.007536206 0.007536206 ✔ 13.01 3.00 0.0 0.0 0.006339150 0.006339150 ✔ 13.01 3.00 0.0 1.0 0.006339150 0.006339150 ✔ 13.01 3.00 0.5 0.0 0.006339150 0.006339150 ✔ 13.01 3.00 0.5 1.0 0.006339150 0.006339150 ✔ 13.01 5.00 0.0 0.0 0.004661025 0.004661025 ✔ 13.01 5.00 0.0 1.0 0.004661025 0.004661025 ✔ 13.01 5.00 0.5 0.0 0.004661025 0.004661025 ✔ 13.01 5.00 0.5 1.0 0.004661025 0.004661025 ✔ 1.96 0.00 0.0 0.0 0.128641256 0.128641256 ✔ 1.96 0.00 0.0 1.0 0.128641256 0.128641256 ✔ 1.96 0.00 0.5 0.0 0.128641256 0.128641256 ✔ 1.96 0.00 0.5 1.0 0.128641256 0.128641256 ✔ 1.96 3.00 0.0 0.0 0.040865441 0.040865441 ✔ 1.96 3.00 0.0 1.0 0.040865441 0.040865441 ✔ 1.96 3.00 0.5 0.0 0.040865441 0.040865441 ✔ 1.96 3.00 0.5 1.0 0.040865441 0.040865441 ✔ 1.96 5.00 0.0 0.0 0.005320838 0.005320838 ✔ 1.96 5.00 0.0 1.0 0.005320838 0.005320838 ✔ 1.96 5.00 0.5 0.0 0.005320838 0.005320838 ✔ 1.96 5.00 0.5 1.0 0.005320838 0.005320838 ✔ 0.44 0.00 0.0 0.0 1.192902253 1.192902253 ✔ 0.44 0.00 0.0 1.0 1.192902253 1.192902253 ✔ 0.44 0.00 0.5 0.0 1.192902253 1.192902253 ✔ 0.44 0.00 0.5 1.0 1.192902253 1.192902253 ✔ 0.44 3.00 0.0 0.0 0.007558006 0.007558006 ✔ 0.44 3.00 0.0 1.0 0.007558006 0.007558006 ✔ 0.44 3.00 0.5 0.0 0.007558007 0.007558006 ✔ 0.44 3.00 0.5 1.0 0.007558006 0.007558006 ✔ 0.44 5.00 0.0 0.0 0.000000950 0.000000934 ✔ 0.44 5.00 0.0 1.0 0.000000950 0.000000934 ✔ 0.44 5.00 0.5 0.0 0.000000850 0.000000934 ✔ 0.44 5.00 0.5 1.0 0.000000850 0.000000934 ✔ 0.12 0.00 0.0 0.0 8.302073477 8.302073482 ✔ 0.12 0.00 0.0 1.0 8.302073477 8.302073482 ✔ 0.12 0.00 0.5 0.0 8.302073477 8.302073482 ✔ 0.12 0.00 0.5 1.0 8.302073477 8.302073482 ✔ 0.12 3.00 0.0 0.0 0.000000604 0.000000081 ✔ 0.12 3.00 0.0 1.0 0.000000604 0.000000081 ✔ 0.12 3.00 0.5 0.0 0.000005964 0.000000081 ✔ 0.12 3.00 0.5 1.0 0.000005971 0.000000081 ✔ 0.12 5.00 0.0 0.0 0.000000935 0.000000000 ✔ 0.12 5.00 0.0 1.0 0.000000935 0.000000000 ✔ 0.12 5.00 0.5 0.0 0.000554601 0.000000000 ✔ 0.12 5.00 0.5 1.0 0.000546580 0.000000000 ✔ 4π×∫|ψ(r)|²r²dr = 1 i numerical analytical 1 1.000000000 1.000000000 ✔ 2 1.000000000 1.000000000 ✔ 3 1.000000000 1.000000000 ✔ 4 1.000000000 1.000000000 ✔ <ψₙ|ψₙ> = cₙ' * S * cₙ = 1 i numerical analytical 1 1.000000000 1.000000000 ✔ 2 1.000000000 1.000000000 ✔ 3 1.000000000 1.000000000 ✔ 4 1.000000000 1.000000000 ✔ |<ψₙ|H|ψₙ> - E| = |cₙ' * H * cₙ - E| = 0 i numerical analytical 1 0.000000000 0.000000000 ✔ 2 0.000000000 0.000000000 ✔ 3 0.000000000 0.000000000 ✔ 4 0.000000000 0.000000000 ✔ Thijssen(2007) i numerical analytical 1 -0.499278406 -0.499278000 ✔ ψ(r) r numerical analytical 0.2 0.463487237 0.461919363 ✔ 0.3 0.417639827 0.417961923 ✔ 0.4 0.376208630 0.378187588 ✔ 0.5 0.341090546 0.342198280 ✔ 0.6 0.310006041 0.309633808 ✔ 0.7 0.281181506 0.280168256 ✔ 0.8 0.254263019 0.253506721 ✔ 0.9 0.229509210 0.229382367 ✔ 1.0 0.207138965 0.207553749 ✔ 1.1 0.187146290 0.187802398 ✔ 1.2 0.169342309 0.169930637 ✔ 1.3 0.153447357 0.153759599 ✔ 1.4 0.139168631 0.139127438 ✔ 1.5 0.126248348 0.125887712 ✔ 1.6 0.114484277 0.113907912 ✔ 1.7 0.103730392 0.103068141 ✔ 1.8 0.093886391 0.093259911 ✔ 1.9 0.084883363 0.084385057 ✔ 2.0 0.076670326 0.076354757 ✔ Kinetic(hbar=1, m=1) i j numerical analytical 1 1 0.818785829 0.818785829 ✔ 2 1 0.491726279 0.491726279 ✔ 3 1 0.145532378 0.145532378 ✔ 4 1 0.042422010 0.042422010 ✔ 1 2 0.491726279 0.491726279 ✔ 2 2 2.108204955 2.108204955 ✔ 3 2 1.621620634 1.621620634 ✔ 4 2 0.637503437 0.637503437 ✔ 1 3 0.145532378 0.145532378 ✔ 2 3 1.621620634 1.621620634 ✔ 3 3 4.429156494 4.429156494 ✔ 4 3 3.749446097 3.749446097 ✔ 1 4 0.042422010 0.042422010 ✔ 2 4 0.637503437 0.637503437 ✔ 3 4 3.749446097 3.749446097 ✔ 4 4 8.456323657 8.456323657 ✔ Constant(constant=1) i j numerical analytical 1 1 0.041964064 0.041964064 ✔ 2 1 0.096139181 0.096139181 ✔ 3 1 0.112857904 0.112857904 ✔ 4 1 0.117042513 0.117042513 ✔ 1 2 0.096139181 0.096139181 ✔ 2 2 0.716316708 0.716316708 ✔ 3 2 1.491477737 1.491477737 ✔ 4 2 1.850842324 1.850842324 ✔ 1 3 0.112857904 0.112857904 ✔ 2 3 1.491477737 1.491477737 ✔ 3 3 6.642471011 6.642471011 ✔ 4 3 13.060205392 13.060205392 ✔ 1 4 0.117042513 0.117042513 ✔ 2 4 1.850842324 1.850842324 ✔ 3 4 13.060205392 13.060205392 ✔ 4 4 46.228668204 46.228668204 ✔ Linear(coefficient=1) i j numerical analytical 1 1 0.009283609 0.009283609 ✔ 2 1 0.028038021 0.028038021 ✔ 3 1 0.034720776 0.034720776 ✔ 4 1 0.036447827 0.036447827 ✔ 1 2 0.028038021 0.028038021 ✔ 2 2 0.408025117 0.408025117 ✔ 3 2 1.084848658 1.084848658 ✔ 4 2 1.446680694 1.446680694 ✔ 1 3 0.034720776 0.034720776 ✔ 2 3 1.084848658 1.084848658 ✔ 3 3 7.949131472 7.949131472 ✔ 4 3 19.580035080 19.580035080 ✔ 1 4 0.036447827 0.036447827 ✔ 2 4 1.446680694 1.446680694 ✔ 3 4 19.580035080 19.580035080 ✔ 4 4 105.623843246 105.623843246 ✔ Coulomb(coefficient=1) i j numerical analytical 1 1 0.241517363 0.241517363 ✔ 2 1 0.419723813 0.419723813 ✔ 3 1 0.467072877 0.467072877 ✔ 4 1 0.478548273 0.478548273 ✔ 1 2 0.419723813 0.419723813 ✔ 2 2 1.601155027 1.601155027 ✔ 3 2 2.610805460 2.610805460 ✔ 4 2 3.014923362 3.014923362 ✔ 1 3 0.467072877 0.467072877 ✔ 2 3 2.610805460 2.610805460 ✔ 3 3 7.067238928 7.067238928 ✔ 4 3 11.091663028 11.091663028 ✔ 1 4 0.478548273 0.478548273 ✔ 2 4 3.014923362 3.014923362 ✔ 3 4 11.091663028 11.091663028 ✔ 4 4 25.761486370 25.761486370 ✔ PowerLaw(coefficient=1, exponent=1) i j numerical analytical 1 1 0.009283609 0.009283609 ✔ 2 1 0.028038021 0.028038021 ✔ 3 1 0.034720776 0.034720776 ✔ 4 1 0.036447827 0.036447827 ✔ 1 2 0.028038021 0.028038021 ✔ 2 2 0.408025117 0.408025117 ✔ 3 2 1.084848658 1.084848658 ✔ 4 2 1.446680694 1.446680694 ✔ 1 3 0.034720776 0.034720776 ✔ 2 3 1.084848658 1.084848658 ✔ 3 3 7.949131472 7.949131472 ✔ 4 3 19.580035080 19.580035080 ✔ 1 4 0.036447827 0.036447827 ✔ 2 4 1.446680694 1.446680694 ✔ 3 4 19.580035080 19.580035080 ✔ 4 4 105.623843246 105.623843246 ✔ PowerLaw(coefficient=1, exponent=2) i j numerical analytical 1 1 0.002419565 0.002419565 ✔ 2 1 0.009633307 0.009633307 ✔ 3 1 0.012584270 0.012584270 ✔ 4 1 0.013371520 0.013371520 ✔ 1 2 0.009633307 0.009633307 ✔ 2 2 0.273810347 0.273810347 ✔ 3 2 0.929614048 0.929614048 ✔ 4 2 1.332162149 1.332162149 ✔ 1 3 0.012584270 0.012584270 ✔ 2 3 0.929614048 0.929614048 ✔ 3 3 11.207037691 11.207037691 ✔ 4 3 34.582633697 34.582633697 ✔ 1 4 0.013371520 0.013371520 ✔ 2 4 1.332162149 1.332162149 ✔ 3 4 34.582633697 34.582633697 ✔ 4 4 284.311017647 284.311017647 ✔ Gaussian(coefficient=1, exponent=1) i j numerical analytical 1 1 0.039655758 0.039655758 ✔ 2 1 0.087251967 0.087251967 ✔ 3 1 0.101349405 0.101349405 ✔ 4 1 0.104839842 0.104839842 ✔ 1 2 0.087251967 0.087251967 ✔ 2 2 0.509596973 0.509596973 ✔ 3 2 0.885608072 0.885608072 ✔ 4 2 1.028128264 1.028128264 ✔ 1 3 0.101349405 0.101349405 ✔ 2 3 0.885608072 0.885608072 ✔ 3 3 2.144652191 2.144652191 ✔ 4 3 2.840130371 2.840130371 ✔ 1 4 0.104839842 0.104839842 ✔ 2 4 1.028128264 1.028128264 ✔ 3 4 2.840130371 2.840130371 ✔ 4 4 4.013723445 4.013723445 ✔ # method FiniteDifferenceMethod(Δr=0.1, rₘₐₓ=50.0, R=0.1:0.1:50.0, l=0, direction=c, solver=LinearAlgebra) # eigenvalue E₁ = -0.4987562112094783 E₂ = -0.12492197250426312 E₃ = -0.05554012469010373 E₄ = -0.031200723330794027 # others n norm, <ψₙ|ψₙ> = cₙ' * cₙ 1 1.0000000000000002 2 1.0 3 1.0 4 0.9999999999999999 n error check, |<ψₙ|H|ψₙ> - E| = |cₙ' * H * cₙ - E| = 0 1 6.161182675157306e-13 2 5.69044811271624e-13 3 4.260133912303843e-13 4 4.2897976837430463e-13 n expectation value of Kinetic(hbar=1, m=1) 1 3.2786923701710293 2 3.5307031141544245 3 3.575999797923303 4 3.593408391582286 n expectation value of Coulomb(coefficient=-1) 1 -3.7774485813798924 2 -3.6556250866581097 3 -3.6315399226129723 4 -3.624609114912647 <ψₙ|ψₙ> = cₙ' * cₙ = 1 i numerical analytical 1 1.000000000 1.000000000 ✔ 2 1.000000000 1.000000000 ✔ 3 1.000000000 1.000000000 ✔ 4 1.000000000 1.000000000 ✔ |<ψₙ|H|ψₙ> - E| = |cₙ' * H * cₙ - E| = 0 i numerical analytical 1 0.000000000 0.000000000 ✔ 2 0.000000000 0.000000000 ✔ 3 0.000000000 0.000000000 ✔ 4 0.000000000 0.000000000 ✔ Energy i numerical analytical 1 -0.498756211 -0.500000000 ✔ 2 -0.124921973 -0.125000000 ✔ 3 -0.055540125 -0.055555556 ✔ 4 -0.031200723 -0.031250000 ✔ Wave Function i r numerical analytical n = 1 1 0.1 0.509316013 0.510499846 ✔ 2 0.2 0.460924657 0.461919363 ✔ 3 0.3 0.417131082 0.417961923 ✔ 4 0.4 0.377498441 0.378187588 ✔ 5 0.5 0.341631393 0.342198280 ✔ 6 0.6 0.309172162 0.309633808 ✔ 7 0.7 0.279796961 0.280168256 ✔ 8 0.8 0.253212770 0.253506721 ✔ 9 0.9 0.229154407 0.229382367 ✔ 10 1.0 0.207381888 0.207553749 ✔ n = 2 1 0.1 0.180383829 0.180255677 ✔ 2 0.2 0.162570785 0.162440056 ✔ 3 0.3 0.146065834 0.145933441 ✔ 4 0.4 0.130783769 0.130650525 ✔ 5 0.5 0.116644583 0.116511210 ✔ 6 0.6 0.103573165 0.103440299 ✔ 7 0.7 0.091499008 0.091367209 ✔ 8 0.8 0.080355944 0.080225702 ✔ 9 0.9 0.070081887 0.069953628 ✔ 10 1.0 0.060618589 0.060492681 ✔ n = 3 1 0.1 0.098220407 0.098095259 ✔ 2 0.2 0.088452918 0.088333318 ✔ 3 0.3 0.079365730 0.079251565 ✔ 4 0.4 0.070919969 0.070811120 ✔ 5 0.5 0.063078736 0.062975081 ✔ 6 0.6 0.055807013 0.055708425 ✔ 7 0.7 0.049071574 0.048977924 ✔ 8 0.8 0.042840900 0.042752058 ✔ 9 0.9 0.037085101 0.037000932 ✔ 10 1.0 0.031775834 0.031696206 ✔ n = 4 1 0.1 0.064323843 0.063709397 ✔ 2 0.2 0.057911528 0.057354210 ✔ 3 0.3 0.051937413 0.051433487 ✔ 4 0.4 0.046377792 0.045923715 ✔ 5 0.5 0.041210060 0.040802476 ✔ 6 0.6 0.036412667 0.036048396 ✔ 7 0.7 0.031965071 0.031641104 ✔ 8 0.8 0.027847701 0.027561189 ✔ 9 0.9 0.024041911 0.023790159 ✔ 10 1.0 0.020529943 0.020310405 ✔ Test Summary: | Pass Total Time TwoBody.jl | 551 551 36m56.6s Hamiltonian.jl | 3 3 1.3s Database | 14 14 2.8s Basis.jl | 102 102 27m25.0s Free Complement | 17 17 17.5s Rayleigh-Ritz.jl | 177 177 1m01.4s GEM.jl | 34 34 58.5s FDM.jl | 52 52 31.0s QTT.jl | 82 82 2m48.3s VNN.jl | 37 37 3m18.8s VMC.jl | 33 33 22.9s Testing TwoBody tests passed Testing completed after 2227.03s PkgEval succeeded after 2336.35s