Package evaluation to test TwoBody on Julia 1.14.0-DEV.1893 (b4aba01002*) started at 2026-03-15T17:07:17.372 ################################################################################ # Set-up # Installing PkgEval dependencies (TestEnv)... Activating project at `~/.julia/environments/v1.14` Set-up completed after 16.12s ################################################################################ # Installation # Installing TwoBody... Resolving package versions... Updating `~/.julia/environments/v1.14/Project.toml` [a92d7657] + TwoBody v0.0.9 Updating `~/.julia/environments/v1.14/Manifest.toml` [47edcb42] + ADTypes v1.21.0 [79e6a3ab] + Adapt v4.5.0 [66dad0bd] + AliasTables v1.1.3 [ec485272] + ArnoldiMethod v0.4.0 [4fba245c] + ArrayInterface v7.23.0 [bbf7d656] + CommonSubexpressions v0.3.1 [34da2185] + Compat v4.18.1 [187b0558] + ConstructionBase v1.6.0 [9a962f9c] + DataAPI v1.16.0 [864edb3b] + DataStructures v0.19.3 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [a0c0ee7d] + DifferentiationInterface v0.7.16 [ffbed154] + DocStringExtensions v0.9.5 [4e289a0a] + EnumX v1.0.7 [1a297f60] + FillArrays v1.16.0 [6a86dc24] + FiniteDiff v2.29.0 [a7a66f33] + FiniteDifferenceMatrices v0.1.0 [f6369f11] + ForwardDiff v1.3.2 [92d709cd] + IrrationalConstants v0.2.6 [692b3bcd] + JLLWrappers v1.7.1 ⌃ [d3d80556] + LineSearches v7.5.1 [2ab3a3ac] + LogExpFunctions v0.3.29 [1914dd2f] + MacroTools v0.5.16 [e1d29d7a] + Missings v1.2.0 ⌅ [d41bc354] + NLSolversBase v7.10.0 [77ba4419] + NaNMath v1.1.3 ⌅ [429524aa] + Optim v1.13.3 [bac558e1] + OrderedCollections v1.8.1 [85a6dd25] + PositiveFactorizations v0.2.4 [aea7be01] + PrecompileTools v1.3.3 [21216c6a] + Preferences v1.5.2 [43287f4e] + PtrArrays v1.4.0 [ae029012] + Requires v1.3.1 [efcf1570] + Setfield v1.1.2 [a2af1166] + SortingAlgorithms v1.2.2 [276daf66] + SpecialFunctions v2.7.1 [90137ffa] + StaticArrays v1.9.18 [1e83bf80] + StaticArraysCore v1.4.4 [10745b16] + Statistics v1.11.1 [82ae8749] + StatsAPI v1.8.0 [2913bbd2] + StatsBase v0.34.10 [2b7f82d5] + Subscripts v0.1.3 [a92d7657] + TwoBody v0.0.9 [efe28fd5] + OpenSpecFun_jll v0.5.6+0 [56f22d72] + Artifacts v1.11.0 [ade2ca70] + Dates v1.11.0 [8ba89e20] + Distributed v1.11.0 [9fa8497b] + Future v1.11.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.13.0 [de0858da] + Printf v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v1.0.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.13.0 [fa267f1f] + TOML v1.0.3 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.3.0+1 [4536629a] + OpenBLAS_jll v0.3.30+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 6.77s ################################################################################ # Precompilation # Precompiling PkgEval dependencies... Precompiling package dependencies... Precompiling packages... 2311.2 ms ✓ Antique 7452.1 ms ✓ Optim 5757.3 ms ✓ TwoBody 3 dependencies successfully precompiled in 16 seconds. 82 already precompiled. 9 dependencies precompiled but different versions are currently loaded (Base64, Dates, JuliaSyntaxHighlighting, Logging, Markdown, Printf, StyledStrings, TOML and UUIDs). Restart julia to access the new versions. Otherwise, 36 dependents of these packages may trigger further precompilation to work with the unexpected versions. Precompilation completed after 41.13s ################################################################################ # Testing # Testing TwoBody Status `/tmp/jl_4G6V3d/Project.toml` [be6e5d0e] Antique v0.12.0 [f6369f11] ForwardDiff v1.3.2 [1fd47b50] QuadGK v2.11.2 [276daf66] SpecialFunctions v2.7.1 [a92d7657] TwoBody v0.0.9 [de0858da] Printf v1.11.0 [8dfed614] Test v1.11.0 Status `/tmp/jl_4G6V3d/Manifest.toml` [47edcb42] ADTypes v1.21.0 [79e6a3ab] Adapt v4.5.0 [66dad0bd] AliasTables v1.1.3 [be6e5d0e] Antique v0.12.0 [ec485272] ArnoldiMethod v0.4.0 [4fba245c] ArrayInterface v7.23.0 [bbf7d656] CommonSubexpressions v0.3.1 [34da2185] Compat v4.18.1 [187b0558] ConstructionBase v1.6.0 [9a962f9c] DataAPI v1.16.0 [864edb3b] DataStructures v0.19.3 [163ba53b] DiffResults v1.1.0 [b552c78f] DiffRules v1.15.1 [a0c0ee7d] DifferentiationInterface v0.7.16 [ffbed154] DocStringExtensions v0.9.5 [4e289a0a] EnumX v1.0.7 [1a297f60] FillArrays v1.16.0 [6a86dc24] FiniteDiff v2.29.0 [a7a66f33] FiniteDifferenceMatrices v0.1.0 [f6369f11] ForwardDiff v1.3.2 [92d709cd] IrrationalConstants v0.2.6 [692b3bcd] JLLWrappers v1.7.1 ⌃ [d3d80556] LineSearches v7.5.1 [2ab3a3ac] LogExpFunctions v0.3.29 [1914dd2f] MacroTools v0.5.16 [e1d29d7a] Missings v1.2.0 ⌅ [d41bc354] NLSolversBase v7.10.0 [77ba4419] NaNMath v1.1.3 ⌅ [429524aa] Optim v1.13.3 [bac558e1] OrderedCollections v1.8.1 [85a6dd25] PositiveFactorizations v0.2.4 [aea7be01] PrecompileTools v1.3.3 [21216c6a] Preferences v1.5.2 [43287f4e] PtrArrays v1.4.0 [1fd47b50] QuadGK v2.11.2 [ae029012] Requires v1.3.1 [efcf1570] Setfield v1.1.2 [a2af1166] SortingAlgorithms v1.2.2 [276daf66] SpecialFunctions v2.7.1 [90137ffa] StaticArrays v1.9.18 [1e83bf80] StaticArraysCore v1.4.4 [10745b16] Statistics v1.11.1 [82ae8749] StatsAPI v1.8.0 [2913bbd2] StatsBase v0.34.10 [2b7f82d5] Subscripts v0.1.3 [a92d7657] TwoBody v0.0.9 [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 v1.13.0 [56ddb016] Logging v1.11.0 [d6f4376e] Markdown v1.11.0 [de0858da] Printf v1.11.0 [9a3f8284] Random v1.11.0 [ea8e919c] SHA v1.0.0 [9e88b42a] Serialization v1.11.0 [6462fe0b] Sockets v1.11.0 [2f01184e] SparseArrays v1.13.0 [f489334b] StyledStrings v1.13.0 [fa267f1f] TOML v1.0.3 [8dfed614] Test v1.11.0 [cf7118a7] UUIDs v1.11.0 [4ec0a83e] Unicode v1.11.0 [e66e0078] CompilerSupportLibraries_jll v1.3.0+1 [4536629a] OpenBLAS_jll v0.3.30+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 ✔ # method Rayleigh-Ritz method with SimpleGaussianBasis J. Thijssen, Computational Physics 2nd Edition (2013) https://doi.org/10.1017/CBO9781139171397 # basis function φ₁(r) = TwoBody.φ(SimpleGaussianBasis(a=13.00773), r) φ₂(r) = TwoBody.φ(SimpleGaussianBasis(a=1.962079), r) φ₃(r) = TwoBody.φ(SimpleGaussianBasis(a=0.444529), r) φ₄(r) = TwoBody.φ(SimpleGaussianBasis(a=0.1219492), r) # eigenfunction ψ₁(r) = + 0.096102φ₁(r) + 0.163017φ₂(r) + 0.185587φ₃(r) + 0.073701φ₄(r) ψ₂(r) = + 0.119454φ₁(r) + 0.081329φ₂(r) + 0.496216φ₃(r) - 0.205916φ₄(r) ψ₃(r) = - 0.010362φ₁(r) + 1.744891φ₂(r) - 0.629196φ₃(r) + 0.097774φ₄(r) ψ₄(r) = - 6.155100φ₁(r) + 1.240202φ₂(r) - 0.226412φ₃(r) + 0.030780φ₄(r) # eigenvalue E₁ = -0.4992784056674876 E₂ = 0.11321392045798988 E₃ = 2.592299571959808 E₄ = 21.144365190122507 # others n norm, <ψₙ|ψₙ> = cₙ' * S * cₙ 1 1.0 2 1.0000000000000004 3 1.0 4 0.9999999999999988 n error check, |<ψₙ|H|ψₙ> - E| = |cₙ' * H * cₙ - E| = 0 1 1.8318679906315083e-15 2 3.4833247397614286e-15 3 3.552713678800501e-15 4 1.7763568394002505e-14 n expectation value of NonRelativisticKinetic(ħ=1, m=1) 1 0.4992783686700055 2 0.8428088332141157 3 4.432656608731447 4 26.465623640332108 n expectation value of CoulombPotential(coefficient=-1) 1 -0.9985567743374912 2 -0.7295949127561296 3 -1.8403570367716342 4 -5.321258450209621 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 ✔ NonRelativisticKinetic(ħ=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 ✔ ConstantPotential(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 ✔ LinearPotential(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 ✔ CoulombPotential(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 ✔ PowerLawPotential(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 ✔ PowerLawPotential(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 ✔ GaussianPotential(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 = -0.498756211209236 E₂ = -0.12492197250360043 E₃ = -0.055540124690378084 E₄ = -0.03120072333122497 # others n norm, <ψₙ|ψₙ> = cₙ' * cₙ 1 1.0 2 1.0 3 1.0000000000000004 4 0.9999999999999999 n error check, |<ψₙ|H|ψₙ> - E| = |cₙ' * H * cₙ - E| = 0 1 2.2465362903290043e-13 2 6.444844657949034e-14 3 5.910549827348177e-14 4 8.365183545855359e-14 n expectation value of NonRelativisticKinetic(ħ=1, m=1) 1 3.2786923701705035 2 3.530703114153817 3 3.5759997979270093 4 3.593408391587335 n expectation value of CoulombPotential(coefficient=-1) 1 -3.7774485813795184 2 -3.6556250866573565 3 -3.6315399226173324 4 -3.624609114918476 <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 | 257 257 27m35.9s Basis.jl | 80 80 26m36.3s Rayleigh-Ritz.jl | 125 125 30.0s FDM.jl | 52 52 26.6s Testing TwoBody tests passed Testing completed after 1668.22s PkgEval succeeded after 1750.27s