Package evaluation of TwoBody on Julia 1.13.0-DEV.853 (3e868b27cf*) started at 2025-07-17T03:30:52.869 ################################################################################ # Set-up # Installing PkgEval dependencies (TestEnv)... Set-up completed after 8.55s ################################################################################ # Installation # Installing TwoBody... Resolving package versions... Updating `~/.julia/environments/v1.13/Project.toml` [a92d7657] + TwoBody v0.0.9 Updating `~/.julia/environments/v1.13/Manifest.toml` [47edcb42] + ADTypes v1.15.0 [79e6a3ab] + Adapt v4.3.0 [66dad0bd] + AliasTables v1.1.3 [ec485272] + ArnoldiMethod v0.4.0 [4fba245c] + ArrayInterface v7.19.0 [bbf7d656] + CommonSubexpressions v0.3.1 [34da2185] + Compat v4.17.0 [187b0558] + ConstructionBase v1.6.0 [9a962f9c] + DataAPI v1.16.0 [864edb3b] + DataStructures v0.18.22 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [a0c0ee7d] + DifferentiationInterface v0.7.3 [ffbed154] + DocStringExtensions v0.9.5 [4e289a0a] + EnumX v1.0.5 [1a297f60] + FillArrays v1.13.0 [6a86dc24] + FiniteDiff v2.27.0 [a7a66f33] + FiniteDifferenceMatrices v0.1.0 [f6369f11] + ForwardDiff v1.0.1 [92d709cd] + IrrationalConstants v0.2.4 [692b3bcd] + JLLWrappers v1.7.0 [d3d80556] + LineSearches v7.4.0 [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 v1.13.2 [bac558e1] + OrderedCollections v1.8.1 [d96e819e] + Parameters v0.12.3 [85a6dd25] + PositiveFactorizations v0.2.4 [aea7be01] + PrecompileTools v1.3.2 [21216c6a] + Preferences v1.4.3 [43287f4e] + PtrArrays v1.3.0 [ae029012] + Requires v1.3.1 [efcf1570] + Setfield v1.1.2 [a2af1166] + SortingAlgorithms v1.2.1 [276daf66] + SpecialFunctions v2.5.1 [90137ffa] + StaticArrays v1.9.14 [1e83bf80] + StaticArraysCore v1.4.3 [10745b16] + Statistics v1.11.1 [82ae8749] + StatsAPI v1.7.1 [2913bbd2] + StatsBase v0.34.5 [2b7f82d5] + Subscripts v0.1.3 [a92d7657] + TwoBody v0.0.9 [3a884ed6] + UnPack v1.0.2 [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 v1.12.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.12.0 [d6f4376e] + Markdown v1.11.0 [de0858da] + Printf v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.12.0 [f489334b] + StyledStrings v1.11.0 [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 v0.3.29+0 [05823500] + OpenLibm_jll v0.8.5+0 [bea87d4a] + SuiteSparse_jll v7.10.1+0 [8e850b90] + libblastrampoline_jll v5.13.1+0 Installation completed after 4.34s ################################################################################ # Precompilation # Precompiling PkgEval dependencies... Precompiling package dependencies... Precompilation completed after 24.11s ################################################################################ # Testing # Testing TwoBody Status `/tmp/jl_FkvMJa/Project.toml` [be6e5d0e] Antique v0.12.0 [f6369f11] ForwardDiff v1.0.1 [1fd47b50] QuadGK v2.11.2 [276daf66] SpecialFunctions v2.5.1 [a92d7657] TwoBody v0.0.9 [de0858da] Printf v1.11.0 [8dfed614] Test v1.11.0 Status `/tmp/jl_FkvMJa/Manifest.toml` [47edcb42] ADTypes v1.15.0 [79e6a3ab] Adapt v4.3.0 [66dad0bd] AliasTables v1.1.3 [be6e5d0e] Antique v0.12.0 [ec485272] ArnoldiMethod v0.4.0 [4fba245c] ArrayInterface v7.19.0 [bbf7d656] CommonSubexpressions v0.3.1 [34da2185] Compat v4.17.0 [187b0558] ConstructionBase v1.6.0 [9a962f9c] DataAPI v1.16.0 [864edb3b] DataStructures v0.18.22 [163ba53b] DiffResults v1.1.0 [b552c78f] DiffRules v1.15.1 [a0c0ee7d] DifferentiationInterface v0.7.3 [ffbed154] DocStringExtensions v0.9.5 [4e289a0a] EnumX v1.0.5 [1a297f60] FillArrays v1.13.0 [6a86dc24] FiniteDiff v2.27.0 [a7a66f33] FiniteDifferenceMatrices v0.1.0 [f6369f11] ForwardDiff v1.0.1 [92d709cd] IrrationalConstants v0.2.4 [692b3bcd] JLLWrappers v1.7.0 [d3d80556] LineSearches v7.4.0 [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 v1.13.2 [bac558e1] OrderedCollections v1.8.1 [d96e819e] Parameters v0.12.3 [85a6dd25] PositiveFactorizations v0.2.4 [aea7be01] PrecompileTools v1.3.2 [21216c6a] Preferences v1.4.3 [43287f4e] PtrArrays v1.3.0 [1fd47b50] QuadGK v2.11.2 [ae029012] Requires v1.3.1 [efcf1570] Setfield v1.1.2 [a2af1166] SortingAlgorithms v1.2.1 [276daf66] SpecialFunctions v2.5.1 [90137ffa] StaticArrays v1.9.14 [1e83bf80] StaticArraysCore v1.4.3 [10745b16] Statistics v1.11.1 [82ae8749] StatsAPI v1.7.1 [2913bbd2] StatsBase v0.34.5 [2b7f82d5] Subscripts v0.1.3 [a92d7657] TwoBody v0.0.9 [3a884ed6] UnPack v1.0.2 [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 v1.12.0 [8f399da3] Libdl v1.11.0 [37e2e46d] LinearAlgebra v1.12.0 [56ddb016] Logging v1.11.0 [d6f4376e] Markdown v1.11.0 [de0858da] Printf v1.11.0 [9a3f8284] Random v1.11.0 [ea8e919c] SHA v0.7.0 [9e88b42a] Serialization v1.11.0 [6462fe0b] Sockets v1.11.0 [2f01184e] SparseArrays v1.12.0 [f489334b] StyledStrings v1.11.0 [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 v0.3.29+0 [05823500] OpenLibm_jll v0.8.5+0 [bea87d4a] SuiteSparse_jll v7.10.1+0 [8e850b90] libblastrampoline_jll v5.13.1+0 Testing Running tests... Precompiling packages... 2833.9 ms ✓ Antique 1 dependency successfully precompiled in 4 seconds. 12 already precompiled. 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 33m07.4s Basis.jl | 80 80 32m10.4s Rayleigh-Ritz.jl | 125 125 26.7s FDM.jl | 52 52 28.4s Testing TwoBody tests passed Testing completed after 2002.74s PkgEval succeeded after 2058.66s