Package evaluation of TwoBody on Julia 1.11.4 (a71dd056e0*) started at 2025-04-08T15:36:22.947 ################################################################################ # Set-up # Installing PkgEval dependencies (TestEnv)... Set-up completed after 9.17s ################################################################################ # Installation # Installing TwoBody... Resolving package versions... Updating `~/.julia/environments/v1.11/Project.toml` [a92d7657] + TwoBody v0.0.8 Updating `~/.julia/environments/v1.11/Manifest.toml` [47edcb42] + ADTypes v1.14.0 [79e6a3ab] + Adapt v4.3.0 [66dad0bd] + AliasTables v1.1.3 [ec485272] + ArnoldiMethod v0.4.0 [4fba245c] + ArrayInterface v7.18.0 [bbf7d656] + CommonSubexpressions v0.3.1 [34da2185] + Compat v4.16.0 [187b0558] + ConstructionBase v1.5.8 [9a962f9c] + DataAPI v1.16.0 [864edb3b] + DataStructures v0.18.22 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [a0c0ee7d] + DifferentiationInterface v0.6.50 [ffbed154] + DocStringExtensions v0.9.4 [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 v7.3.0 [2ab3a3ac] + LogExpFunctions v0.3.29 [1914dd2f] + MacroTools v0.5.15 [e1d29d7a] + Missings v1.2.0 [d41bc354] + NLSolversBase v7.9.1 [77ba4419] + NaNMath v1.1.3 [429524aa] + Optim v1.12.0 [bac558e1] + OrderedCollections v1.8.0 [d96e819e] + Parameters v0.12.3 [85a6dd25] + PositiveFactorizations v0.2.4 ⌅ [aea7be01] + PrecompileTools v1.2.1 [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 v2.5.0 [90137ffa] + StaticArrays v1.9.13 [1e83bf80] + StaticArraysCore v1.4.3 [10745b16] + Statistics v1.11.1 [82ae8749] + StatsAPI v1.7.0 [2913bbd2] + StatsBase v0.34.4 [2b7f82d5] + Subscripts v0.1.3 [a92d7657] + TwoBody v0.0.8 [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 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra 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 v1.11.0 [fa267f1f] + TOML v1.0.3 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [4536629a] + OpenBLAS_jll v0.3.27+1 [05823500] + OpenLibm_jll v0.8.5+0 [bea87d4a] + SuiteSparse_jll v7.7.0+0 [8e850b90] + libblastrampoline_jll v5.11.0+0 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m` Installation completed after 4.44s ################################################################################ # Precompilation # Precompiling PkgEval dependencies... Precompiling package dependencies... Precompilation completed after 24.96s ################################################################################ # Testing # Testing TwoBody Status `/tmp/jl_uTpet4/Project.toml` [be6e5d0e] Antique v0.11.3 [f6369f11] ForwardDiff v1.0.1 [1fd47b50] QuadGK v2.11.2 [276daf66] SpecialFunctions v2.5.0 [a92d7657] TwoBody v0.0.8 [de0858da] Printf v1.11.0 [8dfed614] Test v1.11.0 Status `/tmp/jl_uTpet4/Manifest.toml` [47edcb42] ADTypes v1.14.0 [79e6a3ab] Adapt v4.3.0 [66dad0bd] AliasTables v1.1.3 [be6e5d0e] Antique v0.11.3 [ec485272] ArnoldiMethod v0.4.0 [4fba245c] ArrayInterface v7.18.0 [bbf7d656] CommonSubexpressions v0.3.1 [34da2185] Compat v4.16.0 [187b0558] ConstructionBase v1.5.8 [9a962f9c] DataAPI v1.16.0 [864edb3b] DataStructures v0.18.22 [163ba53b] DiffResults v1.1.0 [b552c78f] DiffRules v1.15.1 [a0c0ee7d] DifferentiationInterface v0.6.50 [ffbed154] DocStringExtensions v0.9.4 [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 v7.3.0 [2ab3a3ac] LogExpFunctions v0.3.29 [1914dd2f] MacroTools v0.5.15 [e1d29d7a] Missings v1.2.0 [d41bc354] NLSolversBase v7.9.1 [77ba4419] NaNMath v1.1.3 [429524aa] Optim v1.12.0 [bac558e1] OrderedCollections v1.8.0 [d96e819e] Parameters v0.12.3 [85a6dd25] PositiveFactorizations v0.2.4 ⌅ [aea7be01] PrecompileTools v1.2.1 [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 v2.5.0 [90137ffa] StaticArrays v1.9.13 [1e83bf80] StaticArraysCore v1.4.3 [10745b16] Statistics v1.11.1 [82ae8749] StatsAPI v1.7.0 [2913bbd2] StatsBase v0.34.4 [2b7f82d5] Subscripts v0.1.3 [a92d7657] TwoBody v0.0.8 [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 [8f399da3] Libdl v1.11.0 [37e2e46d] LinearAlgebra v1.11.0 [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 v1.11.0 [fa267f1f] TOML v1.0.3 [8dfed614] Test v1.11.0 [cf7118a7] UUIDs v1.11.0 [4ec0a83e] Unicode v1.11.0 [e66e0078] CompilerSupportLibraries_jll v1.1.1+0 [4536629a] OpenBLAS_jll v0.3.27+1 [05823500] OpenLibm_jll v0.8.5+0 [bea87d4a] SuiteSparse_jll v7.7.0+0 [8e850b90] libblastrampoline_jll v5.11.0+0 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. Testing Running tests... Precompiling Antique... 2155.6 ms ✓ Antique 1 dependency successfully precompiled in 3 seconds. 13 already precompiled. # 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 |error| 1 0.9999999999999997 1.0000000000000000 0.0000000000000333% ✔ 2 1.0000000000000004 1.0000000000000000 0.0000000000000444% ✔ 3 0.9999999999999997 1.0000000000000000 0.0000000000000333% ✔ 4 0.9999999999999987 1.0000000000000000 0.0000000000001332% ✔ <ψₙ|ψₙ> = cₙ' * S * cₙ = 1 i numerical analytical |error| 1 1.0000000000000000 1.0000000000000000 0.0000000000000000% ✔ 2 1.0000000000000004 1.0000000000000000 0.0000000000000444% ✔ 3 1.0000000000000000 1.0000000000000000 0.0000000000000000% ✔ 4 0.9999999999999988 1.0000000000000000 0.0000000000001221% ✔ |<ψₙ|H|ψₙ> - E| = |cₙ' * H * cₙ - E| = 0 i numerical analytical |error| 1 0.0000000000000018 0.0000000000000000 0.0000000000001832% ✔ 2 0.0000000000000035 0.0000000000000000 0.0000000000003483% ✔ 3 0.0000000000000036 0.0000000000000000 0.0000000000003553% ✔ 4 0.0000000000000178 0.0000000000000000 0.0000000000017764% ✔ Thijssen(2007) i numerical analytical |error| 1 -0.4992784056674876 -0.4992780000000000 0.0000812508237098% ✔ ψ(r) r numerical analytical |error| 0.2 0.4634872367236802 0.4619193626168075 0.3394259331305194% ✔ 0.3 0.4176398271605594 0.4179619234110083 0.0770635391425826% ✔ 0.4 0.3762086301866182 0.3781875876165602 0.5232740298046139% ✔ 0.5 0.3410905455654228 0.3421982803122166 0.3237113716010157% ✔ 0.6 0.3100060408581586 0.3096338084140516 0.1202169898737884% ✔ 0.7 0.2811815061037919 0.2801682557420114 0.3616578041994507% ✔ 0.8 0.2542630188828578 0.2535067211412400 0.2983343945332605% ✔ 0.9 0.2295092095140989 0.2293823670122016 0.0552974073593524% ✔ 1.0 0.2071389649573306 0.2075537487102974 0.1998440189802379% ✔ 1.1 0.1871462898501720 0.1878023980867099 0.3493609470497447% ✔ 1.2 0.1693423091477105 0.1699306369857400 0.3462164612958712% ✔ 1.3 0.1534473568855001 0.1537595988153829 0.2030715040156504% ✔ 1.4 0.1391686311396211 0.1391274383903561 0.0296079261873981% ✔ 1.5 0.1262483477365183 0.1258877121310868 0.2864740325536486% ✔ 1.6 0.1144842771147344 0.1139079124071467 0.5059918098819717% ✔ 1.7 0.1037303916450949 0.1030681413563489 0.6425363648077144% ✔ 1.8 0.0938863909786113 0.0932599109066440 0.6717570989257921% ✔ 1.9 0.0848833630813963 0.0843850569910314 0.5905146102085247% ✔ 2.0 0.0766703259179940 0.0763547570885822 0.4132929518009507% ✔ NonRelativisticKinetic(ħ=1, m=1) i j numerical analytical |error| 1 1 0.8187858292908893 0.8187858292911329 0.0000000000297493% ✔ 2 1 0.4917262794904377 0.4917262794904377 0.0000000000000000% ✔ 3 1 0.1455323778314588 0.1455323778314588 0.0000000000000381% ✔ 4 1 0.0424220103511675 0.0424220103511675 0.0000000000000818% ✔ 1 2 0.4917262794856195 0.4917262794904377 0.0000000009798544% ✔ 2 2 2.1082049553705651 2.1082049553705651 0.0000000000000000% ✔ 3 2 1.6216206338929844 1.6216206338929851 0.0000000000000411% ✔ 4 2 0.6375034372046851 0.6375034372046856 0.0000000000000871% ✔ 1 3 0.1455323778314589 0.1455323778314588 0.0000000000001144% ✔ 2 3 1.6216206338929691 1.6216206338929851 0.0000000000009859% ✔ 3 3 4.4291564937602557 4.4291564937602548 0.0000000000000201% ✔ 4 3 3.7494460970746371 3.7494460970746326 0.0000000000001184% ✔ 1 4 0.0424220103511676 0.0424220103511675 0.0000000000002944% ✔ 2 4 0.6375034372046978 0.6375034372046857 0.0000000000018983% ✔ 3 4 3.7494460970746335 3.7494460970746331 0.0000000000000118% ✔ 4 4 8.4563236568716764 8.4563236568716782 0.0000000000000210% ✔ ConstantPotential(constant=1) i j numerical analytical |error| 1 1 0.0419640644084278 0.0419640644084265 0.0000000000031417% ✔ 2 1 0.0961391814715394 0.0961391814715395 0.0000000000000722% ✔ 3 1 0.1128579035560789 0.1128579035560786 0.0000000000002459% ✔ 4 1 0.1170425126318233 0.1170425126318229 0.0000000000003320% ✔ 1 2 0.0961391814715394 0.0961391814715395 0.0000000000000866% ✔ 2 2 0.7163167080668228 0.7163167080668228 0.0000000000000000% ✔ 3 2 1.4914777365294452 1.4914777365294443 0.0000000000000596% ✔ 4 2 1.8508423236885669 1.8508423236885296 0.0000000000020155% ✔ 1 3 0.1128579035560789 0.1128579035560786 0.0000000000002213% ✔ 2 3 1.4914777365294452 1.4914777365294443 0.0000000000000596% ✔ 3 3 6.6424710105306266 6.6424710105306284 0.0000000000000267% ✔ 4 3 13.0602053918895447 13.0602053918895447 0.0000000000000000% ✔ 1 4 0.1170425126318233 0.1170425126318229 0.0000000000003320% ✔ 2 4 1.8508423236885669 1.8508423236885296 0.0000000000020155% ✔ 3 4 13.0602053918895447 13.0602053918895447 0.0000000000000000% ✔ 4 4 46.2286682043106296 46.2286682043106367 0.0000000000000154% ✔ LinearPotential(coefficient=1) i j numerical analytical |error| 1 1 0.0092836091851980 0.0092836091851969 0.0000000000117534% ✔ 2 1 0.0280380205643924 0.0280380205643924 0.0000000000000619% ✔ 3 1 0.0347207763801290 0.0347207763801290 0.0000000000000200% ✔ 4 1 0.0364478267735820 0.0364478267735820 0.0000000000000000% ✔ 1 2 0.0280380205643924 0.0280380205643924 0.0000000000000619% ✔ 2 2 0.4080251168985116 0.4080251168985116 0.0000000000000000% ✔ 3 2 1.0848486584815014 1.0848486584814923 0.0000000000008392% ✔ 4 2 1.4466806936527483 1.4466806936526788 0.0000000000048041% ✔ 1 3 0.0347207763801290 0.0347207763801290 0.0000000000000200% ✔ 2 3 1.0848486584815011 1.0848486584814923 0.0000000000008187% ✔ 3 3 7.9491314721546793 7.9491314721546980 0.0000000000002346% ✔ 4 3 19.5800350801255689 19.5800350801255689 0.0000000000000000% ✔ 1 4 0.0364478267735820 0.0364478267735820 0.0000000000000000% ✔ 2 4 1.4466806936527483 1.4466806936526788 0.0000000000048041% ✔ 3 4 19.5800350801255689 19.5800350801255689 0.0000000000000000% ✔ 4 4 105.6238432464115959 105.6238432464115675 0.0000000000000269% ✔ CoulombPotential(coefficient=1) i j numerical analytical |error| 1 1 0.2415173634131254 0.2415173634131238 0.0000000000006436% ✔ 2 1 0.4197238125870266 0.4197238125870267 0.0000000000000397% ✔ 3 1 0.4670728765465776 0.4670728765465775 0.0000000000000119% ✔ 4 1 0.4785482730743024 0.4785482730743023 0.0000000000000348% ✔ 1 2 0.4197238125870266 0.4197238125870267 0.0000000000000397% ✔ 2 2 1.6011550266782288 1.6011550266782293 0.0000000000000277% ✔ 3 2 2.6108054602908264 2.6108054602908268 0.0000000000000170% ✔ 4 2 3.0149233619677580 3.0149233619677438 0.0000000000004714% ✔ 1 3 0.4670728765465776 0.4670728765465775 0.0000000000000119% ✔ 2 3 2.6108054602908264 2.6108054602908268 0.0000000000000170% ✔ 3 3 7.0672389283709123 7.0672389283709114 0.0000000000000126% ✔ 4 3 11.0916630281263853 11.0916630281263888 0.0000000000000320% ✔ 1 4 0.4785482730743024 0.4785482730743023 0.0000000000000348% ✔ 2 4 3.0149233619677580 3.0149233619677438 0.0000000000004714% ✔ 3 4 11.0916630281263853 11.0916630281263888 0.0000000000000320% ✔ 4 4 25.7614863696505871 25.7614863696505871 0.0000000000000000% ✔ PowerLawPotential(coefficient=1, exponent=1) i j numerical analytical |error| 1 1 0.0092836091851980 0.0092836091851969 0.0000000000117534% ✔ 2 1 0.0280380205643924 0.0280380205643924 0.0000000000000619% ✔ 3 1 0.0347207763801290 0.0347207763801290 0.0000000000000200% ✔ 4 1 0.0364478267735820 0.0364478267735820 0.0000000000000000% ✔ 1 2 0.0280380205643924 0.0280380205643924 0.0000000000000619% ✔ 2 2 0.4080251168985116 0.4080251168985116 0.0000000000000000% ✔ 3 2 1.0848486584815014 1.0848486584814923 0.0000000000008392% ✔ 4 2 1.4466806936527483 1.4466806936526788 0.0000000000048041% ✔ 1 3 0.0347207763801290 0.0347207763801290 0.0000000000000200% ✔ 2 3 1.0848486584815011 1.0848486584814923 0.0000000000008187% ✔ 3 3 7.9491314721546793 7.9491314721546980 0.0000000000002346% ✔ 4 3 19.5800350801255689 19.5800350801255689 0.0000000000000000% ✔ 1 4 0.0364478267735820 0.0364478267735820 0.0000000000000000% ✔ 2 4 1.4466806936527483 1.4466806936526788 0.0000000000048041% ✔ 3 4 19.5800350801255689 19.5800350801255689 0.0000000000000000% ✔ 4 4 105.6238432464115959 105.6238432464115675 0.0000000000000269% ✔ PowerLawPotential(coefficient=1, exponent=2) i j numerical analytical |error| 1 1 0.0024195650052954 0.0024195650052945 0.0000000000360808% ✔ 2 1 0.0096333074261208 0.0096333074261208 0.0000000000005222% ✔ 3 1 0.0125842697002874 0.0125842697002874 0.0000000000000276% ✔ 4 1 0.0133715200709347 0.0133715200709347 0.0000000000000000% ✔ 1 2 0.0096333074261208 0.0096333074261208 0.0000000000005222% ✔ 2 2 0.2738103466018020 0.2738103466018020 0.0000000000000000% ✔ 3 2 0.9296140479854916 0.9296140479854496 0.0000000000045263% ✔ 4 2 1.3321621490212059 1.3321621490212054 0.0000000000000333% ✔ 1 3 0.0125842697002874 0.0125842697002874 0.0000000000000276% ✔ 2 3 0.9296140479854916 0.9296140479854496 0.0000000000045263% ✔ 3 3 11.2070376913496599 11.2070376913496563 0.0000000000000317% ✔ 4 3 34.5826336968206647 34.5826336968206576 0.0000000000000205% ✔ 1 4 0.0133715200709347 0.0133715200709347 0.0000000000000000% ✔ 2 4 1.3321621490212059 1.3321621490212054 0.0000000000000333% ✔ 3 4 34.5826336968206647 34.5826336968206576 0.0000000000000205% ✔ 4 4 284.3110176469627390 284.3110176469626822 0.0000000000000200% ✔ GaussianPotential(coefficient=1, exponent=1) i j numerical analytical |error| 1 1 0.0396557582952546 0.0396557582952539 0.0000000000016973% ✔ 2 1 0.0872519669275283 0.0872519669275287 0.0000000000004294% ✔ 3 1 0.1013494053892576 0.1013494053892577 0.0000000000000411% ✔ 4 1 0.1048398416754345 0.1048398416754345 0.0000000000000397% ✔ 1 2 0.0872519669275283 0.0872519669275287 0.0000000000004772% ✔ 2 2 0.5095969730802077 0.5095969730802077 0.0000000000000000% ✔ 3 2 0.8856080715064218 0.8856080715064220 0.0000000000000125% ✔ 4 2 1.0281282636443403 1.0281282636443403 0.0000000000000000% ✔ 1 3 0.1013494053892576 0.1013494053892577 0.0000000000000411% ✔ 2 3 0.8856080715064218 0.8856080715064218 0.0000000000000000% ✔ 3 3 2.1446521911569878 2.1446521911570509 0.0000000000029404% ✔ 4 3 2.8401303708983914 2.8401303708980978 0.0000000000103355% ✔ 1 4 0.1048398416754345 0.1048398416754345 0.0000000000000397% ✔ 2 4 1.0281282636443403 1.0281282636443401 0.0000000000000216% ✔ 3 4 2.8401303708983914 2.8401303708980978 0.0000000000103355% ✔ 4 4 4.0137234447912444 4.0137234447912444 0.0000000000000000% ✔ Test Summary: | Pass Total Time Rayleigh–Ritz.jl | 125 125 27.2s # method FiniteDifferenceMethod(Δr=0.1, rₘₐₓ=50.0, R=0.1:0.1:50.0, l=0, direction=c, solver=LinearAlgebra) # eigenvalue E₁ = -0.498756211208873 E₂ = -0.12492197250421044 E₃ = -0.05554012469068426 E₄ = -0.031200723331206007 # others n norm, <ψₙ|ψₙ> = cₙ' * cₙ 1 1.0000000000000002 2 0.9999999999999996 3 1.0000000000000002 4 1.0000000000000002 n error check, |<ψₙ|H|ψₙ> - E| = |cₙ' * H * cₙ - E| = 0 1 3.0031532816110484e-14 2 2.4313884239290928e-14 3 2.2447321779139884e-14 4 1.1397133237167623e-14 n expectation value of NonRelativisticKinetic(ħ=1, m=1) 1 3.2786923701708517 2 3.530703114155255 3 3.5759997979259124 4 3.5934083915842283 n expectation value of CoulombPotential(coefficient=-1) 1 -3.777448581379753 2 -3.655625086659438 3 -3.6315399226165677 4 -3.6246091149154087 <ψₙ|ψₙ> = cₙ' * cₙ = 1 i numerical analytical |error| 1 1.0000000000000002 1.0000000000000000 0.0000000000000222% ✔ 2 0.9999999999999996 1.0000000000000000 0.0000000000000444% ✔ 3 1.0000000000000002 1.0000000000000000 0.0000000000000222% ✔ 4 1.0000000000000002 1.0000000000000000 0.0000000000000222% ✔ |<ψₙ|H|ψₙ> - E| = |cₙ' * H * cₙ - E| = 0 i numerical analytical |error| 1 0.0000000000000300 0.0000000000000000 0.0000000000030032% ✔ 2 0.0000000000000243 0.0000000000000000 0.0000000000024314% ✔ 3 0.0000000000000224 0.0000000000000000 0.0000000000022447% ✔ 4 0.0000000000000114 0.0000000000000000 0.0000000000011397% ✔ Energy i numerical analytical |error| 1 -0.4987562112088730 -0.5000000000000000 0.2487577582254041% ✔ 2 -0.1249219725042104 -0.1250000000000000 0.0624219966316453% ✔ 3 -0.0555401246906843 -0.0555555555555556 0.0277755567683211% ✔ 4 -0.0312007233312060 -0.0312500000000000 0.1576853401407785% ✔ Wave Function i r numerical analytical |error| n = 1 1 0.1 0.5093160129260775 0.5104998460601352 0.2318968640625653% ✔ 2 0.2 0.4609246568826209 0.4619193626168075 0.2153418571916013% ✔ 3 0.3 0.4171310815495533 0.4179619234110083 0.1987841032681884% ✔ 4 0.4 0.3774984405727094 0.3781875876165602 0.1822236018358133% ✔ 5 0.5 0.3416313934350096 0.3421982803122166 0.1656603524394684% ✔ 6 0.6 0.3091721618857059 0.3096338084140516 0.1490943546217701% ✔ 7 0.7 0.2797969610578687 0.2801682557420114 0.1325256079277625% ✔ 8 0.8 0.2532127696741301 0.2535067211412400 0.1159541119014717% ✔ 9 0.9 0.2291544071230411 0.2293823670122016 0.0993798660855203% ✔ 10 1.0 0.2073818882495237 0.2075537487102974 0.0828028700235713% ✔ n = 2 1 0.1 0.1803838292001299 0.1802556770027472 0.0710946803526931% ✔ 2 0.2 0.1625707853176327 0.1624400563247146 0.0804782981956007% ✔ 3 0.3 0.1460658338446038 0.1459334412217540 0.0907212368470298% ✔ 4 0.4 0.1307837688970492 0.1306505254670850 0.1019846108447352% ✔ 5 0.5 0.1166445834347485 0.1165112101413479 0.1144724986022612% ✔ 6 0.6 0.1035731648694667 0.1034402986125937 0.1284472866523880% ✔ 7 0.7 0.0914990079960635 0.0913672088823367 0.1442520958438139% ✔ 8 0.8 0.0803559442809275 0.0802257023292754 0.1623444206416230% ✔ 9 0.9 0.0700818865951263 0.0699536279354387 0.1833481171355231% ✔ 10 1.0 0.0606185885297684 0.0604926811297859 0.2081365838495451% ✔ n = 3 1 0.1 0.0982204073484220 0.0980952587142884 0.1275786778830151% ✔ 2 0.2 0.0884529183502928 0.0883333181423033 0.1353964851596314% ✔ 3 0.3 0.0793657299424227 0.0792515645529642 0.1440544298431846% ✔ 4 0.4 0.0709199689794240 0.0708111198892195 0.1537175098696666% ✔ 5 0.5 0.0630787361051704 0.0629750806225284 0.1645976180058988% ✔ 6 0.6 0.0558070129999727 0.0557084249443714 0.1769715365310575% ✔ 7 0.7 0.0490715737555859 0.0489779240889505 0.1912079133147957% ✔ 8 0.8 0.0428409002015962 0.0427520576104432 0.2078089245728680% ✔ 9 0.9 0.0370851010140412 0.0370009324454951 0.2274768849948846% ✔ 10 1.0 0.0317758344441374 0.0316962055986658 0.2512251670747603% ✔ n = 4 1 0.1 0.0643238427533872 0.0637093968494299 0.9644509826539754% ✔ 2 0.2 0.0579115279822619 0.0573542100245145 0.9717123773637540% ✔ 3 0.3 0.0519374129472330 0.0514334866762165 0.9797629979642872% ✔ 4 0.4 0.0463777920551354 0.0459237153184930 0.9887630682605765% ✔ 5 0.5 0.0412100601682092 0.0408024763078652 0.9989194216268992% ✔ 6 0.6 0.0364126666327478 0.0360483962134114 1.0105038159805830% ✔ 7 0.7 0.0319650710871229 0.0316411039537113 1.0238806265594567% ✔ 8 0.8 0.0278477009841630 0.0275611886361362 1.0395500419427366% ✔ 9 0.9 0.0240419107651253 0.0237901590361396 1.0582179320586749% ✔ 10 1.0 0.0205299426247033 0.0203104046563856 1.0809138076361302% ✔ Test Summary: | Pass Total Time FDM.jl | 52 52 26.3s Testing TwoBody tests passed Testing completed after 78.57s PkgEval succeeded after 124.28s