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Generalized Eigenvalue Problems
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GeneralizedEigenvalueProblems.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 一般化固有値問題\n",
"\n",
"JuliaのLinearAlgebra.jlを利用して一般化固有値問題を解く. 一般化固有値問題の例として[J.M.ティッセン著『計算物理学』(丸善出版, 2012)](https://www.maruzen-publishing.co.jp/item/b294596.html)から水素原子の変分計算を取り上げる.\n",
"\n",
"© 2021 Shuhei Ohno\n",
"<br>Source: https://gist.github.com/ohno\n",
"<br>License: https://opensource.org/licenses/MIT"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Julia Version 1.9.2\n",
"Commit e4ee485e90 (2023-07-05 09:39 UTC)\n",
"Platform Info:\n",
" OS: Windows (x86_64-w64-mingw32)\n",
" CPU: 8 × 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz\n",
" WORD_SIZE: 64\n",
" LIBM: libopenlibm\n",
" LLVM: libLLVM-14.0.6 (ORCJIT, tigerlake)\n",
" Threads: 9 on 8 virtual cores\n"
]
}
],
"source": [
"# using Pkg\n",
"# Pkg.add(\"Plots\")\n",
"# Pkg.add(\"Optim\")\n",
"using Plots\n",
"using Optim\n",
"using LinearAlgebra\n",
"versioninfo()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 一般化固有値問題\n",
"\n",
"時間に依存しないSchrödinger方程式\n",
"\n",
"$$\n",
" \\hat{H}\\psi(\\boldsymbol{r}) = E\\psi(\\boldsymbol{r})\n",
"$$\n",
"\n",
"を非直交な基底関数で展開すると, 一般化固有値問題\n",
"\n",
"$$\n",
" \\boldsymbol{H}\\boldsymbol{C} = E\\boldsymbol{S}\\boldsymbol{C}\n",
"$$\n",
"\n",
"に帰着できる. 直交基底を用いれば$\\boldsymbol{S}=\\boldsymbol{I}$となり, 標準固有値問題$\\boldsymbol{H}\\boldsymbol{C} = E\\boldsymbol{C}$となる. 導出の詳細は[J.M.ティッセン著『計算物理学』(丸善出版, 2012) 3.1](https://www.maruzen-publishing.co.jp/item/b294596.html)または[A.ザボ, Ｎ.Ｓ.オストランド著『新しい量子化学 上 電子構造の理論入門』(東京大学出版会, 1987) 3.2.1](http://www.utp.or.jp/book/b302128.html)を参照されたい."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 水素原子\n",
"\n",
"水素原子の時間に依存しないSchrödinger方程式は\n",
"\n",
"$$\n",
" \\left[ -\\frac{\\hbar^2}{2m_\\mathrm{e}}\\nabla_\\mathrm{e}^2 -\\frac{\\hbar^2}{2m_\\mathrm{p}}\\nabla_\\mathrm{p}^2 - \\frac{e^2}{4\\pi\\varepsilon_0 r} \\right] \\psi_\\mathrm{tot}(\\boldsymbol{r}_\\mathrm{e},\\boldsymbol{r}_\\mathrm{p}) = E_\\mathrm{tot} \\psi_\\mathrm{tot}(\\boldsymbol{r}_\\mathrm{e},\\boldsymbol{r}_\\mathrm{p})\n",
"$$\n",
"\n",
"である. これを換算質量$\\frac{1}{\\mu}:=\\frac{1}{m_\\mathrm{e}}+\\frac{1}{m_\\mathrm{p}}$と相対運動$\\boldsymbol{r}:=\\boldsymbol{r}_\\mathrm{e}-\\boldsymbol{r}_\\mathrm{p}$を用いて並進運動の自由度を分離すると\n",
"\n",
"$$\n",
" \\left[ -\\frac{\\hbar^2}{2\\mu}\\nabla^2 - \\frac{e^2}{4\\pi\\varepsilon_0 r} \\right] \\psi(\\boldsymbol{r}) = E \\psi(\\boldsymbol{r})\n",
"$$\n",
"\n",
"が得られる. 分離の詳細は[原田義也『量子化学 下巻』(裳華房, 2007) §A2.3](https://www.shokabo.co.jp/mybooks/ISBN978-4-7853-3074-3.htm), [高柳和夫『朝倉物理学大系 11 原子分子物理学』(2000, 朝倉書店) pp.11-22](http://www.asakura.co.jp/books/isbn/978-4-254-13681-4/), [河合光路, 吉田思郎『朝倉物理学大系 19 原子核反応論』(朝倉書店, 2002) pp.8-12,25-38](http://www.asakura.co.jp/books/isbn/978-4-254-13689-0/), [Frank Jensen『Introduction to Computational Chemistry, 2nd Edition』(John Wiley & Sons, 2007) pp.14-17](https://www.wiley.com/en-us/Introduction+to+Computational+Chemistry%2C+2nd+Edition-p-9780470058046)などを参照されたい. さらに$m_\\mathrm{p}\\rightarrow\\infty$を仮定し, 原子単位を用いると\n",
"\n",
"$$\n",
" \\left[ -\\frac{1}{2}\\nabla^{*2} - \\frac{1}{r^*} \\right] \\psi^*(\\boldsymbol{r^*}) = E^* \\psi^*(\\boldsymbol{r}^*)\n",
"$$\n",
"\n",
"のように無次元化できる. 以降はこのアスタリスクを省略する. 無次元化については[IUPAC GreenBook 3.9.2](https://unit.aist.go.jp/nmij/public/report/translation/IUPAC/)を参照されたい."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 変分計算\n",
"\n",
"ここでは, [J.M.ティッセン著『計算物理学』(丸善出版, 2012) 3.2.2](https://www.maruzen-publishing.co.jp/item/b294596.html)より水素原子の例を取り上げる. 任意の方位量子数$l$や2体以上の系を考える場合は, [Hiyama,Kino,Kamimura(2003)](https://doi.org/10.1016/S0146-6410(03)90015-9)または[Hiyama,Kamimura(2018)](https://doi.org/10.1007/s11467-018-0828-5)を参照されたい. 以下では, $l=0$の場合に制限し, ガウス関数の線形結合として波動関数を表現する.\n",
"\n",
"$$\n",
" \\phi_i(\\boldsymbol{r}) = \\exp(-\\alpha_i r^2)\n",
"$$\n",
"\n",
"$$\n",
" \\psi(\\boldsymbol{r}) = \\sum_{i=1}^{N} C_i \\phi_i(\\boldsymbol{r}) = \\sum_{i=1}^{N} C_i \\exp(-\\alpha_i r^2)\n",
"$$\n",
"\n",
"このとき, [J.M.ティッセン著『計算物理学』(丸善出版, 2012) 3.2.2](https://www.maruzen-publishing.co.jp/item/b294596.html)によれば, ハミルトニアン行列$\\boldsymbol{H}$, 運動エネルギー行列$\\boldsymbol{T}$, クーロン行列$\\boldsymbol{V}$, 重なり行列$\\boldsymbol{S}$の各要素はそれぞれ\n",
"\n",
"$$\n",
"\\begin{align}\n",
" H_{ij} &= \\langle\\phi_i|\\hat{H}|\\phi_j\\rangle = T_{ij} + V_{ij}\\\\\n",
" T_{ij} &= \\langle\\phi_i|\\hat{T}|\\phi_j\\rangle = \\frac{3\\pi^{3/2} \\alpha_i \\alpha_j}{(\\alpha_i + \\alpha_j)^{5/2}} \\\\\n",
" V_{ij} &= \\langle\\phi_i|\\hat{V}|\\phi_j\\rangle = -\\frac{2\\pi}{\\alpha_i + \\alpha_j}\\\\\n",
" S_{ij} &= \\langle\\phi_i|\\phi_j\\rangle = \\left(\\frac{\\pi}{\\alpha_i + \\alpha_j}\\right)^{3/2}\\\\\n",
"\\end{align}\n",
"$$\n",
"\n",
"である. 演習として $S_{ij} = \\int \\exp(-\\alpha_i r^2) \\exp(-\\alpha_j r^2) r^2 \\mathrm{d}r \\iint \\sin(\\theta)\\mathrm{d}\\theta\\mathrm{d}\\varphi$ を実際に計算せよ. 動径部分の計算には[この積分公式](https://zenn.dev/ohno/articles/440234fbb2adec#%E4%B8%80%E8%88%AC%E5%8C%96%E3%81%95%E3%82%8C%E3%81%9F%E3%82%AC%E3%82%A6%E3%82%B9%E7%A9%8D%E5%88%86)を用いてよい. 角度部分の積分は $4\\pi$ になるはずである. この行列$\\boldsymbol{H}$と$\\boldsymbol{S}$を`eigen()`に渡すと$E$と$\\boldsymbol{C}$が得られる. 文献に従って$\\alpha_1=13.00773$, $\\alpha_2=1.962079$, $\\alpha_3=0.444529$, $\\alpha_4=0.1219492$を用いると$E_\\mathrm{1s}= -0.499 278 E_\\mathrm{h}$が得られる. 厳密解$E_\\mathrm{1s}= -0.5 E_\\mathrm{h}$に近い値である."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"GeneralizedEigen{Float64, Float64, Matrix{Float64}, Vector{Float64}}\n",
"values:\n",
"4-element Vector{Float64}:\n",
" -0.49927840566748566\n",
" 0.11321392045798838\n",
" 2.592299571959815\n",
" 21.144365190122496\n",
"vectors:\n",
"4×4 Matrix{Float64}:\n",
" 0.0961015 0.119454 -0.0103621 -6.1551\n",
" 0.163017 0.0813295 1.74489 1.2402\n",
" 0.185587 0.496216 -0.629196 -0.226412\n",
" 0.0737008 -0.205916 0.0977745 0.0307798"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 軌道指数\n",
"α = [13.00773, 1.962079, 0.444529, 0.1219492]\n",
"\n",
"# 重なり行列S & ハミルトニアン行列H\n",
"nₘₐₓ = length(α)\n",
"S = [(pi/(α[i]+α[j]))^(3/2) for i=1:nₘₐₓ, j=1:nₘₐₓ]\n",
"T = [3*pi^(3/2)*α[i]*α[j]/(α[i]+α[j])^(5/2) for i=1:nₘₐₓ, j=1:nₘₐₓ]\n",
"V = [-2*pi/(α[i]+α[j]) for i=1:nₘₐₓ, j=1:nₘₐₓ]\n",
"H = T + V\n",
"\n",
"# 固有値計算\n",
"E, C = eigen(Symmetric(H),Symmetric(S))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"さらに, エネルギーの固有値 $E$ と, 固有ベクトルから計算できる期待値 $\\langle H\\rangle$ が倍精度の範疇で一致し, ビリアル定理 $2\\langle T\\rangle+\\langle V\\rangle=0$ が成り立っていることも確認できた. なお, 期待値は行列積で計算できる：$\\langle H\\rangle = \\langle \\psi | \\hat{H} | \\psi \\rangle = \\langle \\sum_i C_{i}\\psi_i | \\hat{H} | C_{j}\\sum_j \\psi_j \\rangle = \\sum_{i,j} C_{i}^* C_{j} \\langle \\phi_i | \\hat{H} | \\phi_j \\rangle = \\sum_{i,j} C_{i}^* H_{ij} C_{j} = \\pmb{C}^* \\pmb{H} \\pmb{C}$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"E = -0.49927840566748566\n",
"<H> = -0.49927840566748566\n",
"2<T>+<V> = -3.699747808116882e-8\n"
]
}
],
"source": [
"println(\"E = \", E[1])\n",
"println(\"<H> = \", C[:,1]' * H * C[:,1])\n",
"println(\"2<T>+<V> = \", 2*C[:,1]' * T * C[:,1] + C[:,1]' * V * C[:,1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"なお, 固有関数が規格化されていない場合は $E = \\frac{\\langle \\psi | \\hat{H} | \\psi \\rangle}{\\langle \\psi | \\psi \\rangle}$ でエネルギーを評価すべきだが, 今回は規格化されているため $E = \\langle \\psi | \\hat{H} | \\psi \\rangle$ でよい. 各準位の固有関数が規格直交 $\\langle \\psi_i | \\psi_j \\rangle = \\delta_{ij}$ であることは次のように確認できる."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4×4 Matrix{Float64}:\n",
" 1.0 2.90146e-16 7.15674e-17 -4.11751e-17\n",
" 4.2962e-17 1.0 2.16237e-16 6.95197e-17\n",
" 2.48667e-16 -7.27456e-17 1.0 -1.68329e-16\n",
" 6.12104e-19 -4.60313e-17 -2.58422e-16 1.0"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"C' * S * C"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"波動関数および動径分布も1s軌道の厳密解(Slater型関数)と非常に近い形をしていることも確認できた. なお, 線形代数のソルバ(LAPACK, NUMPACなど)で得られる固有ベクトルは正負が逆になることがある（符号が逆でも解であることには違いないが, 適当な基準で符号を決めないと描写する上で困る）ため, 動径波動関数を描写する際は正負の値を確認するか, 絶対値を取るなどの工夫が必要である. ここでは絶対値を取って描写した."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Y(θ,φ) = 1/sqrt(pi)\n",
"R(r) = exp(-r)\n",
"ψ(r,θ,φ) = R(r) * Y(θ,φ)\n",
"ρ(r,θ,φ) = r^2*ψ(r,θ,φ)^2\n",
"data2ψ(α,C,r,θ,φ) = sum(C[:,1] .* exp.(-α*r^2))\n",
"data2ρ(α,C,r,θ,φ) = r^2*data2ψ(α,C,r,θ,φ)^2\n",
"\n",
"plot(xlims=(0,4), xlabel=\"\\$r\\$\", ylabel=\"\\$|\\\\psi_\\\\mathrm{1s}(r,\\\\theta,\\\\phi)|\\$\")\n",
"plot!(0:0.01:4,r->abs(data2ψ(α,C,r,0,0)), label=\"4G\")\n",
"plot!(r->ψ(r,0,0), label=\"exact\", lc=\"#000000\")"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(xlims=(0,6), xlabel=\"\\$r\\$\", ylabel=\"\\$r^2 |\\\\psi_\\\\mathrm{1s}(r,\\\\theta,\\\\phi)|^2\\$\")\n",
"plot!(0:0.01:6,r->data2ρ(α,C,r,0,0), label=\"4G\")\n",
"plot!(r->ρ(r,0,0), label=\"exact\", lc=\"#000000\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 最適化\n",
"\n",
"教科書に書いてあるパラメータを使ったところ, 厳密値の$E_\\mathrm{1s}= -0.5 E_\\mathrm{h}$に近い値が得られた. このパラメータはエネルギーを目的関数として, 各軌道指数を説明変数とした最適化計算を行うことで得られる. ここでは`Optim.jl`の[Nelder-Mead法(ANMS)](https://julianlsolvers.github.io/Optim.jl/stable/#algo/nelder_mead/)を用いて最適化を行う. パラメータの最適化にあたって最低でも3までの安全対策を施す必要がある.\n",
"\n",
"1. $0<\\alpha_i+\\alpha_j$を判定すること\n",
"2. `try` `catch` `end`でソルバが異常終了した場合に停止しないよう対策すること\n",
"3. `eigen()`に渡す前に`Symmetric()`を通して対称行列の型を指定すること\n",
"4. 固有ベクトルから計算した期待値が固有値と`1e-8`以内の誤差で一致するか確認すること"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"STOnG(0.27) = ([-0.4241859587312052;;], [0.266951837978708;;])\n",
"STOnG([13.00773, 1.962079, 0.444529, 0.1219492]) = ([-0.49927840566748566, 0.11321392045798838, 2.592299571959815, 21.144365190122496], [0.09610151618612507 0.11945380574493299 -0.01036206188168874 -6.155100006789124; 0.1630171696390599 0.08132945379475155 1.7448913023470436 1.2402020851506472; 0.18558698714513733 0.4962162636683257 -0.6291955141735308 -0.2264116081952988; 0.073700760692756 -0.20591550816511814 0.09777447415099837 0.03077984254671438])\n"
]
},
{
"data": {
"text/plain": [
"([-0.49927840566748566, 0.11321392045798838, 2.592299571959815, 21.144365190122496], [0.09610151618612507 0.11945380574493299 -0.01036206188168874 -6.155100006789124; 0.1630171696390599 0.08132945379475155 1.7448913023470436 1.2402020851506472; 0.18558698714513733 0.4962162636683257 -0.6291955141735308 -0.2264116081952988; 0.073700760692756 -0.20591550816511814 0.09777447415099837 0.03077984254671438])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# using Plots\n",
"# using LinearAlgebra\n",
"\n",
"function STOnG(α)\n",
"\n",
" # 重なり行列S & ハミルトニアン行列H\n",
" nₘₐₓ = length(α)\n",
" S = [(pi/(α[i]+α[j]))^(3/2) for i=1:nₘₐₓ, j=1:nₘₐₓ]\n",
" T = [3*pi^(3/2)*α[i]*α[j]/(α[i]+α[j])^(5/2) for i=1:nₘₐₓ, j=1:nₘₐₓ]\n",
" V = [-2*pi/(α[i]+α[j]) for i=1:nₘₐₓ, j=1:nₘₐₓ]\n",
" H = T + V\n",
"\n",
" if nₘₐₓ == 1\n",
" # 固有値計算\n",
" E = H ./ S\n",
" C = ones(nₘₐₓ,nₘₐₓ) ./ sqrt.(S)\n",
" else\n",
" # 固有値計算\n",
" E, C = try; eigen(Symmetric(H),Symmetric(S)); catch; (fill(Inf,nₘₐₓ), zeros(nₘₐₓ,nₘₐₓ)); end\n",
" # 検証\n",
" if 1e-9 < abs(E[1] - transpose(C[:,1]) * H * C[:,1])\n",
" E .= Inf\n",
" end\n",
" end\n",
"\n",
" return E, C\n",
"end\n",
"\n",
"@show STOnG(0.27)\n",
"@show STOnG([13.00773, 1.962079, 0.444529, 0.1219492])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"nₘₐₓ\tenergy\t\t\tcalls\n",
"1\t-0.42441318157838753\t11\n",
"2\t-0.4858127166162751\t115\n",
"3\t-0.4969792527050513\t262\n",
"4\t-0.4992784057143483\t403\n",
"5\t-0.49980983223189135\t3682\n",
"6\t-0.49994557039665505\t2428\n",
"7\t-0.4999832977891682\t2024\n",
"8\t-0.4999945613762664\t1565\n",
"9\t-0.4999978978456621\t1478\n",
"10\t-0.4999992447453602\t1491\n",
"11\t-0.49999948785393544\t1503\n",
"12\t-0.4999997955098435\t1541\n",
"13\t-0.4999999127438995\t1437\n",
"14\t-0.49999992730021203\t1843\n",
"15\t-0.4999999281984859\t3697\n",
"16\t-0.4999999270562452\t18\n",
"17\t-0.4999999270891153\t19\n",
"18\tInf\t20\n",
"19\tInf\t21\n",
"20\tInf\t22\n",
"∞ \t-0.5\n"
]
}
],
"source": [
"αs = []\n",
"Cs = []\n",
"\n",
"println(\"nₘₐₓ\\tenergy\\t\\t\\tcalls\")\n",
"\n",
"res = optimize(X->STOnG(X)[1][1], [0.5], method=GradientDescent())\n",
"α = Optim.minimizer(res)\n",
"C = STOnG(α)[2]\n",
"println(1, \"\\t\", Optim.minimum(res), \"\\t\", Optim.f_calls(res))\n",
"push!(αs, α)\n",
"push!(Cs, C)\n",
"\n",
"α = [0.00001, 0.0001]\n",
"for i in 2:20\n",
" res = optimize(X->STOnG(X)[1][1], α, g_tol=1e-16)\n",
" α = Optim.minimizer(res)\n",
" C = STOnG(α)[2]\n",
" println(i, \"\\t\", Optim.minimum(res), \"\\t\", Optim.f_calls(res))\n",
" push!(αs, α[:])\n",
" push!(Cs, C)\n",
" push!(α, α[end]*0.99)\n",
"end\n",
"\n",
"println(\"∞ \\t\", -0.50000000000000000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"かなり低いエネルギーが得られているが, いずれも評価回数が非常に大きいことがわかる. 2体より大きな系では, 小さな基底でない限り全ての軌道指数を最適化するのはほぼ不可能であるから, 何らかの制約を課すなどしてパラメータを減らす必要がある. つまり全ての軌道指数を完璧に最適化した場合に比べればエネルギーを妥協することになる.\n",
"\n",
"先ほどと同様に動径波動関数および動径分布関数を描写する. 下図の比較対象としては[J.M.ティッセン著『計算物理学』(丸善出版, 2012) 図4.3](https://www.maruzen-publishing.co.jp/item/b294596.html)や[A.ザボ, Ｎ.Ｓ.オストランド著『新しい量子化学 上 電子構造の理論入門』(東京大学出版会, 1987) 図3.3](http://www.utp.or.jp/book/b302128.html)を挙げる. 基底関数を増やすほどにカスプ($r=0$の点)の記述が良くなっていくことが見て取れる."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
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]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Y(θ,φ) = 1/sqrt(pi)\n",
"R(r) = exp(-r)\n",
"ψ(r,θ,φ) = R(r) * Y(θ,φ)\n",
"ρ(r,θ,φ) = r^2*ψ(r,θ,φ)^2\n",
"data2ψ(α,C,r,θ,φ) = sum(C[:,1] .* exp.(-α*r^2))\n",
"data2ρ(α,C,r,θ,φ) = r^2*data2ψ(α,C,r,θ,φ)^2\n",
"\n",
"plot(xlims=(0,4), xlabel=\"\\$r\\$\", ylabel=\"\\$|\\\\psi_\\\\mathrm{1s}(r,\\\\theta,\\\\phi)|\\$\")\n",
"\n",
"for i in 1:10\n",
" plot!(0:0.01:4, r->abs(data2ψ(αs[i],Cs[i],r,0,0)), label=\"nₘₐₓ=$(i)\")\n",
"end\n",
"\n",
"plot!(r->ψ(r,0,0), label=\"exact\", lc=\"#000000\")"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
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