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pabloferz/Free Electron.ipynb

Created February 6, 2016 22:24
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Free Electron
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Free Electron.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Free Electron\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some useful packages"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"using FastAnonymous\n",
"using Interact\n",
"using Plots\n",
"using SymPy\n",
"\n",
"const ∫ = quadgk;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Auxiliar functions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
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"outputs": [],
"source": [
"# Simplification method to match closer those of Mathematica\n",
"function exptrigsimp(x::Sym)\n",
" X = expand(x)\n",
" A = atoms(X, :exp)\n",
" length(A) ≠ 2 && return sympy_meth(:exptrigsimp, X)\n",
" y = exp(simplify(sum([ex.x[:exp] for ex in A]) / 2))\n",
" X = sum([simplify(ex) for ex in args(expand(X / y))])\n",
" return y * sympy_meth(:exptrigsimp, X)\n",
"end;"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"\"Heaviside function. Returns 0.5 if `x == 0`, 0.0 if `x < 0` and 1.0 otherwise.\"\n",
"heaviside(x) = ifelse(x < 0, 0., ifelse(x > 0, 1., 0.5))\n",
"heaviside(x::Sym) = sympy_meth(:Heaviside, x);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Initialize ploting libraries"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"gadfly() # Use Gadfly as backend for plotting\n",
"backend() # Force backend initialization;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Physical parameters**"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [],
"source": [
"\"nanometers scaling factor\"\n",
"const nm = 1e-9;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Useful definitions**"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"\"Wavevector `k(n, c) = 2π * n / c`\"\n",
"@inline k(n, c) = 2π * n / c;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Problem data**"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Semi-length of the model box in meters\n",
"const L = 1e-2;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* **Flat wavefunction**"
]
},
{
"cell_type": "code",
"execution_count": 10,
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",
"image/svg+xml": [],
"text/plain": [
"Plot{Plots.GadflyPackage() n=1}"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(x -> real(exp(im * k(1e7, L) * x)) / L, linspace(0, 10nm, 500); size=(400,250), legend=false)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* **Superposition of a finite set of wave functions**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example of a non-normilized wavefunction which is the sum of all of the $(b - a + 1)$ planewaves with wavector $k(n,c)$, for $n$ from $a$ to $b$"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"function Ψ_discrete(x, a::Integer, b::Integer, c)\n",
" z = im * k(1, c) * x\n",
" Ψₓ = zero(exp(z))\n",
" for n = a:b\n",
" Ψₓ += exp(n * z)\n",
" end\n",
" return Ψₓ / √c\n",
"end;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plotting this doesn't take too much time. The same would have taken around 11 minutes using *Mathematica 7* in the same machine in which this was tested. Although the notation is not as nice as that of *Mathematica*, but it isn't that bad either."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 15.560465 seconds (42.68 k allocations: 1.711 MB)\n"
]
}
],
"source": [
"@time plot(x -> abs(Ψ_discrete(x, 1000, 1000000, L)), linspace(-100nm, 100nm, 499), label=\"n = 10³ : 10⁶\");"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/svg+xml": [
"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\"\n",
" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
" xmlns:gadfly=\"http://www.gadflyjl.org/ns\"\n",
" version=\"1.2\"\n",
" width=\"132.28mm\" height=\"66.14mm\" viewBox=\"0 0 132.28 66.14\"\n",
" stroke=\"none\"\n",
" fill=\"#000000\"\n",
" stroke-width=\"0.3\"\n",
" font-size=\"3.88\"\n",
">\n",
"<g stroke=\"#000000\" stroke-opacity=\"0.000\" fill=\"#FFFFFF\" id=\"img-a0187c6a-1\">\n",
" <rect x=\"0\" y=\"0\" width=\"132.28\" height=\"66.14\"/>\n",
"</g>\n",
"<g class=\"plotroot xscalable yscalable\" id=\"img-a0187c6a-2\">\n",
" <g class=\"guide xlabels\" font-size=\"2.82\" font-family=\"Helvetica\" fill=\"#000000\" id=\"img-a0187c6a-3\">\n",
" <text x=\"16.13\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">-1.0×10⁻⁷</text>\n",
" <text x=\"39.09\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">-5.0×10⁻⁸</text>\n",
" <text x=\"62.05\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">0</text>\n",
" <text x=\"85.01\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">5.0×10⁻⁸</text>\n",
" <text x=\"107.97\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">1.0×10⁻⁷</text>\n",
" </g>\n",
" <g class=\"guide colorkey\" id=\"img-a0187c6a-4\">\n",
" <g fill=\"#000000\" font-size=\"2.82\" font-family=\"Helvetica\" id=\"img-a0187c6a-5\">\n",
" <text x=\"113.78\" y=\"32.57\" dy=\"0.35em\">n = 10³ : 10⁶</text>\n",
" </g>\n",
" <g fill=\"#009AFA\" stroke=\"#000000\" stroke-opacity=\"0.000\" id=\"img-a0187c6a-6\">\n",
" <rect x=\"110.97\" y=\"31.66\" width=\"1.82\" height=\"1.82\"/>\n",
" </g>\n",
" <g fill=\"#000000\" font-size=\"3.88\" font-family=\"Helvetica\" stroke=\"#000000\" stroke-opacity=\"0.000\" id=\"img-a0187c6a-7\">\n",
" <text x=\"110.97\" y=\"28.75\"></text>\n",
" </g>\n",
" </g>\n",
"<g clip-path=\"url(#img-a0187c6a-8)\">\n",
" <g id=\"img-a0187c6a-9\">\n",
" <g pointer-events=\"visible\" opacity=\"1\" fill=\"#000000\" fill-opacity=\"0.000\" stroke=\"#000000\" stroke-opacity=\"0.000\" class=\"guide background\" id=\"img-a0187c6a-10\">\n",
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",
"image/svg+xml": [],
"text/plain": [
"Plot{Plots.GadflyPackage() n=1}"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot!(; xlims=(-1e-7,1e-7), size=(500,250))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is what happens if we reduce the wavenumbers from the range $10^3:10^6$ to the range $10^5:10^6$"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 14.311196 seconds (310.33 k allocations: 14.532 MB, 0.05% gc time)\n"
]
}
],
"source": [
"@time plot!(x -> abs(Ψ_discrete(x, 100000, 1000000, L)), linspace(-100nm, 100nm, 499), label=\"n = 10⁵ : 10⁶\");"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
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},
"outputs": [
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"Compose.SVG(132.2751322751323mm,66.13756613756615mm,IOBuffer(data=UInt8[...], readable=true, writable=true, seekable=true, append=false, size=15491, maxsize=Inf, ptr=15492, mark=-1),nothing,\"img-f0321124\",0,Compose.SVGPropertyFrame[],Dict{Type{T},Union{Compose.Property{P<:Compose.PropertyPrimitive},Void}}(Compose.Property{Compose.FillPrimitive}=>nothing),Dict{Compose.ClipPrimitive{P<:NTuple{N,Measures.Measure}},ASCIIString}(Compose.ClipPrimitive{Tuple{Measures.Length{:mm,Float64},Measures.Length{:mm,Float64}}}([(14.13333333333334mm,1.0mm),(109.9651322751323mm,1.0mm),(109.9651322751323mm,60.50423280423282mm),(14.13333333333334mm,60.50423280423282mm)])=>\"img-f0321124-8\"),Tuple{Compose.FormPrimitive,ASCIIString}[],Set{AbstractString}(),true,false,nothing,true,\"img-f0321124-16\",false,16,AbstractString[\"/home/pabloferz/.julia/v0.4/Gadfly/src/gadfly.js\"],Tuple{AbstractString,AbstractString}[(\"Snap.svg\",\"Snap\"),(\"Gadfly\",\"Gadfly\")],AbstractString[\"fig.select(\\\"#img-f0321124-4\\\")\\n .drag(function() {}, function() {}, function() {});\",\"fig.select(\\\"#img-f0321124-9\\\")\\n .init_gadfly();\"],false,:none)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"image/svg+xml": [],
"text/plain": [
"Plot{Plots.GadflyPackage() n=2}"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot!()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we took out $10^5-10^3$ terms, which is about $10\\%$ of the number of planewaves composing the total wave function, we got a reduction of approximately $10\\%$ in time. Also the new wavefunction is somewhat but not too different from the original.\n",
"\n",
"If we now consider only the planewaves with wavenumbers from $9\\times10^5$ to $10^6$, (that is, we consider only about $10\\%$ of the original terms, we get the following."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1.657566 seconds (2.38 k allocations: 76.359 KB)\n"
]
}
],
"source": [
"@time plot!(x -> abs(Ψ_discrete(x, 900000, 1000000, L)), linspace(-100nm, 100nm, 499), label=\"n = 9×10⁵ : 10⁶\");"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/svg+xml": [
"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\"\n",
" xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
" xmlns:gadfly=\"http://www.gadflyjl.org/ns\"\n",
" version=\"1.2\"\n",
" width=\"132.28mm\" height=\"66.14mm\" viewBox=\"0 0 132.28 66.14\"\n",
" stroke=\"none\"\n",
" fill=\"#000000\"\n",
" stroke-width=\"0.3\"\n",
" font-size=\"3.88\"\n",
">\n",
"<g stroke=\"#000000\" stroke-opacity=\"0.000\" fill=\"#FFFFFF\" id=\"img-b501ef63-1\">\n",
" <rect x=\"0\" y=\"0\" width=\"132.28\" height=\"66.14\"/>\n",
"</g>\n",
"<g class=\"plotroot xscalable yscalable\" id=\"img-b501ef63-2\">\n",
" <g class=\"guide xlabels\" font-size=\"2.82\" font-family=\"Helvetica\" fill=\"#000000\" id=\"img-b501ef63-3\">\n",
" <text x=\"16.13\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">-1.0×10⁻⁷</text>\n",
" <text x=\"38.19\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">-5.0×10⁻⁸</text>\n",
" <text x=\"60.25\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">0</text>\n",
" <text x=\"82.3\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">5.0×10⁻⁸</text>\n",
" <text x=\"104.36\" y=\"61.5\" text-anchor=\"middle\" dy=\"0.6em\">1.0×10⁻⁷</text>\n",
" </g>\n",
" <g class=\"guide colorkey\" id=\"img-b501ef63-4\">\n",
" <g fill=\"#000000\" font-size=\"2.82\" font-family=\"Helvetica\" id=\"img-b501ef63-5\">\n",
" <text x=\"110.18\" y=\"28.94\" dy=\"0.35em\">n = 10³ : 10⁶</text>\n",
" <text x=\"110.18\" y=\"32.57\" dy=\"0.35em\">n = 10⁵ : 10⁶</text>\n",
" <text x=\"110.18\" y=\"36.2\" dy=\"0.35em\">n = 9×10⁵ : 10⁶</text>\n",
" </g>\n",
" <g stroke=\"#000000\" stroke-opacity=\"0.000\" id=\"img-b501ef63-6\">\n",
" <rect x=\"107.36\" y=\"28.03\" width=\"1.82\" height=\"1.82\" fill=\"#009AFA\"/>\n",
" <rect x=\"107.36\" y=\"31.66\" width=\"1.82\" height=\"1.82\" fill=\"#E36F47\"/>\n",
" <rect x=\"107.36\" y=\"35.29\" width=\"1.82\" height=\"1.82\" fill=\"#3EA44E\"/>\n",
" </g>\n",
" <g fill=\"#000000\" font-size=\"3.88\" font-family=\"Helvetica\" stroke=\"#000000\" stroke-opacity=\"0.000\" id=\"img-b501ef63-7\">\n",
" <text x=\"107.36\" y=\"25.11\"></text>\n",
" </g>\n",
" </g>\n",
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",
"image/svg+xml": [],
"text/plain": [
"Plot{Plots.GadflyPackage() n=3}"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot!()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Which, accordingly, can be done in $10\\%$ of the time. Additionally as all of the plane waves have same amplitude it is not surprising that the last wavefunction shows the shape (and height at $x=0$) observed above.\n",
"\n",
"We can do better by approximating the wavefunction \\``Ψ_discrete`\\` by a similar numeric integral."
]
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"Ψ_discrete(1.5nm, 1000, 1000000, L)\n",
"@time Ψ_discrete(1.5nm, 1000, 1000000, L)"
]
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]
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"source": [
"let Ψ = @anon n -> exp(im * k(n, L) * 1.5nm) / √L\n",
" ∫(Ψ, 1000, 1000000)\n",
" @time ∫(Ψ, 1000, 1000000)[1]\n",
"end"
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"Of course, instead of calculating the above integral we can compute the equivalent Fourier Transform of the difference of two Heaviside functions and use that directly as the wavefunction."
]
},
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"text/latex": [
"$$- \\frac{\\sqrt{c}}{\\pi x} e^{- \\frac{i \\pi}{c} x \\left(a + b\\right)} \\sin{\\left (\\frac{\\pi x}{c} \\left(a - b\\right) \\right )}$$"
],
"text/plain": [
" -I*pi*x*(a + b) \n",
" ---------------- \n",
" ___ c /pi*x*(a - b)\\ \n",
"-\\/ c *e *sin|------------| \n",
" \\ c / \n",
"-------------------------------------------\n",
" pi*x "
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let\n",
" local k\n",
" a, b, k, x = symbols(\"a b k x\", real=true)\n",
" c = symbols(\"c\", positive=true)\n",
" F = fourier_transform(heaviside(k-a), k, x/c) - fourier_transform(heaviside(k-b), k, x/c)\n",
" global const Ψ_symbolic = exptrigsimp(F) / √c\n",
" @eval Ψ_continuous(x, a, b, c) = $(parse(replace(string(Ψ_symbolic), r\"I\", \"im\")))\n",
" Ψ_symbolic\n",
"end"
]
},
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"text": [
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]
}
],
"source": [
"Ψ_continuous(1.5nm, 1000, 1000000, L)\n",
"@time Ψ_continuous(1.5nm, 1000, 1000000, L)"
]
},
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",
"image/svg+xml": [],
"text/plain": [
"Plot{Plots.GadflyPackage() n=1}"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.002493 seconds (6.77 k allocations: 237.363 KB)\n"
]
}
],
"source": [
"@time plot(x -> abs(Ψ_continuous(x, 1000, 1000000, L)), linspace(-100nm, 100nm, 499))\n",
"plot!(; xlims=(-1e-7,1e-7), size=(450,250), legend=false)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.4.1",
"language": "julia",
"name": "julia-0.4"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.4.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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