{ "cells": [ { "cell_type": "markdown", "id": "e42e6e61", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "# 確率論的解釈\n", "\n", " ミクロな粒子を用いた二重スリット実験で、干渉縞が現れるということは、\n", " \n", "* 1つの粒子が一方のスリットを通ったのと同時に\n", "\n", "* もう一方のスリットを通ったことを意味する\n", "\n", "このミクロな粒子は何らかの空間的な広がりを持つことを示している。" ] }, { "cell_type": "markdown", "id": "9f85ca3b-083b-4031-ad0e-8ae5a66e3ab1", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "このような実験結果を解釈するアイデアとして、以下のような量子力学のコペンハーゲン解釈が生まれました。\n", "\n", "* 観測前には波動関数が空間的な広がりをもちシュレディンガー方程式に従う\n", "\n", "* 観測時点では一点に収束している\n", "\n", "* 検出確率が波動関数の二乗に比例する\n", "\n", " ここでは確率をつかって出来事を解釈する問題について取り上げていきます。\n", "\n", "" ] }, { "cell_type": "markdown", "id": "d13f917b-051a-4820-b15b-68c180f8147e", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 3 枚のコインの裏表\n", "\n", " 3つのコインを投げて、表 (H:heads) と裏 (T:tails) の枚数を数えてみます。\n", "\n", "|Coin 1 | Coin 2| Coin 3|\n", "|:-----:|:-----:|:-----:|\n", "|H|H|H|\n", "|H|H|T|\n", "|H|T|H|\n", "|T|H|H|\n", "|H|T|T|\n", "|T|T|H|\n", "|T|H|T|\n", "|T|H|T|\n", "\n", " すべてのコインは見分けがつかないこととします。このとき H の個数を考えます。" ] }, { "cell_type": "markdown", "id": "4434f883", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " 上記の表から数を数えると、\n", "\n", "* 3つHがある場合は、HHH \n", "\n", "* 2つHがある場合は、HHT, HTH, THH\n", "\n", "* 1つHがある場合は、HTT, TTH, THT\n", "\n", "* Hがない場合は、TTT\n", "\n", "となっていることがわかります。" ] }, { "cell_type": "markdown", "id": "cf0fbcc8-def5-4d27-afbd-c03cbdbabcb2", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " ここで特定の数の H 状態をまとめてマクロ状態(macrostate)、またそれぞれの状態をミクロ状態(microstate)と呼びます。マクロ状態は一般的に観測することが容易なもの、ミクロ状態は観測が難しいものに対応させて考えるとよいでしょう。\n", " \n", " 各ミクロ状態は等確率で存在しますが、マクロ状態は存在確率が異なります。\n", " \n", " 上の例を見ると、3つが H のマクロ状態よりも、2つが H のマクロ状態の方が存在確率が高いことがわかります。\n", " " ] }, { "cell_type": "markdown", "id": "db73a805", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " ここで **多重度** $\\Omega$ (multiplicity)という量を導入します。多重度とは、特定のマクロ状態におけるミクロ状態の数です。\n", "\n", " 上のコインゲームで、 n 回表が出た場合の数として $\\Omega(n)$ を定義します。\n", " \n", " コインの総数を N とすると、多重度について次の式を導くことができます。\n", "\n", "$$\\Omega(N,n) == \\frac{N!}{n!\\cdot(N-n)!} = \\binom{N}{n}$$" ] }, { "cell_type": "markdown", "id": "9c37b9cf-30b6-40e3-8961-32f5044ccad4", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " このような多重度を計算するプログラムを作成してください。正しい実行例は以下のようになります。\n", "\n", "```\n", "type a value for N: 3\n", "when n= 0 ; the multiplicity is 1.0\n", "when n= 1 ; the multiplicity is 3.0\n", "when n= 2 ; the multiplicity is 3.0\n", "when n= 3 ; the multiplicity is 1.0\n", "```\n", "\n", "N を増やすとどうなるでしょうか。5、10、20 などでも N を試してみましょう。" ] }, { "cell_type": "markdown", "id": "249b34cf", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 多重度 $\\Omega$ (multiplicity)の関数を定義する" ] }, { "cell_type": "code", "execution_count": 2, "id": "13f32cba", "metadata": {}, "outputs": [], "source": [ "import matplotlib.ticker as mtick\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "#Multiplicity calculation\n", "def factor(N):\n", " if N == 0 or N == 1:\n", " return 1\n", " else: \n", " total = 1\n", " for i in range(2,N+1):\n", " total *= i\n", " return total \n", "\n", "def Multiplicity(N,n):\n", " return factor(N)/factor(n)/factor(N-n)" ] }, { "cell_type": "markdown", "id": "02e5b48b", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 入力されたNに対して多重度を計算する" ] }, { "cell_type": "code", "execution_count": 3, "id": "ba26ec54", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "type a positive integer value for N: 3\n", "when n= 0 ; the multiplicity is 1.0\n", "when n= 1 ; the multiplicity is 3.0\n", "when n= 2 ; the multiplicity is 3.0\n", "when n= 3 ; the multiplicity is 1.0\n" ] } ], "source": [ " \n", "N=int(input(\"type a positive integer value for N: \"))\n", "N_series = range(N+1) \n", "Omega = []\n", "\n", "for n in N_series:\n", " print(\"when n=\", n, \"; the multiplicity is\", Multiplicity(N,n))\n" ] }, { "cell_type": "markdown", "id": "1cd8691c-b668-408a-92f6-ffa0e85f3856", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 確率をグラフにして考える\n", "\n", " 次にNによる違いを詳しくみていきましょう。以下では曲線をプロットするための関数Plot_Omegaを定義しています。\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "6793a89c", "metadata": {}, "outputs": [], "source": [ "def Plot_Omega(N): \n", "\n", " N_series = range(N+1) \n", " Omega = []\n", "\n", " for n in N_series:\n", " Omega.append(Multiplicity(N,n))\n", " \n", " plt.plot(N_series, Omega)\n", " plt.title('N='+str(N))\n", " plt.xlabel('n')\n", " plt.ylabel('$\\Omega(n)$')\n", "\n", " plt.show()" ] }, { "cell_type": "markdown", "id": "c18e1061-7d9f-4da4-b428-eb2253560e27", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Plot_Omega関数\n", "これで任意の N の結果をより便利に呼び出すことができます。\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "587a6d02-9384-432b-a248-9d3db6c7de3f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Plot_Omega(50)" ] }, { "cell_type": "markdown", "id": "632e6692-a0a4-439d-8f02-a90af55034dc", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "数を増やしましょう" ] }, { "cell_type": "code", "execution_count": 4, "id": "9e583991-cabb-4730-a904-6ae2b5a16901", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Plot_Omega(100)" ] }, { "cell_type": "markdown", "id": "65b71909-ae9d-4599-afee-eecc302d1667", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Nが大きい場合:統計物理学\n", "\n", " このように、Nに非常に大きな数値を代入すると、ランダム性に由来する揺らぎは測定不能なほど小さくなります。\n", " \n", " この場合に観測される可能性が最も高いマクロ状態は、非常に限られた局所状態になります。\n", "\n", " 実在の物質において物理的特性を測定した場合、測定結果はほとんどばらつきのない値が得られます。\n", " \n", " これは、アボガドロ数=6.02$\\times 10^{23}$オーダーの多数の原子や分子で構成された大きな N の効果によるものです。\n", " \n", " このような状態を記述する物理学を統計物理学といいます。\n", " \n", " \n", " " ] }, { "cell_type": "markdown", "id": "c989982b-2739-4be8-962a-5d77d9d72b73", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "さらに数を増やしましょう" ] }, { "cell_type": "code", "execution_count": 5, "id": "a72d760a-3c30-40b5-bdeb-97a41b7e6f80", "metadata": {}, "outputs": [ { "ename": "OverflowError", "evalue": "integer division result too large for a float", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mOverflowError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[5], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m Plot_Omega(\u001b[38;5;241m1000\u001b[39m)\n", "Cell \u001b[0;32mIn[2], line 25\u001b[0m, in \u001b[0;36mPlot_Omega\u001b[0;34m(N)\u001b[0m\n\u001b[1;32m 22\u001b[0m Omega \u001b[38;5;241m=\u001b[39m []\n\u001b[1;32m 24\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m n \u001b[38;5;129;01min\u001b[39;00m N_series:\n\u001b[0;32m---> 25\u001b[0m Omega\u001b[38;5;241m.\u001b[39mappend(Multiplicity(N,n))\n\u001b[1;32m 27\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(N_series, Omega)\n\u001b[1;32m 28\u001b[0m plt\u001b[38;5;241m.\u001b[39mtitle(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mN=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m+\u001b[39m\u001b[38;5;28mstr\u001b[39m(N))\n", "Cell \u001b[0;32mIn[2], line 16\u001b[0m, in \u001b[0;36mMultiplicity\u001b[0;34m(N, n)\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mMultiplicity\u001b[39m(N,n):\n\u001b[0;32m---> 16\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m factor(N)\u001b[38;5;241m/\u001b[39mfactor(n)\u001b[38;5;241m/\u001b[39mfactor(N\u001b[38;5;241m-\u001b[39mn)\n", "\u001b[0;31mOverflowError\u001b[0m: integer division result too large for a float" ] } ], "source": [ "Plot_Omega(1000)" ] }, { "cell_type": "markdown", "id": "d5174f57-0879-4884-9dff-c1b0fe724eb2", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Diagnostics(診断)\n", "プログラムは除算について問題があるようです。\n", "\n", " N1/N2\n", "\n", "実は、2 つの大きな整数の間で除算を行うことはできません。そこで、2 つの数値を除算する代わりに、次のようにします。 \n", "log() 関数を使用します。\n", "\n", " log(N1/N2) = log(N1) - log(N2)\n", "\n", "最終的に、次の式が得られます。\n", "\n", " exp(log(N1) - log(N2))" ] }, { "cell_type": "code", "execution_count": null, "id": "4f644356", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from math import log, exp\n", "\n", "#Multiplicity calculation\n", "def factor(N):\n", " N = int(N)\n", " total = 1\n", " if N<0:\n", " print('Error, N must be greater than 0')\n", " elif N>1: \n", " for i in range(2,N+1):\n", " total *= i\n", " return total" ] }, { "cell_type": "code", "execution_count": 17, "id": "f1bc1798-a3bd-4d32-8140-e688be4a8e49", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "def Multiplicity(N,n):\n", " #return factor(N)/factor(n)/factor(N-n)\n", " return exp(log(factor(N)) - log(factor(n)) - log(factor(N-n))) #change it to log funtion\n", "\n", "def Plot_Omega2(N): \n", "\n", " N_series = range(N+1) \n", " Omega = []\n", "\n", " for n in N_series:\n", " Omega.append(Multiplicity(N,n))\n", " \n", " plt.plot(N_series, Omega)\n", " plt.title('N='+str(N))\n", " plt.xlabel('n')\n", " plt.ylabel('$\\Omega(n)$')\n", "\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "id": "287e27b0-4094-4120-bb0e-0f3c6cca493d", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Plot_Omega2(1000)" ] }, { "cell_type": "markdown", "id": "8546fa9c-49ee-45c3-ada6-6276e29ee4b0", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 課題1:固体のアインシュタインモデル\n", "\n", " 固体結晶は原子で構成されています。 アインシュタインは、各原子を調和振動子と考えるモデルを提案しました。\n", " \n", " このモデルでは、結晶格子内の隣接する原子はバネによって繋がれていると考えます。\n", " \n", " " ] }, { "cell_type": "markdown", "id": "dea58bdd", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " 各振動子で、エネルギーは量子化された状態 (0,1,2,.....) をとります。\n", " \n", " 振動子が 2 つしかないと仮定すると、エネルギーは、\n", "\n", "|Oscillator | 1| 2|\n", "|:-----:|:-----:|:-----:|\n", "|Energy|0|0|\n", "| |1|0|\n", "| |0|1|\n", "| |1|1|\n", "| |2|0|\n", "| |0|2|\n", "\n", "つまり、全エネルギー $q$ が0のとき, $\\Omega$=1、全エネルギー $q$ が1のとき, $\\Omega$=2、全エネルギー $q$ が2のとき, $\\Omega$=3" ] }, { "cell_type": "markdown", "id": "0b6a1853-834b-4d79-a360-8dc70ee3af79", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "振動子の数をNとしたときの一般式は、\n", "\n", " $$\\Omega(N, q) = \\binom{q+N-1}{q} = \\frac{(q+N-1)!}{q!(N-1)!}$$\n", " \n", " \n", "この式を用いて、任意の ($N$, $q$) について $\\Omega$ を計算するプログラムを作成してください。" ] }, { "cell_type": "code", "execution_count": 21, "id": "c9e9864b", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Plot_Omega3(100,100)" ] }, { "cell_type": "markdown", "id": "b1a9b6ee", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## 課題2:相互作用する 2 つのアインシュタイン固体\n", " ここで、相互作用する 2 つのアインシュタイン固体について考えてみましょう。$A$ と $B$ が弱く結合している (ちょうど理想気体のように) と仮定すると、それぞれの固体のエネルギー $q_A$ と $q_B$ はゆっくりと変化します。 \n", " \n", " この仮定の下では、エネルギーの総数 $q_\\text{total}$ は単純に $q_A$ と $q_B$ の合計になります。簡単のために、$q_\\text{total}$ を固定しましょう。任意の $q_A$ の $\\Omega$ はどうなるでしょうか。" ] }, { "cell_type": "markdown", "id": "c11473db", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "$A$ の振動子の数を $N_A$ として $A$ だけを数えると、\n", "\n", "$$\\Omega(A) = \\binom{q_A+N_A-1}{q_A} = \\frac{(q_A+N_A-1)!}{q_A!(N_A-1)!}$$\n", " \n", "同様に $B$ の振動子の数を $N_B$ として、\n", "\n", " $$\\Omega(B) = \\binom{q_B+N_B-1}{q_B} = \\frac{(q_B+N_B-1)!}{q_B!(N_B-1)!}$$\n", " \n", "これを用いると総数は以下のようになります。\n", "\n", " $$\\Omega(\\text{total}) = \\Omega(A) \\Omega(B) $$" ] }, { "cell_type": "markdown", "id": "16f6ec0b-70c6-4826-b156-a68d3a4cabfb", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "$q_A + q_B = 2, N_A = N_B = 3$の場合、結果は以下のような表にまとめられます。\n", "\n", "|q_A|$\\Omega$(A)|q_B|$\\Omega$(B)|$\\Omega$(total)|\n", "|-|-|-|-|-|\n", "|0|1|2|6|6|\n", "|1|3|1|3|9|\n", "|2|6|0|1|6|\n", "\n", "この $\\Omega(total)$ を $q_A$ に対してプロットすると以下のようになります。" ] }, { "cell_type": "code", "execution_count": 22, "id": "6b6608f6", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$\\\\Omega(total)$')" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "qa = [0, 1, 2]\n", "omega = [6, 9, 6]\n", "\n", "plt.plot(qa, omega, '.r')\n", "plt.xlabel('$q_A$')\n", "plt.ylabel('$\\Omega(total)$')" ] }, { "cell_type": "markdown", "id": "2c32963c", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "任意の$N_A$、$N_B$、$q_\\text{total}$について、$\\Omega(\\text{total})$ を $q_A$ の関数として計算するコードを書いてください。 \n", "\n", "次に以下の2つの場合のグラフを作成し、$N$ が増加したときの傾向を調べてください。\n", "\n", "1, $N_A$=300、$N_B$=200、および $q_\\text{total}$=100\n", "\n", "2, $N_A$=3000、$N_B$=2000、および $q_\\text{total}$=100\n", " " ] }, { "cell_type": "code", "execution_count": 10, "id": "d642bd7c", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Plot_Omega(3000,2000,100)" ] }, { "cell_type": "code", "execution_count": 16, "id": "4e1ad18a", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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