340 lines
61 KiB
Plaintext
340 lines
61 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": true,
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"ExecuteTime": {
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"end_time": "2023-07-25T12:34:53.272379700Z",
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"start_time": "2023-07-25T12:34:52.798126900Z"
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 54,
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"outputs": [],
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"source": [
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"def find_fwhm(f_x, x):\n",
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" ind = 0\n",
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" for i in range(0, len(f_x)):\n",
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" if f_x[i] > np.max(f_x)/2 and ind ==0:\n",
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" a = i\n",
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" ind = 1\n",
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"\n",
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" if f_x[i] < np.max(f_x)/2 and ind ==1:\n",
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" b = i\n",
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" break\n",
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" return x[b] - x[a]\n",
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"\n",
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"\n",
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"def gaussian(x, x0, sigma, A):\n",
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" return A * np.exp(-0.5 * (x-x0)**2 / sigma**2)\n",
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"\n",
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"def thermal(x, x0, amp, sigma):\n",
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" order = 15\n",
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" res = np.exp(-0.5 * (x-x0)**2 / sigma**2)\n",
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" return amp/1.6 * polylog(2, res)\n",
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"\n",
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"def Thomas_Fermi_1d(x, x0, amp, sigma):\n",
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" res = (1-(( x - x0 ) / sigma) **2) **(3/2)\n",
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" return amp * np.where(res > 0, res, 0)\n",
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"\n",
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"def density_1d(x, x0_bec, x0_th, amp_bec, amp_th, sigma_bec, sigma_th):\n",
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" return thermal(x, x0_th, amp_th, sigma_th) + Thomas_Fermi_1d(x, x0_bec, amp_bec, sigma_bec)\n",
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"\n",
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"\n",
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"def polylog(pow, x):\n",
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" order = 500\n",
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" sum = 0\n",
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" for k in range(1,order):\n",
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" sum += x ** k /k **pow\n",
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" return sum\n",
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"\n",
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"def ThomasFermi_2d(x, y=0.0, centerx=0.0, centery=0.0, amplitude=1.0, sigmax=1.0, sigmay=1.0):\n",
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" res = (1- ((x-centerx)/sigmax)**2 - ((y-centery)/sigmay)**2)**(3 / 2)\n",
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" return amplitude * np.where(res > 0, res, 0)\n",
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" # return amplitude * 5 / 2 / np.pi / max(tiny, sigmax * sigmay) * np.where(res > 0, res, 0)\n",
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"\n",
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"def polylog2_2d(x, y=0.0, centerx=0.0, centery=0.0, amplitude=1.0, sigmax=1.0, sigmay=1.0):\n",
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" ## Approximation of the polylog function with 2D gaussian as argument. -> discribes the thermal part of the cloud\n",
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" return amplitude/1.643 * polylog(2, np.exp( -((x-centerx)**2/(2 * (sigmax)**2))-((y-centery)**2/( 2 * (sigmay)**2)) ))\n",
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" # return amplitude / 2 / np.pi / 1.20206 / max(tiny, sigmax * sigmay) * polylog(2, np.exp( -((x-centerx)**2/(2 * (sigmax)**2))-((y-centery)**2/( 2 * (sigmay)**2)) ))\n",
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"\n",
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"\n",
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"def density_profile_BEC_2d(x, y=0.0, amp_bec=1.0, amp_th=1.0, x0_bec=0.0, y0_bec=0.0, x0_th=0.0, y0_th=0.0,\n",
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" sigmax_bec=1.0, sigmay_bec=1.0, sigmax_th=1.0, sigmay_th=1.0):\n",
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" return ThomasFermi_2d(x=x, y=y, centerx=x0_bec, centery=y0_bec,\n",
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" amplitude=amp_bec, sigmax=sigmax_bec, sigmay=sigmay_bec\n",
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" ) + polylog2_2d(x=x, y=y, centerx=x0_th, centery=y0_th,\n",
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" amplitude=amp_th, sigmax=sigmax_th, sigmay=sigmay_th)\n",
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"\n"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2023-07-25T13:13:41.713691200Z",
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"start_time": "2023-07-25T13:13:41.678934700Z"
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}
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}
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},
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{
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"cell_type": "code",
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"execution_count": 55,
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"C:\\Users\\Jianshun Gao\\AppData\\Local\\Temp\\ipykernel_13296\\3599946220.py:38: RuntimeWarning: invalid value encountered in power\n",
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" res = (1- ((x-centerx)/sigmax)**2 - ((y-centery)/sigmay)**2)**(3 / 2)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"FWHM TF = 1.2161216121612153\n",
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"FWHM Thermal = 1.8241824182418238\n"
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]
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},
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{
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"data": {
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"text/plain": "<Figure size 640x480 with 1 Axes>",
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"image/png": "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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"x = np.linspace(-10, 10, 10000)\n",
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"\n",
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"TF = ThomasFermi_2d(x, y=0, centerx=0, centery=0, amplitude=1, sigmax=1,sigmay=1)\n",
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"th = polylog2_2d(x, sigmax=1)\n",
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"\n",
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"print(f'FWHM TF = {find_fwhm(TF, x)}')\n",
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"print(f'FWHM Thermal = {find_fwhm(th, x)}')\n",
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"\n",
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"plt.plot(x, TF)\n",
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"plt.plot(x, th)\n",
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"plt.show()"
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],
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"metadata": {
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"collapsed": false,
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"ExecuteTime": {
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"end_time": "2023-07-25T13:13:46.864959500Z",
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"start_time": "2023-07-25T13:13:46.226243500Z"
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}
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}
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},
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{
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"cell_type": "code",
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"execution_count": 57,
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"C:\\Users\\Jianshun Gao\\AppData\\Local\\Temp\\ipykernel_13296\\3599946220.py:23: RuntimeWarning: invalid value encountered in power\n",
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" res = (1-(( x - x0 ) / sigma) **2) **(3/2)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"FWHM TF = 1.2161216121612153\n",
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"FWHM Thermal = 1.8241824182418238\n"
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]
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},
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{
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"data": {
|
||
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"text/plain": "<Figure size 640x480 with 1 Axes>",
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|
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"image/png": "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
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"x = np.linspace(-10, 10, 10000)\n",
|
||
|
|
"\n",
|
||
|
|
"TF = Thomas_Fermi_1d(x, x0=0, amp=1, sigma=1)\n",
|
||
|
|
"th = thermal(x, x0=0, amp=1, sigma=1)\n",
|
||
|
|
"\n",
|
||
|
|
"print(f'FWHM TF = {find_fwhm(TF, x)}')\n",
|
||
|
|
"print(f'FWHM Thermal = {find_fwhm(th, x)}')\n",
|
||
|
|
"\n",
|
||
|
|
"plt.plot(x, TF, label='Thomas Fermi')\n",
|
||
|
|
"plt.plot(x, th)\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.show()"
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false,
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2023-07-25T13:13:56.638668600Z",
|
||
|
|
"start_time": "2023-07-25T13:13:55.916676900Z"
|
||
|
|
}
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 42,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": "1.6110390064904865"
|
||
|
|
},
|
||
|
|
"execution_count": 42,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"thermal(0, x0=0, amp=1, sigma=1)"
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false,
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2023-07-25T13:02:21.123800100Z",
|
||
|
|
"start_time": "2023-07-25T13:02:21.081333500Z"
|
||
|
|
}
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 34,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"0.5\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"print(1**3/2)"
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false,
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2023-07-25T12:58:17.116863300Z",
|
||
|
|
"start_time": "2023-07-25T12:58:17.096107400Z"
|
||
|
|
}
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 43,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": "1.0"
|
||
|
|
},
|
||
|
|
"execution_count": 43,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"x0 = 0\n",
|
||
|
|
"sigma = 1\n",
|
||
|
|
"\n",
|
||
|
|
"np.exp(-0.5 * (0-x0)**2 / sigma**2)"
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false,
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2023-07-25T13:03:00.095225200Z",
|
||
|
|
"start_time": "2023-07-25T13:03:00.053138800Z"
|
||
|
|
}
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 53,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"1.642932065514894\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"print(polylog(2,1))"
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false,
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2023-07-25T13:06:46.781843300Z",
|
||
|
|
"start_time": "2023-07-25T13:06:46.758628100Z"
|
||
|
|
}
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 59,
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"1.2166174009154453\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"print(np.sqrt(1-4**(-1/3))*2)"
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false,
|
||
|
|
"ExecuteTime": {
|
||
|
|
"end_time": "2023-07-25T13:23:29.360679300Z",
|
||
|
|
"start_time": "2023-07-25T13:23:29.311184700Z"
|
||
|
|
}
|
||
|
|
}
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"outputs": [],
|
||
|
|
"source": [],
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false
|
||
|
|
}
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 2
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython2",
|
||
|
|
"version": "2.7.6"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 0
|
||
|
|
}
|