{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The relativistic Duffin–Kemmer–Petiau sextic oscillator\n", "F Yasuk, M Karakoc and I Boztosun, Physica Scripta, Volume 78, 045010, 2008. \n", "https://iopscience.iop.org/article/10.1088/0031-8949/78/04/045010/meta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import AIM library " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T08:44:48.243140Z", "start_time": "2019-02-07T08:44:47.914289Z" } }, "outputs": [], "source": [ "# Python program to use AIM tools\n", "from asymptotic import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Definitions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Variables" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T08:44:49.045743Z", "start_time": "2019-02-07T08:44:48.245907Z" } }, "outputs": [], "source": [ "# variables, l0, and s0\n", "En, m, hbar, c, J, r, r0 = se.symbols(\"En, m, hbar, c, J, r, r0\")\n", "w, q = se.symbols('w, q')\n", "beta1, beta2, A0, A1, A2, A3, A4 = se.symbols(\"beta1, beta2, A0, A1, A2, A3, A4\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $\\lambda_0$ and $s_0$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T08:44:49.145804Z", "start_time": "2019-02-07T08:44:49.049722Z" } }, "outputs": [], "source": [ "l0 = 2*beta1 + 4*beta2*r - 2/r\n", "s00 = -beta1**2 + 6*beta2 + 2*beta1/r - 4*beta1*beta2*r - 4*beta1**2*r**2\n", "s01 = -(En**2 + A0 - A1/r**2 - A2*r**2 + A3*r**4 - A4*r**6)/(hbar**2*c**2)\n", "s0 = s00 + s01" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Case: q = $\\omega$ = 0.1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### s states" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Numerical values for variables¶" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T08:44:49.243255Z", "start_time": "2019-02-07T08:44:49.149910Z" } }, "outputs": [], "source": [ "nhbar, nm, nc = o* 1, o* 1, o* 1\n", "\n", "nJ = o* 0\n", "nq, nw = o* 1/10, o* 1/10\n", "\n", "nbeta1, nbeta2 = o* 2, o* 2\n", "nr0 = -o* (nbeta1 - se.sqrt(nbeta1**2 + 8*nbeta2))/(4*nbeta2)\n", "\n", "nA0 = nm*nc**2*(3*nhbar*nw-nm*nc**2)\n", "nA1 = nhbar**2*nc**2*nJ*(nJ+1)\n", "nA2 = nc**2*(nm**2*nw**2+5*nhbar*nq)\n", "nA3 = 2*nm*nc**2*nq*nw\n", "nA4 = nq**2*nc**2\n", "\n", "# parameters of lambda_0 (pl0) and s_0 (ps0)\n", "pl0 = {beta1:nbeta1, beta2:nbeta2}\n", "ps0 = {beta1:nbeta1, beta2:nbeta2, r0:nr0, A0:nA0, A1:nA1, A2:nA2, A3:nA3, A4:nA4, hbar:nhbar, c:nc}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Initialize AIM solver" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T08:44:49.802846Z", "start_time": "2019-02-07T08:44:49.245280Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\text{Values of the parameters of } \\lambda_0:$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\beta_{1} = 2,~~\\beta_{2} = 2$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\text{Values of the parameters of } s_0:$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle A_{0} = -7/10,~~A_{1} = 0,~~A_{2} = 51/100,~~A_{3} = 1/50,~~A_{4} = 1/100,~~\\beta_{1} = 2,~~\\beta_{2} = 2,~~\\hbar = 1,~~c = 1,~~r_{0} = (-1/8)*(2 - sqrt(20))$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \n", " \\begin{align}\n", " \\lambda_0 &= \\left[8 r + 4 - \\frac{2}{r} \\right.\\\\ \n", " s_0 &= \\left[- En^{2} + 0.01 r^{6} - 0.02 r^{4} - 15.49 r^{2} - 16.0 r + 8.7 + \\frac{4.0}{r} \\right.\n", " \\end{align}\n", " $" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 299 ms, sys: 8.52 ms, total: 308 ms\n", "Wall time: 309 ms\n" ] } ], "source": [ "%%time\n", "# pass lambda_0, s_0 and variable values to aim class\n", "sexticOsc_J0 = aim(l0, s0, pl0, ps0)\n", "sexticOsc_J0.display_parameters()\n", "sexticOsc_J0.display_l0s0(2)\n", "sexticOsc_J0.parameters(En, r, nr0, nmax=201, nstep=10, dprec=500, tol=1e-101)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Calculation of Taylor series coefficients of λ0λ0 and s0s0 " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T08:48:32.614149Z", "start_time": "2019-02-07T08:44:49.809594Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 3min 13s, sys: 624 ms, total: 3min 13s\n", "Wall time: 3min 13s\n" ] } ], "source": [ "%%time\n", "# create coefficients for improved AIM\n", "sexticOsc_J0.c0()\n", "sexticOsc_J0.d0()\n", "sexticOsc_J0.cndn()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The solution" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T08:48:56.164854Z", "start_time": "2019-02-07T08:48:32.617984Z" }, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0001 3.36445725728443535\n", "0011 2.06224866748193186 3.71453601866614535\n", "0021 1.79773849991486153 2.95853552211924131 4.21129759560483331 5.54649535945588575\n", "0031 1.73438805878535504 2.68502761908710836 3.66764104203528586 4.70180770713959515\n", "0041 1.72427025965769588 2.60822476751384039 3.44645622846246563 4.29618250218738717\n", "0051 1.72357609738502431 2.59874453628846712 3.39721350565403320 4.15416305172843344\n", "0061 1.72356698735998023 2.59852833595200994 3.39495720783361346 4.14052146658052801\n", "0071 1.72356712662823824 2.59853205012559990 3.39500303047643314 4.14086311173335481\n", "0081 1.72356712428290494 2.59853197531069727 3.39500187424648369 4.14085177697641391\n", "0091 1.72356712431358431 2.59853197665893558 3.39500190340645597 4.14085218844201362\n", "0101 1.72356712431425220 2.59853197667054612 3.39500190331404967 4.14085218204871021\n", "0111 1.72356712431419405 2.59853197666834400 3.39500190327169256 4.14085218152151186\n", "0121 1.72356712431419431 2.59853197666837365 3.39500190327286154 4.14085218154933829\n", "0131 1.72356712431419441 2.59853197666837798 3.39500190327295278 4.14085218155059375\n", "0141 1.72356712431419441 2.59853197666837795 3.39500190327295062 4.14085218155052230\n", "0151 1.72356712431419441 2.59853197666837794 3.39500190327295025 4.14085218155051528\n", "0161 1.72356712431419441 2.59853197666837794 3.39500190327295024 4.14085218155051524\n", "0171 1.72356712431419441 2.59853197666837794 3.39500190327295024 4.14085218155051527\n", "0181 1.72356712431419441 2.59853197666837794 3.39500190327295024 4.14085218155051527\n", "0191 1.72356712431419441 2.59853197666837794 3.39500190327295024 4.14085218155051527\n", "0201 1.72356712431419441 2.59853197666837794 3.39500190327295024 4.14085218155051527\n", "CPU times: user 24.8 s, sys: 72.6 ms, total: 24.9 s\n", "Wall time: 24.7 s\n" ] } ], "source": [ "%%time\n", "sexticOsc_J0.get_arb_roots(showRoots='+r', printFormat=\"{:25.17f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### p states" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T08:52:57.888474Z", "start_time": "2019-02-07T08:48:56.169684Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\text{Values of the parameters of } \\lambda_0:$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\beta_{1} = 2,~~\\beta_{2} = 2$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\text{Values of the parameters of } s_0:$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle A_{0} = -7/10,~~A_{1} = 2,~~A_{2} = 51/100,~~A_{3} = 1/50,~~A_{4} = 1/100,~~\\beta_{1} = 2,~~\\beta_{2} = 2,~~\\hbar = 1,~~c = 1,~~r_{0} = (-1/8)*(2 - sqrt(20))$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \n", " \\begin{align}\n", " \\lambda_0 &= \\left[8 r + 4 - \\frac{2}{r} \\right.\\\\ \n", " s_0 &= \\left[- En^{2} + 0.01 r^{6} - 0.02 r^{4} - 15.49 r^{2} - 16.0 r + 8.7 + \\frac{4.0}{r} + \\frac{2.0}{r^{2}} \\right.\n", " \\end{align}\n", " $" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "0001 4.82187291925769935\n", "0011 2.77436290277683605 4.51757239251514998\n", "0021 2.31776026114239723 3.53387962016352688 4.82832238391099067 6.24051437733093774\n", "0031 2.18609163892967229 3.14346458552742025 4.15525665322138078 5.21421277084299846\n", "0041 2.15929167601387908 3.01161948774625525 3.85209730709065412 4.71827906112208084\n", "0051 2.15696391699341434 2.99030773430463900 3.76752637998941861 4.51621778785434398\n", "0061 2.15692574507381821 2.98965068332447030 3.76206600925062292 4.48938346167429866\n", "0071 2.15692635440678831 2.98966274907362220 3.76218736811237571 4.49012058102627214\n", "0081 2.15692634335014822 2.98966248118758365 3.76218391425178413 4.49009220361544042\n", "0091 2.15692634351752849 2.98966248682243458 3.76218401715307969 4.49009345238929151\n", "0101 2.15692634352009137 2.98966248683912324 3.76218401624244177 4.49009342433839500\n", "0111 2.15692634351979751 2.98966248683045813 3.76218401610122617 4.49009342288485385\n", "0121 2.15692634351979992 2.98966248683062559 3.76218401610652583 4.49009342299305611\n", "0131 2.15692634351980047 2.98966248683064331 3.76218401610684465 4.49009342299665589\n", "0141 2.15692634351980047 2.98966248683064307 3.76218401610683300 4.49009342299633993\n", "0151 2.15692634351980047 2.98966248683064301 3.76218401610683151 4.49009342299631502\n", "0161 2.15692634351980047 2.98966248683064301 3.76218401610683149 4.49009342299631515\n", "0171 2.15692634351980047 2.98966248683064301 3.76218401610683149 4.49009342299631529\n", "0181 2.15692634351980047 2.98966248683064301 3.76218401610683149 4.49009342299631531\n", "0191 2.15692634351980047 2.98966248683064301 3.76218401610683149 4.49009342299631531\n", "0201 2.15692634351980047 2.98966248683064301 3.76218401610683149 4.49009342299631531\n", "CPU times: user 3min 34s, sys: 616 ms, total: 3min 35s\n", "Wall time: 3min 35s\n" ] } ], "source": [ "%%time\n", "nJ = o* 1\n", "nA1 = nhbar**2*nc**2*nJ*(nJ+1)\n", "\n", "# parameters of lambda_0 (pl0) and s_0 (ps0)\n", "pl0 = {beta1:nbeta1, beta2:nbeta2}\n", "ps0 = {beta1:nbeta1, beta2:nbeta2, r0:nr0, A0:nA0, A1:nA1, A2:nA2, A3:nA3, A4:nA4, hbar:nhbar, c:nc}\n", "\n", "# pass lambda_0, s_0 and variable values to aim class\n", "sexticOsc_J1 = aim(l0, s0, pl0, ps0)\n", "sexticOsc_J1.display_parameters()\n", "sexticOsc_J1.display_l0s0(2)\n", "sexticOsc_J1.parameters(En, r, nr0, nmax=201, nstep=10, dprec=500, tol=1e-101)\n", "\n", "# create coefficients for improved AIM\n", "sexticOsc_J1.c0()\n", "sexticOsc_J1.d0()\n", "sexticOsc_J1.cndn()\n", "\n", "# the solution\n", "sexticOsc_J1.get_arb_roots(showRoots='+r', printFormat=\"{:25.17f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### d states" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T08:56:57.802494Z", "start_time": "2019-02-07T08:52:57.892280Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\text{Values of the parameters of } \\lambda_0:$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\beta_{1} = 2,~~\\beta_{2} = 2$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\text{Values of the parameters of } s_0:$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle A_{0} = -7/10,~~A_{1} = 6,~~A_{2} = 51/100,~~A_{3} = 1/50,~~A_{4} = 1/100,~~\\beta_{1} = 2,~~\\beta_{2} = 2,~~\\hbar = 1,~~c = 1,~~r_{0} = (-1/8)*(2 - sqrt(20))$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \n", " \\begin{align}\n", " \\lambda_0 &= \\left[8 r + 4 - \\frac{2}{r} \\right.\\\\ \n", " s_0 &= \\left[- En^{2} + 0.01 r^{6} - 0.02 r^{4} - 15.49 r^{2} - 16.0 r + 8.7 + \\frac{4.0}{r} + \\frac{6.0}{r^{2}} \\right.\n", " \\end{align}\n", " $" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "0001 6.71796084610507275\n", "0011 3.46876391454353238 5.29952520154266871\n", "0021 2.81569356954559334 4.09612757090051198 5.43289869872423591 7.06102335434582362\n", "0031 2.60425013001630686 3.59134722913684855 4.63454617543588826 5.71857232137262456\n", "0041 2.55238230915766284 3.39727882131377914 4.25001824758429294 5.13562634414079308\n", "0051 2.54677288983622212 3.35778858029083239 4.12196893224062712 4.86998485495169561\n", "0061 2.54665755663931973 3.35615070252050024 4.11062667466230666 4.82326398291710868\n", "0071 2.54665948021553734 3.35618288535783258 4.11090129123394419 4.82462842675151302\n", "0081 2.54665944256855839 3.35618209675222476 4.11089245340522475 4.82456698944013368\n", "0091 2.54665944322262613 3.35618211600644651 4.11089276443508312 4.82457030718275413\n", "0101 2.54665944322897081 3.35618211596221919 4.11089275987701934 4.82457020670488945\n", "0111 2.54665944322789604 3.35618211593420368 4.11089275947750660 4.82457020339416883\n", "0121 2.54665944322790947 3.35618211593494049 4.11089275949773220 4.82457020376092585\n", "0131 2.54665944322791156 3.35618211593500017 4.11089275949867385 4.82457020376923346\n", "0141 2.54665944322791155 3.35618211593499885 4.11089275949862284 4.82457020376802745\n", "0151 2.54665944322791154 3.35618211593499861 4.11089275949861770 4.82457020376795044\n", "0161 2.54665944322791154 3.35618211593499860 4.11089275949861766 4.82457020376795204\n", "0171 2.54665944322791154 3.35618211593499860 4.11089275949861769 4.82457020376795258\n", "0181 2.54665944322791154 3.35618211593499860 4.11089275949861769 4.82457020376795262\n", "0191 2.54665944322791154 3.35618211593499860 4.11089275949861769 4.82457020376795262\n", "0201 2.54665944322791154 3.35618211593499860 4.11089275949861769 4.82457020376795262\n", "CPU times: user 3min 36s, sys: 600 ms, total: 3min 36s\n", "Wall time: 3min 36s\n" ] } ], "source": [ "%%time\n", "nJ = o* 2\n", "nA1 = nhbar**2*nc**2*nJ*(nJ+1)\n", "\n", "# parameters of lambda_0 (pl0) and s_0 (ps0)\n", "pl0 = {beta1:nbeta1, beta2:nbeta2}\n", "ps0 = {beta1:nbeta1, beta2:nbeta2, r0:nr0, A0:nA0, A1:nA1, A2:nA2, A3:nA3, A4:nA4, hbar:nhbar, c:nc}\n", "\n", "# pass lambda_0, s_0 and variable values to aim class\n", "sexticOsc_J2 = aim(l0, s0, pl0, ps0)\n", "sexticOsc_J2.display_parameters()\n", "sexticOsc_J2.display_l0s0(2)\n", "sexticOsc_J2.parameters(En, r, nr0, nmax=201, nstep=10, dprec=500, tol=1e-101)\n", "\n", "# create coefficients for improved AIM\n", "sexticOsc_J2.c0()\n", "sexticOsc_J2.d0()\n", "sexticOsc_J2.cndn()\n", "\n", "# the solution\n", "sexticOsc_J2.get_arb_roots(showRoots='+r', printFormat=\"{:25.17f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### f states" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2019-02-07T09:00:58.436906Z", "start_time": "2019-02-07T08:56:57.806334Z" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\text{Values of the parameters of } \\lambda_0:$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\beta_{1} = 2,~~\\beta_{2} = 2$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\text{Values of the parameters of } s_0:$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle A_{0} = -7/10,~~A_{1} = 12,~~A_{2} = 51/100,~~A_{3} = 1/50,~~A_{4} = 1/100,~~\\beta_{1} = 2,~~\\beta_{2} = 2,~~\\hbar = 1,~~c = 1,~~r_{0} = (-1/8)*(2 - sqrt(20))$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \n", " \\begin{align}\n", " \\lambda_0 &= \\left[8 r + 4 - \\frac{2}{r} \\right.\\\\ \n", " s_0 &= \\left[- En^{2} + 0.01 r^{6} - 0.02 r^{4} - 15.49 r^{2} - 16.0 r + 8.7 + \\frac{4.0}{r} + \\frac{12.0}{r^{2}} \\right.\n", " \\end{align}\n", " $" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "0001 8.77525795921239121\n", "0011 4.15929959993047792 6.07848575023158345\n", "0021 3.30463604821916714 4.65002182978383676 6.02988975486865881\n", "0031 3.00635414470137319 4.03218572313430491 5.10759026270516701 6.21709867002266860\n", "0041 2.92172472116760770 3.77170763260858999 4.64288107816498526 5.54929888680002931\n", "0051 2.91054412552470313 3.70740177946627438 4.46519632461924794 5.21873246962450026\n", "0061 2.91025538772731920 3.70385381768827230 4.44424799488364677 5.14475518696186483\n", "0071 2.91026042038319194 3.70392834021144135 4.44479401778934940 5.14693047601440175\n", "0081 2.91026031403008912 3.70392632226785393 4.44477407754451303 5.14681450023362899\n", "0091 2.91026031613854039 3.70392637928431049 4.44477490974680271 5.14682236718064835\n", "0101 2.91026031614830746 3.70392637886211645 4.44477489239945666 5.14682205633173198\n", "0111 2.91026031614504222 3.70392637878365096 4.44477489142071161 5.14682205043574196\n", "0121 2.91026031614509916 3.70392637878638569 4.44477489148839600 5.14682205154605937\n", "0131 2.91026031614510571 3.70392637878655962 4.44477489149078389 5.14682205155980257\n", "0141 2.91026031614510564 3.70392637878655383 4.44477489149059150 5.14682205155571029\n", "0151 2.91026031614510562 3.70392637878655305 4.44477489149057576 5.14682205155550072\n", "0161 2.91026031614510562 3.70392637878655303 4.44477489149057580 5.14682205155550964\n", "0171 2.91026031614510562 3.70392637878655304 4.44477489149057589 5.14682205155551152\n", "0181 2.91026031614510562 3.70392637878655304 4.44477489149057590 5.14682205155551164\n", "0191 2.91026031614510562 3.70392637878655304 4.44477489149057590 5.14682205155551163\n", "0201 2.91026031614510562 3.70392637878655304 4.44477489149057590 5.14682205155551163\n", "CPU times: user 3min 33s, sys: 660 ms, total: 3min 34s\n", "Wall time: 3min 34s\n" ] } ], "source": [ "%%time\n", "nJ = o* 3\n", "nA1 = nhbar**2*nc**2*nJ*(nJ+1)\n", "\n", "# parameters of lambda_0 (pl0) and s_0 (ps0)\n", "pl0 = {beta1:nbeta1, beta2:nbeta2}\n", "ps0 = {beta1:nbeta1, beta2:nbeta2, r0:nr0, A0:nA0, A1:nA1, A2:nA2, A3:nA3, A4:nA4, hbar:nhbar, c:nc}\n", "\n", "# pass lambda_0, s_0 and variable values to aim class\n", "sexticOsc_J3 = aim(l0, s0, pl0, ps0)\n", "sexticOsc_J3.display_parameters()\n", "sexticOsc_J3.display_l0s0(2)\n", "sexticOsc_J3.parameters(En, r, nr0, nmax=201, nstep=10, dprec=500, tol=1e-101)\n", "\n", "# create coefficients for improved AIM\n", "sexticOsc_J3.c0()\n", "sexticOsc_J3.d0()\n", "sexticOsc_J3.cndn()\n", "\n", "# the solution\n", "sexticOsc_J3.get_arb_roots(showRoots='+r', printFormat=\"{:25.17f}\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.9" }, "toc": { "base_numbering": 1, "collapse_to_match_collapsible_headings": false, "colors": { "hover_highlight": "#DAA520", "running_highlight": "#FF0000", "selected_highlight": "#FFD700" }, "moveMenuLeft": true, "nav_menu": { "height": "12px", "width": "252px" }, "navigate_menu": true, "number_sections": true, "sideBar": true, "skip_h1_title": false, "threshold": "5", "title_cell": "İçindekiler", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "785px", "left": "0px", "right": "1708px", "top": "158px", "width": "158px" }, "toc_section_display": "block", "toc_window_display": true }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }