diff --git a/Final/Final - Tight-binding propagation method.ipynb b/Final/Final - Tight-binding propagation method.ipynb index d454443..c612180 100644 --- a/Final/Final - Tight-binding propagation method.ipynb +++ b/Final/Final - Tight-binding propagation method.ipynb @@ -606,7 +606,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 36, "metadata": { "deletable": false, "nbgrader": { @@ -644,7 +644,7 @@ " # away from the atomic positions, which we already saw in the overlap\n", " # above. In fact, 99.7% of all probability mass is under the integral\n", " # for x radius of 3*sigma from the centers x_i.\n", - " h = 1e-6\n", + " h = 1e-5\n", " x = np.arange(positions[0] - 10*sigma, positions[-1] - 10*sigma, h)\n", " \n", " def V(x):\n", @@ -666,7 +666,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 23, "metadata": { "deletable": false, "nbgrader": { @@ -927,7 +927,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 31, "metadata": { "deletable": false, "nbgrader": { @@ -944,20 +944,30 @@ }, "outputs": [], "source": [ - "def TBHamiltonian(n):\n", + "def TBHamiltonian(n, sigma=.25):\n", " \"\"\"\n", + " Generates the tight-binding hamiltonian H_tb for given chain length n,\n", + " using the approximation of constant hopping parameter\n", " \n", + " Args:\n", + " n: number of atoms in the chain\n", + " sigma: standard deviation to the Gaussian wave functions\n", + "\n", + " Returns:\n", + " Tight-binding hamiltonian H_tb.\n", " \"\"\"\n", " \n", " # TODO: Comment on the weird 20% differences in hopping parameters.\n", " \n", - " t = hopping(i, j, n)\n", - " H = np.eye(n) + np.eye(n, -1) + np.eye(n, 1)" + " t = hopping(i, j, n, sigma)\n", + " H_tb = (np.eye(n, n, -1) + np.eye(n, n, 1))*t\n", + " \n", + " return H_tb" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 41, "metadata": { "deletable": false, "nbgrader": { @@ -972,15 +982,85 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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Xu5dGhnOBziHUJSJ1ZPnm3dz43BzW7SjkvnOO4bqTdRQRb+ImKMzsPGCLu88xs1MO4/VjgDEA2dnZtVuciNSJ1+dv5M6pC2iWmc4L1x2vs5riVNwEBfAV4HwzOwfIBFoAjwJZZpYeOaroAmyo7MXuPhYYC5CTk+P1U7KIHI7SsnJ++fZyxn60ipwjW/HE5UN0GY44Fjd9FO5+j7t3cfduwCXA++5+OfABcHFktlHAayGVKCK1YOfeEkY9PZOxH63iqhOO5IXrhysk4lw8HVFU5S5gspn9HJgHjA+5HhE5TEs3FTBm4mzyCop55OKBfCuna9glSTXEZVC4+4fAh5Hnq4BhYdYjIjX31sJN3DFlPi0apzPlhhM4tmtW2CVJNcVlUIhI8igvdx57/3N+9+7nDM7O4s9XHKempgSjoBCROrOvpIwfvDSfNxdu4qIhXXjwwv5kNkwLuyw5RAoKEakTm/OLuO7ZWSzeWMC95/Th+pN76PcRCUpBISK1bmFuPtc9O4s9RaWMuyqH049pH3ZJUgMKChGpVW8v3sztkz+lddMMXr7pRPp0aBF2SVJDCgoRqRXBRf1W839vLWVQlyzGXnUc7Zqr0zoZKChEpMZKy8r56euLeW76Os4d0JFff3uQOq2TiIJCRGpkT3Ept74wlw+Wb+XGrx3FnWf2pkEDdVonEwWFiBy2vIIirnl6FsvzdvOLbw7g0mG6IGcyUlCIyGH5LG831zw9i52FJYwblcOpvduFXZLUEQWFiByyT1ZuZ8zE2WQ2TGPKDSfQv3PLsEuSOqSgEJFD8saCjdzx4nyyj2jCM9cMpUurJmGXJHVMQSEi1fbUx6t54M0lHJfdinGjcshqkhF2SVIPFBQiclDuzkN/W8af/7GKM/u159FLBuv01xSioBCRmPaXlXP3ywt5eW4uVwzP5v7z+5Om019TioJCRKpUWFLKzc8Hv5G444xe3Hra0bqwXwpSUIhIpXYVlnDNM7OYv34X/3fhAC47Xr+RSFUKChH5ks35RVz11AzWbCvkicuHcFb/jmGXJCFSUIjIf1m1dQ9Xjp9J/r79PHPtUE48qk3YJUnIFBQi8oVFG/IZ9dRMHJh0/XAGdNEP6URBISIRM1fvYPQzs2iemc7E647nqLbNwi5J4oSCQkT4YPkWvvvcHDplNea50cfTKatx2CVJHFFQiKS4NxZs5PbJn9KnY3MmXDOMI5o1CrskiTMNwi7gADPramYfmNkSM1tsZrdFxrc2s3fM7PPIv63CrlUkWbw4ax3fmzSPwdlZvHD9cIWEVCpuggIoBb7v7n2B4cDNZtYXuBt4z917Au9FhkWkhsZ/vJq7Xl7IyT3b8uy1x9Mis2HYJUmcipugcPdN7j438nw3sBToDIwEJkRmmwBcEEqBIknC3Xnsvc954I0lnDOgA09elUPjDF23SaoWl30UZtYNGAzMANq7+6bIpM1A+ypeMwYYA5CdrV+QilQm+uJ+Fw3pwsMXDSA9LW6+L0qcirtPiJk1A14Gbnf3guhp7u6AV/Y6dx/r7jnuntO2bdt6qFQksZSXOz+Ztpg//2MVVw4/kkcuHqiQkGqJqyMKM2tIEBLPu/srkdF5ZtbR3TeZWUdgS3gViiSmsnLnrpcXMHVOLjd8tQd3n91HF/eTaoubrxMWfGrHA0vd/TdRk6YBoyLPRwGv1XdtIolsf1k5t02ex9Q5udw+oqdCQg5ZPB1RfAW4ElhoZp9Gxt0LPARMMbPRwFrg2+GUJ5J4ikvLuPWFefx9SR73nN2HG752VNglSQKKm6Bw94+Bqr7mnF6ftYgkg6L9Zdz43Bw+XL6V+8/vx6gTu4VdkiSouAkKEak9hSWlXP/sbP69cju/+OYALh2mMwHl8CkoRJLMnuJSrn16FrPX7uBXFw/iouO6hF2SJDgFhUgSKSjaz9VPzWR+bj6PXjKYbwzqFHZJkgQUFCJJIr9wP1c9NYMlmwr4w2VDOKt/h7BLkiShoBBJAjv3lnDF+Bl8nreHP15+HCP6VnoBA5HDoqAQSXDb9xRz+bgZrNq2l7FXHccpvduFXZIkGQWFSALburuYy8dNZ+32Qp4aNZSTeur+1lL7FBQiCWpLQRGXPjmdjbuKePrqoZx4tEJC6oaCQiQB5RUUcenY6WwuKOLpa4YyvMcRYZckSUxBIZJgNucHRxJbCoqYcO0whnZrHXZJkuQUFCIJorSsnJmrd3DPqwvZvqeEZ0cP47gjFRJS9xQUInFu0YZ8xn+8mveXbSF/335aNm7Is6OHMSRbt4+X+qGgEIlT+8vKeeKDlfz+/c9pkpHGiL7t+Xrf9pzcsy1NG+lPV+qPPm0icWj1tr3cNnkeC3LzOX9QJ342sh9ZTTLCLktSlIJCJM58nrebS5+cTmm584fLhnDuwI5hlyQpTkEhEkc+y9vNZU9Ox8yYeuMJHN2uWdglicTPrVBFUt1nebu5dOx0GpgxecxwhYTEDQWFSBxYvjkIibQGxqQxwzmqrUJC4oeankRCtnxz0NyU1iA4kuihkJA4oyMKkRApJCQRHFZQmFlfMzvbzHSPRZHDpJCQRHG4RxT3A82BMWY2oRbrEUkJCglJJIfbR/GOu08BptRmMVUxs7OAR4E0YJy7P1QfyxWpCwoJSTSHGxQnRnbe24Gl7v6bWqzpv5hZGvAH4AwgF5hlZtPcfUldLVOkrigkJBEdblAscvdfmVk60K82C6rEMGCFu68CMLPJwEhAQSEJRSEhiepwg+I8M9sFfOTu82uxnsp0BtZHDecCx1ecyczGAGMAsrOz67gkkUOjkJBEdtDObDOr7IjhOwQ77wvN7Mlar+owuPtYd89x95y2bduGXY7IFxQSkuiqc9bTxANPzOw6AHfPc/e3gd+7+/V1VVzEBqBr1HCXyDiRuKeQkGRQnaCwqOc3VZj2z1qspSqzgJ5m1t3MMoBLgGn1sFyRGlFISLKoTh+FRz23CtPq/Jfd7l5qZrcAbxOcHvuUuy+u6+WK1IRCQpJJdYKig5ldDczny0HhX5699rn7X4G/1seyRGpq+ebgfhIN04xJ1yskJPFVJyh+ChwHXAN0MbMlwFJgGdCm7koTSTzRITF5zAl0b9M07JJEauygQeHuY6OHI9d3GgAMBD6qo7pEEs6yzQVc9uQMhYQknUP+HYW75xL8luGt2i9HJDEt3VTA5eNmkJHWgEljhiskJKnoMuMiNbR0UwGXPTmdjLQGTFZISBJSUIjUwJKNQUhkNkxj8pjhdFNISBLSHe5EDtPijflcPm4GjSMhceQRCglJTjqiEDkMizbkc9mTM2iakc6LY05QSEhS0xGFyCF6d0ke339pPs0apTN5zHC6tm4SdkkidUpBIVJNe4tL+fmbS5g0cz19OjTnyatyFBKSEhQUIjG4O8s27+aD5Vt4cdZ61u0o5Iav9eCOM3rRKD0t7PJE6oWCQqQK//x8K3dNXcDG/CIABnRuyaTrhzO8xxEhVyZSvxQUIpX4YPkWbpg4h25HNOGXZwzklF5tadciM+yyREKhoBCp4N0ledz0/Fx6tm/Gc6OPp1XTjLBLEgmVgkIkytuLN3PLC3M5pmMLJl57PC2bNAy7JJHQ6XcUIhFvLtjEzc/PpV+nlkwcrZAQOUBBIQK89ukGbp00l8HZWUwcPYyWjRUSIgeo6UlS3tQ5udw5dT7Durdm/KihNG2kPwuRaPqLkJT2wox13PeXhZx0dBvGXplD4wz9NkKkIgWFpKxn/rWan76+hNP6tOOJy4eQ2VAhIVIZBYWkpD//YyW/eGsZZ/Zrz+8vHUJGurrrRKqioJCU4u48+t7n/O7dzzlvYEd++51jaZimkBCJRUEhKcPdefhvy/nTP1Zy8XFdePiigaQ1sLDLEol7cfFVysweMbNlZrbAzF41s6yoafeY2QozW25mZ4ZYpiSw8nLn/teX8Kd/rOSK4dn8UiEhUm1xERTAO0B/dx8IfAbcA2BmfYFLgH7AWcATZqYeRzkkZeXOXS8v4Jl/r+H6k7vzwMj+NFBIiFRbXASFu//d3Usjg9OBLpHnI4HJ7l7s7quBFcCwMGqUxLS/rJzbJs/jpTm53D6iJ/eecwxmCgmRQxEXQVHBtcBbkeedgfVR03Ij477EzMaY2Wwzm71169Y6LlESQdH+Mm6cOIc3FmzivnOO4fYRvRQSIoeh3jqzzexdoEMlk+5z99ci89wHlALPH+r7u/tYYCxATk6O16BUSQJ7iku5fsJspq/ezs8v6M8Vw48MuySRhFVvQeHuI2JNN7OrgfOA0939wI5+A9A1arYukXEiVdpVWMKop2exaEM+v/32sVwwuNKDUBGpprhoejKzs4A7gfPdvTBq0jTgEjNrZGbdgZ7AzDBqlMSwpaCIS8ZOZ+nGAv54+RCFhEgtiJffUTwONALeibQhT3f3G919sZlNAZYQNEnd7O5lIdYpcWz9jkKuGD+DrbuLeerqoZzUs03YJYkkhbgICnc/Osa0B4EH67EcSUCf5e3minEzKC4t5/nrjmdwdquwSxJJGnERFCI1MXfdTq59ZhYZaQ2YcsMJ9O7QPOySRJKKgkIS2j8+28qNE+fQrkUjJl57PNlHNAm7JJGko6CQhDVt/ka+P+VTjm7XnAnXDqVd88ywSxJJSgoKSUjP/Gs197+xhKHdWjNuVA4tMnXrUpG6oqCQhOLu/Prvn/H4Byv4et/2PHbpYN1wSKSOKSgkYZSWlfOjvyxi8qz1XDqsKw+M7E+67iUhUucUFJIQCktKufWFeby3bAu3nnY0d5yh6zaJ1BcFhcS9HXtLuPaZWSzI3cUDF/TnSl23SaReKSgkrq3bXsjVT89kw659/PGK4zizX2XXlRSRuqSgkLg1f/0uRk+Yxf4y57nrjmdot9ZhlySSkhQUEpfeW5rHLS/Mo03zDF68ZhhHtW0WdkkiKUtBIXFn4idr+Mm0xfTv3JLxo4bStnmjsEsSSWkKCokbZeXOL/66lHEfr2bEMe147NLBNMnQR1QkbPorlLiwr6SM21+cx9uL87j6xG78+Ly+pDXQ6a8i8UBBIaHbUlDEdc/OZuGGfP73vL5ce1L3sEsSkSgKCgnVko0FjJ4wi/x9+3nyyhxG9G0fdkkiUoGCQkLz7pI8vjd5Hi0bN+SlG0+gX6eWYZckIpVQUEi9c3f+9I9V/PLtZQzo3JInr8qhfQtdIlwkXikopF4V7S/j3lcW8sq8DZw3sCOPXDyIxhm6+qtIPFNQSL3JKyhizMQ5zF+/izvO6MWtpx2tC/uJJAAFhdSLeet2csPEOewpLuVPVwzhrP4dwy5JRKpJQSF17qXZ67nv1UW0b9mIZ0efSJ8OLcIuSUQOQVzd9cXMvm9mbmZtIsNmZo+Z2QozW2BmQ8KuUaqvpLScH/9lET+cuoCh3Vsx7eaTFBIiCShujijMrCvwdWBd1OizgZ6Rx/HAHyP/SpzbUlDETc/PZfbandzw1R788MzeuhudSIKKm6AAfgvcCbwWNW4k8Ky7OzDdzLLMrKO7bwqlQqmWGau2c/ML89hbXMrvLx3MNwZ1CrskEamBuAgKMxsJbHD3+RXOgukMrI8azo2MU1DEIXfnyX+u4uG/LefI1k14/rrj6d2hedhliUgN1VtQmNm7QGW3J7sPuJeg2akm7z8GGAOQnZ1dk7eSw5C/bz93Tp3P24vzOKtfBx751kCaZzYMuywRqQX1FhTuPqKy8WY2AOgOHDia6ALMNbNhwAaga9TsXSLjKnv/scBYgJycHK+9yuVgFubmc9MLc9i0q4j7zjmG607urt9HiCSR0Jue3H0h0O7AsJmtAXLcfZuZTQNuMbPJBJ3Y+eqfiB/uzsTpa/n5G0s5olkGL95wAscd2SrsskSkloUeFAfxV+AcYAVQCFwTbjlywK7CEu6cuoC/L8njlN5t+c23j6V104ywyxKROhB3QeHu3aKeO3BzeNVIZWat2cFtk+axdU8xPzr3GK79Snca6CZDIkkr7oJC4ldpWTmPvb+Cx9//nC6tmjD1xhMZ1DUr7LJEpI4pKKRa1u8o5LbJ85i7bhffHNKZ+8/vp7OaRFKEgkJicndemp3L/a8vpkED47FLB3O+fkAnklIUFFKlrbuLueeVhby7NI8TehzBI98aSJdWTcIuS0TqmYJCKvXmgk38+LVF7CkuVYe1SIpTUMh/2banmP99bRF/XbiZgV1a8qtvDaJXe12GQySVKSgECPoips3fyP2vL2FPUSk/PLM3N3y1h674KiIKCoENu/bxo1cX8sHyrRzbNYuHLxqoi/mJyBcUFCmstKycCZ+s5Td/X065w4/P68vVJ3YjTX0RIhJFQZGi5q/fxb2vLmTxxgJO6d2WB0b2p2trndEkIl+moEgxO/eW8MjflzNp5jraNmvEE5cP4ez+HXS1VxGpkoIiRZSVO5NnreORt5ezu6iUa07szu1n9KSFfl0tIgehoEgB/16xjZ+9sYRlm3czvEdr7j+/vzqrRaTaFBRJbOXWPTz01jLeWZJH56zGPH7ZYM4d0FHNTCJySBQUSWjL7iIeffdzJs9aT2Z6A354Zm9Gn9SdzIZpYZcmIglIQZFE8vftZ9w/VzH+49WUlJZz+fHZ3HpaT9o2bxR2aSKSwBQUCa6ktJw12/fyzpI8/vyPlRQUlXLugI784MzedG/TNOzyRCQJKCgSkLszaeZ6xn28irXbCykrdwBO79OOO77ei36dWoZcoYgkEwVFginaX8b/vraIKbNzGZKdxTlfO4qe7ZvRr1MLjm6nM5lEpPYpKBLI6m17uX3yPObn5nPLqUfzP2f00uU2RKTOKSjinLvzycrtPPWvNby3LI+mGen8+crjOLNfh7BLE5EUoaCIUwVF+3l17gaen7GWz/L20LppBrecejRXDj+Sdi0ywy5PRFKIgiKOuDuz1+7kpdnreX3+JvbtL2Ngl5b88qKBnH9sJ/0OQkRCETdBYWa3AjcDZcCb7n5nZPw9wOjI+O+5+9vhVVk31m7fy7RPN/LKvA2s3raXJhlpnD+oE5cPz2Zgl6ywyxORFBcXQWFmpwIjgUHuXmxm7SLj+wKXAP2ATsC7ZtbL3cvCq7Z2bNi1j78t2szr8zfy6fpdAAzr3pqbTjmKcwZ0pGmjuNg0IiLxERTAd4GH3L0YwN23RMaPBCZHxq82sxXAMOCTcMo8fO7O0k27+WD5Ft5evJkFufkA9OnQnLvP7sM3BnWic1bjkKsUEfmyeAmKXsDJZvYgUAT8wN1nAZ2B6VHz5UbGfYmZjQHGAGRnZ9dttdW0fU8x/165nX+t2MaHy7eyuaAIgEFdWnLXWX04s197erRtFnKVIiKx1VtQmNm7QGXndN4XqaM1MBwYCkwxsx6H8v7uPhYYC5CTk+M1q/bwbNi1j1mrdzB77Q5mr9nJss27AWjeKJ2Terbh1D7tOKVXW521JCIJpd6Cwt1HVDXNzL4LvOLuDsw0s3KgDbAB6Bo1a5fIuLiRv28/by7YxMtzc5mzdicAzRqlMzg7i28M6sSJRx3BgM4tSU9rEHKlIiKHJ16anv4CnAp8YGa9gAxgGzANeMHMfkPQmd0TmFkfBZWXO7uLS9lTXMqeolJ2FZawuaCIvIIiNu4qYu32vazdXsi6HYWUljs92zXjrrP68NVebejToYV+MS0iSSNeguIp4CkzWwSUAKMiRxeLzWwKsAQoBW6uyzOenvxoFc/NWMuuwv0UFO3Hq2jAatYonezWTejTsTlnD+jAmf06MKBzS90QSESSUlwEhbuXAFdUMe1B4MH6qKNt80YM6pJFVpOGZDVuSIvGDWmR2ZBmmek0z0ynQ4tMOrTMpLnuMy0iKSQugiJeXDC4MxcMrvSkKhGRlKUeVhERiUlBISIiMSkoREQkJgWFiIjEpKAQEZGYFBQiIhKTgkJERGJSUIiISEzmVV2nIoGZ2VZg7SG8pA3BtaVSTSqudyquM6TmeqfiOkPN1vtId29bcWRSBsWhMrPZ7p4Tdh31LRXXOxXXGVJzvVNxnaFu1ltNTyIiEpOCQkREYlJQBMaGXUBIUnG9U3GdITXXOxXXGepgvdVHISIiMemIQkREYlJQiIhITCkfFGZ2lpktN7MVZnZ32PXUBTPramYfmNkSM1tsZrdFxrc2s3fM7PPIv63CrrW2mVmamc0zszciw93NbEZke79oZhlh11jbzCzLzKaa2TIzW2pmJyT7tjaz/4l8theZ2SQzy0zGbW1mT5nZlshtow+Mq3TbWuCxyPovMLMhh7vclA4KM0sD/gCcDfQFLjWzvuFWVSdKge+7e19gOHBzZD3vBt5z957Ae5HhZHMbsDRq+GHgt+5+NLATGB1KVXXrUeBv7t4HGESw/km7rc2sM/A9IMfd+wNpwCUk57Z+Bjirwriqtu3ZQM/IYwzwx8NdaEoHBTAMWOHuqyL37Z4MjAy5plrn7pvcfW7k+W6CHUdngnWdEJltAnBBKAXWETPrApwLjIsMG3AaMDUySzKuc0vgq8B4CO5H7+67SPJtTXBb58Zmlg40ATaRhNva3T8CdlQYXdW2HQk864HpQJaZdTyc5aZ6UHQG1kcN50bGJS0z6wYMBmYA7d19U2TSZqB9WHXVkd8BdwLlkeEjgF3uXhoZTsbt3R3YCjwdaXIbZ2ZNSeJt7e4bgF8B6wgCIh+YQ/Jv6wOq2ra1tn9L9aBIKWbWDHgZuN3dC6KneXCedNKcK21m5wFb3H1O2LXUs3RgCPBHdx8M7KVCM1MSbutWBN+euwOdgKZ8uXkmJdTVtk31oNgAdI0a7hIZl3TMrCFBSDzv7q9ERucdOBSN/LslrPrqwFeA881sDUGT4mkEbfdZkeYJSM7tnQvkuvuMyPBUguBI5m09Aljt7lvdfT/wCsH2T/ZtfUBV27bW9m+pHhSzgJ6RsyMyCDrApoVcU62LtM2PB5a6+2+iJk0DRkWejwJeq+/a6oq73+PuXdy9G8F2fd/dLwc+AC6OzJZU6wzg7puB9WbWOzLqdGAJSbytCZqchptZk8hn/cA6J/W2jlLVtp0GXBU5+2k4kB/VRHVIUv6X2WZ2DkFbdhrwlLs/GG5Ftc/MTgL+CSzkP+319xL0U0wBsgkuy/5td6/YUZbwzOwU4Afufp6Z9SA4wmgNzAOucPfiEMurdWZ2LEEHfgawCriG4Eth0m5rM7sf+A7BGX7zgOsI2uOTalub2STgFIJLiecBPwH+QiXbNhKajxM0wxUC17j77MNabqoHhYiIxJbqTU8iInIQCgoREYlJQSEiIjEpKEREJCYFhYiIxKSgEBGRmBQUIiISk4JCpI6Z2Utm9riZfWxma83sJDObaGafmdn4sOsTOZj0g88iIjU0APjE3W8xs3sJLqdyCsFVXnPNrFGi/2JYkpuCQqQOmVkmkEVwmRgIruw5/sA1d8ysDCgJpTiRalLTk0jd6gfMdfcD19gaRHCNrQM3Vtrouo6OxDkFhUjdGgDMjxoeCCyIPB8U9VwkbikoROrWAOBT+KIZqrG774xMiw4Nkbilq8eKiEhMOqIQEZGYFBQiIhKTgkJERGJSUIiISEwKChERiUlBISIiMSkoREQkpv8HIJgnWSIMgncAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "for n in [10, 20, 40, 80, 100]:\n", - " pass\n", + " #print(\"For n = {}:\".format(n))\n", + " H_tb = TBHamiltonian(n)\n", + " E_m = QREig(H_tb + np.eye(n)) - 1\n", + " #print(\"E_m =\", E_m)\n", + " #print()\n", + " \n", + " plt.figure()\n", + " plt.plot(np.arange(len(E_m)) + 1, np.sort(E_m))\n", + " plt.title(\"Energy eigenstates of $H_{{tb}}$ for $n = {}$\".format(n))\n", + " plt.xlabel(\"$m$\")\n", + " plt.ylabel(\"$E_m$\")\n", + " plt.show()\n", "\n", "# Do your plotting here ...\n", "\n", - "# YOUR CODE HERE\n", - "raise NotImplementedError()\n", "\n", "# Yann had a plot with a couple of logisticly looking rising lines,\n", "# starting at the same x point, but some higher starting y value,\n",