600 lines
75 KiB
Plaintext
600 lines
75 KiB
Plaintext
|
{
|
|||
|
|
"cells": [
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 1,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"import sympy\n",
|
|||
|
|
"sympy.init_printing()"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 2,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"a, b, c, d = sympy.symbols(\"a b c d\")\n",
|
|||
|
|
"i = sympy.I"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 3,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"X = sympy.Matrix([[0, 1], [1, 0]])\n",
|
|||
|
|
"Z = sympy.Matrix([[1, 0], [0, -1]])\n",
|
|||
|
|
"\n",
|
|||
|
|
"M = sympy.Matrix([[a, b], [c, d]])"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 4,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡0 1⎤\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎣1 0⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 4,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"X"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 5,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡1 0 ⎤\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎣0 -1⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 5,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"Z"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 6,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}a & b\\\\c & d\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡a b⎤\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎣c d⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 6,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"M"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 7,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"term_X = M*M + i*X\n",
|
|||
|
|
"term_Z = M*M - i*Z"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 8,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}a^{2} + b c & a b + b d + i\\\\a c + c d + i & b c + d^{2}\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡ 2 ⎤\n",
|
|||
|
|
"⎢ a + b⋅c a⋅b + b⋅d + ⅈ⎥\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎢ 2 ⎥\n",
|
|||
|
|
"⎣a⋅c + c⋅d + ⅈ b⋅c + d ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 8,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"term_X"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 9,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}a^{2} + b c - i & a b + b d\\\\a c + c d & b c + d^{2} + i\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡ 2 ⎤\n",
|
|||
|
|
"⎢a + b⋅c - ⅈ a⋅b + b⋅d ⎥\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎢ 2 ⎥\n",
|
|||
|
|
"⎣ a⋅c + c⋅d b⋅c + d + ⅈ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 9,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"term_Z"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 10,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[ \\left\\{ a : - \\frac{\\sqrt{2}}{2}, \\ b : \\frac{\\sqrt{2} i}{2}, \\ c : \\frac{\\sqrt{2} i}{2}, \\ d : - \\frac{\\sqrt{2}}{2}\\right\\}, \\ \\left\\{ a : \\frac{\\sqrt{2}}{2}, \\ b : - \\frac{\\sqrt{2} i}{2}, \\ c : - \\frac{\\sqrt{2} i}{2}, \\ d : \\frac{\\sqrt{2}}{2}\\right\\}, \\ \\left\\{ a : - \\frac{\\sqrt{2} i}{2}, \\ b : \\frac{\\sqrt{2}}{2}, \\ c : \\frac{\\sqrt{2}}{2}, \\ d : - \\frac{\\sqrt{2} i}{2}\\right\\}, \\ \\left\\{ a : \\frac{\\sqrt{2} i}{2}, \\ b : - \\frac{\\sqrt{2}}{2}, \\ c : - \\frac{\\sqrt{2}}{2}, \\ d : \\frac{\\sqrt{2} i}{2}\\right\\}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡⎧ -√2 √2⋅ⅈ √2⋅ⅈ -√2 ⎫ ⎧ √2 -√2⋅ⅈ -√2⋅ⅈ √2⎫ ⎧\n",
|
|||
|
|
"⎢⎨a: ────, b: ────, c: ────, d: ────⎬, ⎨a: ──, b: ──────, c: ──────, d: ──⎬, ⎨\n",
|
|||
|
|
"⎣⎩ 2 2 2 2 ⎭ ⎩ 2 2 2 2 ⎭ ⎩\n",
|
|||
|
|
"\n",
|
|||
|
|
" -√2⋅ⅈ √2 √2 -√2⋅ⅈ ⎫ ⎧ √2⋅ⅈ -√2 -√2 √2⋅ⅈ⎫⎤\n",
|
|||
|
|
"a: ──────, b: ──, c: ──, d: ──────⎬, ⎨a: ────, b: ────, c: ────, d: ────⎬⎥\n",
|
|||
|
|
" 2 2 2 2 ⎭ ⎩ 2 2 2 2 ⎭⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 10,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"sympy.solve(term_X)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 11,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[ \\left\\{ a : - \\sqrt{i}, \\ b : 0, \\ c : 0, \\ d : - \\sqrt{- i}\\right\\}, \\ \\left\\{ a : - \\sqrt{i}, \\ b : 0, \\ c : 0, \\ d : \\sqrt{- i}\\right\\}, \\ \\left\\{ a : \\sqrt{i}, \\ b : 0, \\ c : 0, \\ d : - \\sqrt{- i}\\right\\}, \\ \\left\\{ a : \\sqrt{i}, \\ b : 0, \\ c : 0, \\ d : \\sqrt{- i}\\right\\}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡⎧ ____⎫ ⎧ ____⎫ ⎧ \n",
|
|||
|
|
"⎢⎨a: -√ⅈ, b: 0, c: 0, d: -╲╱ -ⅈ ⎬, ⎨a: -√ⅈ, b: 0, c: 0, d: ╲╱ -ⅈ ⎬, ⎨a: √ⅈ, b:\n",
|
|||
|
|
"⎣⎩ ⎭ ⎩ ⎭ ⎩ \n",
|
|||
|
|
"\n",
|
|||
|
|
" ____⎫ ⎧ ____⎫⎤\n",
|
|||
|
|
" 0, c: 0, d: -╲╱ -ⅈ ⎬, ⎨a: √ⅈ, b: 0, c: 0, d: ╲╱ -ⅈ ⎬⎥\n",
|
|||
|
|
" ⎭ ⎩ ⎭⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 11,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"sympy.solve(term_Z)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 12,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAHkAAAA/CAYAAADE+2c4AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGKElEQVR4Ae2cgXHbOBBFrYwLyLkEXQdJrgOlg7gE2x3kJhXcJB3kWkgJuXQQp4Okg3PcgfI+A2IkmJQocgEsOcIMTACkgP1/sQsR0Hp1cXGxIX8mp+nHdrv9M208130ysFqt7pHsRYd015c7ja93yio+JPVz1TcDN4h3lYjYGG9UMlb7X/JA9Sqzc3tMCOReHXvG0/1cmODhW4qTsR7V9iy94aWOgLfIciclHspe5B0iRy1M0ZKHCFn4mWuUmy4hhUUwH+4kTEyK50hwBQ8/pkjiUsmAewuojwIWgL4LINfhegPwxhWFuvvLSEzC/T/5w1SAGzqAs63+uMjI87mVhfLHtqyr6uTvu21zKCNzcUyM+ZP8hty8QsGTGwXLit+08lCWZjc7dVmz2l60bd6vyFoFE+M2SnblroNrfo3SdtfiO4T9Sp5lGoOJz8i76p33L7i4tgBe1F0jsCzxtsv6aH9PjlZ74BlX7toaU+BBX7rksZ538TCkjc+Wd9cMqgklRT4RnjaBiutWFwjua3Z/17Nd92u0IYspJvqTEYgLraWTJjOfL6/kVgkMri24921dV5K+UPWus9wTeO3guFFwIr8ppoD17e4Yp5bpo6qSNUujNUtxAtUHgntS8Kf2PmVZ9Lqte7gijxkm+oquWljH4uOz9ZQsoUlyu401c+21Yu61FizFtlnPu7NoZDLBRD+aMPeBpz2Pd4rC6aO6kgVEQkhx0UpTEOEZzYq9nD7noY6MJpjoR5b8iaxXr9Eei882Stbmvr44yFUW3+jnVUEz/4r8kvEnbd3Rh4vkCROySMk3l5WZ+Zvx9V68CAUHLt1hqmrJlSfY4ocfbMk8qPXhC1nXoUmnLXvnm/TTfNsa2sHQ52osM61suTC1/afXsViPums6fmSwl+mAp9bHCnjqOCWfnwumZyVJOY9Vh4GjllxKrLAsvAvj6d1YaXbnxr/F3v9bG5sbJUOLXvp14tQkiNGGh7YKl/CL0arYPLnrWxS7+a3i5q8OMta0abNk7qkqNk9KnvW58ZFZWBWbG3eNq/43IUrE6Af+e69iyTOzqNbG5smSo8KCi9Y+8ORXt9ipk0INbO6UDAlr9KH1WPvZekdfTKqFzY27liZbElBu8xuvMOsfqc9+b7smNjeWHEjQa9M/Um5QsNbl2cdk1cbm5oACInQs9mR/HCsufgSKHKapFrYwbvWjxkgmyvwjVhZWqI2t+JrM7Dp6GrUE67WYp1ZcFV2TEXpxkYoWyuzqw5Kr0pZ8UlSfwANW6/TkyL4uIp23ncxVH55iSkZZYyMVdTJlEtnXR4K39glc9ULZcIdlMG/AG2PE31VTXkSkYi7OrLiin+bXmlzzRzUyRpWovlxKyNmvJVf01Sg5u7sOa+rJkYp8Th5Gx4xmkX305TqN5WoIqMnumkG032waqUh/2r/Wly69crmLlhhrzWAx56pPFsaycdd0pEliGqkYiJCCdRI1KbKvj4Aa7WAx5+oQDsazUXI7CB2aRvWpX5KiGCdF9rXyebrm4KoLH+OYK1lWF10rZVli/EadCsE9ua0YA0VZ62+M+6EcXbXupZ+fcx08plz1ccE4tkrWQCSTqL7Ql4iYHNnXR0Dtdkuu+rAwRhYlSzHqWFYZrTQVIjyjWbGXd5/jnix5cmTfbp+eymAz46oPF2M0SjY/auQ1YHGRipCVJeXmiv6l5CxHje6i+rJoyKbTIlxdTpGVmdIsxF19cE8nTqYJt1T8BwTg0LKRNeBvCldDOJmk5CEDmGq5QmdgfGTYyb8arclV0fPkCjo6DwkDkyx5KIPB5S0ymG0oB4eey81PESUDsGrA1yGCndzLyk8pd1014MuJIg+JkZWfUkquGvB1iF0n97LyU8Rd881yscFsFpMkNz+lLDlywZcMbXlqS2/ya0nsdEGFHPwUVTIA1uhjkcFsFvMsFz9F3LUIaAHgmhYXzGap4Bz8FLHkoOBFBrMZKjgbP+anUF2gUbJOQ7QHvJeYtcX3ovcEcFLJxU/oN8sp1BPqUOZig9megB3RkJuf6K7R+jbJOhc+p5kwgO7uE/3phLDxnnKXKrzqwPLADJv9P2XpwLXIJhSsV9OrDnBffwEnjy+5Ug1d0wAAAABJRU5ErkJggg==\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡-√2 √2⋅ⅈ⎤\n",
|
|||
|
|
"⎢──── ────⎥\n",
|
|||
|
|
"⎢ 2 2 ⎥\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎢√2⋅ⅈ -√2 ⎥\n",
|
|||
|
|
"⎢──── ────⎥\n",
|
|||
|
|
"⎣ 2 2 ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 12,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"sqrt_miX = sympy.Matrix([[-sympy.sqrt(2)/2, i*sympy.sqrt(2)/2], [i*sympy.sqrt(2)/2, -sympy.sqrt(2)/2]])\n",
|
|||
|
|
"sqrt_miX"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 13,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}- \\sqrt{i} & 0\\\\0 & - \\sqrt{- i}\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡-√ⅈ 0 ⎤\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎢ ____⎥\n",
|
|||
|
|
"⎣ 0 -╲╱ -ⅈ ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 13,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"sqrt_iZ = sympy.Matrix([[-sympy.sqrt(i), 0], [0, -sympy.sqrt(-i)]])\n",
|
|||
|
|
"sqrt_iZ"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 14,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}0 & - i\\\\- i & 0\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡0 -ⅈ⎤\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎣-ⅈ 0 ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 14,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"sqrt_miX**2"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 15,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}i & 0\\\\0 & - i\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡ⅈ 0 ⎤\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎣0 -ⅈ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 15,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"sqrt_iZ**2"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 16,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAA/CAYAAADAInVAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAKjUlEQVR4Ae1di5HVNhTdZbaADSVABxA6WDpgJxXs0gGZVMCQDqAF0gHQAdABdBCyHWzOEZaR9XRt/SxLlj3jZ0uWdO8519f6WM86Pzs7u8L+Abu9fb+/v39sRx7hg4GDgTYYOD8//wJNnzi0vb4wIp8b5zz9YYWP4MHAwUBbDNxA3YeWyqqSHx0ftftHK0G1QTzJ7nMpB9znucpauxzgfg8ZL1xyWsLh0j8mTroPWuNCwhHDiYkd51/tMiDrjnEP7Au1h6H4LXR8SYA59trxav0G3B8kzDpdL8e5+6AlDuZwSLaei/fFPtb4vhlypAPYS5TzEAC+R5R3jXx2tySomET5QbIyJj7BLeGQ4jPqUkNREz4axjzBEUNsDPatavy/ANDZZJ0DDoCvcP3tXBrPa1HyPcvOnmwGt4RDis+u2xYFCnw0h1nAEUNpMHb2b9WoPpsPMRJL5gFRbOom1fYl9c0lq1fcEn974WMLHJD5H3i92arGl2wqxkPhXLW9KKPGC73ilmyxFz62xlG0jw+wbF3wveIz1NzXknHteOTjmMDz1No+Vr6tT6mwhFvCIcWX0ndtOS4+WsTswhHDXSp2OiN86p4/q+6Q8wY7nZiv4y5NeQg/wn5rxulzxDPflQ7HHodynPJjy0zNB52CcUs4pPhUHUvmD+WjVsyhOGI4jsGOPGzqq/G1Io4/EEGno9BvJlCEqQOd2/VAYB727ZMeSiiDDuaUn1p2bH7oE4xbwiHFx+q2Rb5QPmrFHIojhutY7MinHL/44B6aJ5w5REf+G8fJhmucYvgR1/7UFxD3FudvETeZjIB4dhn4sFja+M5/fG04J3+poLWuh+DWOkg4pHidr4VjKB+1Yg7BgbRF7mfIUYN7vA+K1PhwPsoam9k4f8I4c0ccWwNjrT+kT67ttYyhPFU+zk/k63Slj9AlCLeEQ4ovjSdVXggfOTGjLPqCs7sZgykER2T5s/7kKhM6qRq/9Kg+if0Khe5w/AP7ZEP8P4hg7cz3ktxYo4+1v4pJ+5mVn1Z0fO4I3BIOKT5euQ1yBvKREzMdiXuWLRBHjMxo7KUdn/8H+I7mxtyrOTr67dD04ey+SRM/hh0jj498I3nR0xDcEg4pviiQTMJ8+agdsy+OGNqisRfv4/ugg9N/Qzr+q+gpHH/sn/vkbTlNr7glm5XmA/LY5XqEe+5k/EnS0Se+NI45naCL6uNfzCXa8Bqfknxv343TD1z3ilu61fbCR3U4qqzxpbvgiD8YWJOBtWr8NXUOLdu7xkdCDnZ8wh4y6MF/HE365ihHDeuHKloiPXQV/6eQC7+NoxQfc9hsnWLCufjJzcccbsjiK2IOjNkbu5dnuP7SvoAwB6UXZ5vmxuHQYzFqDrvOfNT4monj2D0DcNpV+vg1EQuMqo9felS/Jg4OXQ4GumWg1sG9E4PgScWuhn6/z+m33G7QrLn7ebrP315xa2v2gH8LjM04Pm6EN3Dyse8FsthP4xTfvX8JuFfc2vd7wF8cY0tNfU7qMQdkOKvvEeI4x3nPW6+4tU17wF8cY0uOz9r+s74bOjr2ilubuAf8xTE209RHM/+dvhOGI8nioh+T14ZWmuaDveLWhiuMn+NFxceMCmNU1Dbj+PpG4HFo3vPVy1Mzfu/nveLWdl0bPxyQc9833dbGqMG11NRXOoMYjuizf895/MWfzpq40sdecWuee8BfEmNTNb4mBg6vvrSLMAf27hDe9Zz+XnHbTr9nu5e2cTM1/kAMX+G9psNzxzn7+T/0DbLHY6+4tS17wL8Fxmam7IIcTjW81DeEPqIWEOfZ6zQtH3vFrW3WA/6SGAdZN8009eHgv+mboadjr7i1jXvAvwXGZhxf3wg84qnl/KcfCGym9gcGceVbE6vveUvYbUx7sKeNaSm8tf2b6eNrIkGYuFquTlP7ccDAj4gmrfgLnGwFPW7c6Zu0J2x4iZ1vmIK3GuzfnOODZf7Xf5zMk2KAYIvlyzDBkFAs/7TE+QwtbxMuJHtK8RsCT+F+gjkBQ7QOzQzukRwYnx/p5Gw9fo1XbYjjO/1/EZf1O2lD8dkPLgzZhTRSoIsLyZ5SfCNQRzVdmMeLBU4gX/0fvzXHZ/O46dVyQXzzGHLdnz1ysTVm7fjNDO5B4blPcue6F1ctJxcGlHMFRTmP4RkehIufg1oVVGThubiIFB+dLYX7XJhTdNDAm+jjAyjf3/Oru2YT/4pEYufoePWbC0OC0mz1cJzjxVBuQlHls7q4QJzTnlJ8ea1HiVHcuzCPJYafROlgi2HtAZ+aLmdVOgwdOELqXL4I8ezHT1bLHeL4QBiX3Cqtsy0PugRhsPP7hAcZxM1Bvcnioz75S6UJ5QLpaeMTe0rxpXCYcgZMIvfDde972Czb93xJh6VykJ99fDUgvLnjQxHqQMOfODHiSPRk/TyE6WCiAZbAr3Ed+gRh0DogH5vsaiHRhSMXehjXGhzSvjLjajmHbkFcIL3TnlL81jhd3Idi1hiQr6j9Ia8exzdI4Ke0+Bki8wbn/HznApeIp8Mk3/wogzeq80lt6uJzjnKCMPiUaaeBjLFmxLmTGzvPFuFQLpDeaU8pPhQTykm2M8qY5R7Xq7Y/9FOO/wAnNW2voQz77SSXr+94ZE138rGN4RoN+Q7nfGqmbJSjZKYUMuT1xpAgi7jFxUcTys2d1ZsLyZ5SfKSiOey8xL035kgMzLakw2LRVTk+HDxktdxk8IvsRCQIxBAhQWWJXiwxVmBMvkAuJHtK8TEq5cgzy30g5lh9ZnXwLZTEQt9fzestz6ELBx7YHGEt/l7SBdf49OaIPl/zTfq/Uh4pHvkpM7nLoMsfylvEoNPv+ejLBdI57SnFx3A26JLNzpIOvpil/GvGQzfV1K9yAg+ad0VXy4U8On7WVVJLY4D+1W61cLGGnSXSa8Fs6we96PjV/i23utVFbQI9wnvA4AHTK0mPXFSNObrGx5ODTbPqFtNEM4mYnBt05hsCdm3s7eEQ4fqaz+JiiSjX+TdhW8ia4Tnca8q1yy7FxRzePdvZ5luH5/jQaXgEN6rGj3Z8s7DWz0FG9qZ+65zsUf/Dzr8cv6pR/T3ebAemg4EaGbioUSnqhKczuxL8vzE3zuzitqtFMnvA+NNs099ecZOFWrBX6/jgqPhCgtPbs0ioB4wuInvFTS6qwF5zU7/4QoKuO3TluB4wuijsFTe5qAJ7zY7/EiTtfZHMHjC6HL9X3OSiCuzVNvXxemL8rt5w55CwtRbJvEPZ3ItuhTEWxTYnbEPcm9jZ5GJD7KYaZ9U6vqklBkQ4fZev3FZZJBPG6GaxRJPXGs7Xtq2JsQY7m/qUxG7K5XnNTX2lK8jhiD7/q7/bRTJ7wKiMaf30ips0bI296hpfk4MntfrAJsKs+Xe1SGYPGC1/V8FecRN8DdirrfEHcjjFdreLZPaAUXm59dMrbtJQC/Zqp+yCIM4p5iSeyYbaX5yLP0nYQKAHjC4z9IqbXGyNfZBf7b/z+IGA3S+S2QNGl+P3iptc1IJ9bOrjSXBv7fxP/LEdDBwMNMoA/PmL5dPqY7aEw2Yzm9O/M2BtP/B0OvnWnZXmCB4MHAxUygCcnoPh+i/nppaf/wfk7BIal8UrlgAAAABJRU5ErkJggg==\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}- \\frac{i \\sqrt{- i}}{2} - \\frac{\\sqrt{i} i}{2} & - \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2}\\\\- \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2} & \\frac{\\sqrt{i} i}{2} + \\frac{i \\sqrt{- i}}{2}\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡ ____ ____ ⎤\n",
|
|||
|
|
"⎢ ⅈ⋅╲╱ -ⅈ √ⅈ⋅ⅈ √ⅈ ╲╱ -ⅈ ⎥\n",
|
|||
|
|
"⎢- ──────── - ──── - ── + ────── ⎥\n",
|
|||
|
|
"⎢ 2 2 2 2 ⎥\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎢ ____ ____⎥\n",
|
|||
|
|
"⎢ √ⅈ ╲╱ -ⅈ √ⅈ⋅ⅈ ⅈ⋅╲╱ -ⅈ ⎥\n",
|
|||
|
|
"⎢ - ── + ────── ──── + ────────⎥\n",
|
|||
|
|
"⎣ 2 2 2 2 ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 16,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"H_ = sqrt_miX * sqrt_iZ**3 * sqrt_miX\n",
|
|||
|
|
"H_"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 17,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}\\frac{i \\left(- \\sqrt{i} + \\left(- i\\right)^{\\frac{5}{2}}\\right)}{2} & - \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2}\\\\- \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2} & \\frac{i \\left(\\sqrt{- i} + \\sqrt{i}\\right)}{2}\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡ ⎛ 5/2⎞ ____ ⎤\n",
|
|||
|
|
"⎢ⅈ⋅⎝-√ⅈ + (-ⅈ) ⎠ √ⅈ ╲╱ -ⅈ ⎥\n",
|
|||
|
|
"⎢───────────────── - ── + ────── ⎥\n",
|
|||
|
|
"⎢ 2 2 2 ⎥\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎢ ____ ⎛ ____ ⎞⎥\n",
|
|||
|
|
"⎢ √ⅈ ╲╱ -ⅈ ⅈ⋅⎝╲╱ -ⅈ + √ⅈ⎠⎥\n",
|
|||
|
|
"⎢ - ── + ────── ───────────────⎥\n",
|
|||
|
|
"⎣ 2 2 2 ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 17,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"H_.simplify()\n",
|
|||
|
|
"H_"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 18,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡√2 √2 ⎤\n",
|
|||
|
|
"⎢── ── ⎥\n",
|
|||
|
|
"⎢2 2 ⎥\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎢√2 -√2 ⎥\n",
|
|||
|
|
"⎢── ────⎥\n",
|
|||
|
|
"⎣2 2 ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 18,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"H = sympy.Matrix([[1, 1], [1, -1]]) / sympy.sqrt(2)\n",
|
|||
|
|
"H"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 19,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [],
|
|||
|
|
"source": [
|
|||
|
|
"phi = sympy.symbols(\"phi\")"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 20,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAVCAYAAAB7R6/OAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAARUlEQVQoFWNgYGAoA+K7UGyEhc/QCRR0+f//PwMyBoqBxZmADLxgVAEkeEbDgchwYIEmp5mMjIwgZigQuwBxOhALAfFuAP68FOR8/BSoAAAAAElFTkSuQmCC\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[ \\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"[]"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 20,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"sympy.solve(sympy.exp(i*phi)*H_ - H)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 28,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}\\frac{i \\left(\\left(- i\\right)^{\\frac{9}{2}} + \\sqrt{i}\\right)}{2} & \\frac{\\left(- i\\right)^{\\frac{5}{2}}}{2} + \\frac{\\sqrt{i}}{2}\\\\\\frac{\\left(- i\\right)^{\\frac{5}{2}}}{2} + \\frac{\\sqrt{i}}{2} & \\frac{i \\left(- \\sqrt{i} + \\left(- i\\right)^{\\frac{5}{2}}\\right)}{2}\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡ ⎛ 9/2 ⎞ 5/2 ⎤\n",
|
|||
|
|
"⎢ⅈ⋅⎝(-ⅈ) + √ⅈ⎠ (-ⅈ) √ⅈ ⎥\n",
|
|||
|
|
"⎢──────────────── ─────── + ── ⎥\n",
|
|||
|
|
"⎢ 2 2 2 ⎥\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎢ 5/2 ⎛ 5/2⎞⎥\n",
|
|||
|
|
"⎢ (-ⅈ) √ⅈ ⅈ⋅⎝-√ⅈ + (-ⅈ) ⎠⎥\n",
|
|||
|
|
"⎢ ─────── + ── ─────────────────⎥\n",
|
|||
|
|
"⎣ 2 2 2 ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 28,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"H__ = H_ * sympy.exp(i * sympy.pi )\n",
|
|||
|
|
"H__.simplify()\n",
|
|||
|
|
"H__"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "markdown",
|
|||
|
|
"metadata": {},
|
|||
|
|
"source": [
|
|||
|
|
"Some other calculatuions:"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 30,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAAcAAAAOCAYAAADjXQYbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAo0lEQVQYGX2QARGCQBBF9xgDkAErGMEIWEEb0AEaaAVtYATHCFhBGpzv3+ydDCPuzGd3///HfbAYo81hZh04i6sYlnWCmEQGOdbq18ni/StuZAsh1LQj2IKRqwa6paS03u/eM781CxWnGogHUB3AK03+qLOTXdG7spfBrHXxa56JT8Rr3tVzIKXVK9tEesD8nTsEGW8ecNRefh/knV2YMF0kfgByKG0w9dMLeQAAAABJRU5ErkJggg==\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle i$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"ⅈ"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 30,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"sympy.exp(i * sympy.pi/2)"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
{
|
|||
|
|
"cell_type": "code",
|
|||
|
|
"execution_count": 31,
|
|||
|
|
"metadata": {},
|
|||
|
|
"outputs": [
|
|||
|
|
{
|
|||
|
|
"data": {
|
|||
|
|
"image/png": "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\n",
|
|||
|
|
"text/latex": [
|
|||
|
|
"$\\displaystyle \\left[\\begin{matrix}- \\frac{\\sqrt{i}}{2} + \\frac{\\sqrt{- i}}{2} & \\frac{\\sqrt{i} i}{2} + \\frac{i \\sqrt{- i}}{2}\\\\\\frac{\\sqrt{i} i}{2} + \\frac{i \\sqrt{- i}}{2} & - \\frac{\\sqrt{- i}}{2} + \\frac{\\sqrt{i}}{2}\\end{matrix}\\right]$"
|
|||
|
|
],
|
|||
|
|
"text/plain": [
|
|||
|
|
"⎡ ____ ____⎤\n",
|
|||
|
|
"⎢ √ⅈ ╲╱ -ⅈ √ⅈ⋅ⅈ ⅈ⋅╲╱ -ⅈ ⎥\n",
|
|||
|
|
"⎢ - ── + ────── ──── + ────────⎥\n",
|
|||
|
|
"⎢ 2 2 2 2 ⎥\n",
|
|||
|
|
"⎢ ⎥\n",
|
|||
|
|
"⎢ ____ ____ ⎥\n",
|
|||
|
|
"⎢√ⅈ⋅ⅈ ⅈ⋅╲╱ -ⅈ ╲╱ -ⅈ √ⅈ ⎥\n",
|
|||
|
|
"⎢──── + ──────── - ────── + ── ⎥\n",
|
|||
|
|
"⎣ 2 2 2 2 ⎦"
|
|||
|
|
]
|
|||
|
|
},
|
|||
|
|
"execution_count": 31,
|
|||
|
|
"metadata": {},
|
|||
|
|
"output_type": "execute_result"
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"source": [
|
|||
|
|
"sqrt_miX * sqrt_iZ * sqrt_miX"
|
|||
|
|
]
|
|||
|
|
}
|
|||
|
|
],
|
|||
|
|
"metadata": {
|
|||
|
|
"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": "3.7.3"
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
"nbformat": 4,
|
|||
|
|
"nbformat_minor": 2
|
|||
|
|
}
|