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Correct a typo and convert to .jl file
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david-pl committed Mar 24, 2017
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},
"source": [
"## Two fermions with conserved particle number\n",
"Now, as a first example, we consider two fermionic particles. Each of them can occupy one of the four levels in the system, but not at the same time. To this end, we define a many-body basis associated to this N-level system. Calculating the many-body operators from the corresponding n-level operators can be done with the **manybodyoperator()** function. Basically it uses the relation\n",
"Now, as a first example, we consider two fermionic particles. Each of them can occupy one of the four levels in the system, but not at the same time. To this end, we define a many-body basis associated to this N-level system. Calculating the many-body operators from the corresponding N-level operators can be done with the **manybodyoperator()** function. Basically it uses the relation\n",
"$$\n",
" \\tilde{A} = \\sum_{st} c_s^\\dagger c_t \\langle u_s| A |u_t \\rangle\n",
"$$\n",
"to convert the one-body operator $A$ to the many-body operator $\\tilde{A}$."
"to convert the one-body operator $A$ to the many-body operator $\\tilde{A}$. Here, $|u_i\\rangle$ is the $i$-th basis state of the initial basis (N-level system) and $c_s$ is the particle annihilation operator at site $s$."
]
},
{
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],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.5.1",
"display_name": "Julia 0.5.0",
"language": "julia",
"name": "julia-0.5"
},
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