add sections to fermion operator guide

docs/explanations/hamiltonians.ipynb

@@ -75,7 +75,7 @@
    "source": [
     "The arguments passed to the initialization are now available as attributes of the same name, i.e., `mol_hamiltonian.one_body_tensor` accesses the one-body tensor.\n",
     "\n",
-    "## Operator action via SciPy LinearOperators\n",
+    "## Operator action\n",
     "\n",
     "The basic operation that a Hamiltonian represention should support is applying its action, as a linear operator, to a vector. This basic operation can be used to implement more complex ones, such as operator exponentiation and eigenvalue computation. ffsim uses Scipy's [LinearOperator](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html) class to support these operations for Hamiltonians. To obtain a LinearOperator, call the `linear_operator` function:"
    ]
@@ -192,7 +192,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "ffsim-1cfkSnAR",
+   "display_name": "ffsim",
    "language": "python",
    "name": "python3"
   },
@@ -206,7 +206,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.3"
+   "version": "3.13.1"
   }
  },
  "nbformat": 4,

docs/how-to-guides/fermion-operator.ipynb

@@ -88,6 +88,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## Arithmetic\n",
+    "\n",
     "FermionOperators support arithmetic operations. Note that when multiplying a FermionOperator by a scalar, the scalar must go on the left, i.e. `2 * op` and not `op * 2`."
    ]
   },
@@ -184,6 +186,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## Normal-ordering\n",
+    "\n",
     "Operators can be normal-ordered by calling the `normal_ordered` method, which returns a new FermionOperator. In the normal-ordered form of a FermionOperator, the operators comprising each term appear from left to right in descending lexicographic order by `(action, spin, orb)`. That is, all creation operators appear before all annihilation operators; within creation/annihilation operators, spin beta operators appear before spin alpha operators, and larger orbital indices appear before smaller orbital indices."
    ]
   },
@@ -222,6 +226,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## Operator action\n",
+    "\n",
     "If a FermionOperator conserves particle number and the Z component of spin, then it can be converted to a [LinearOperator](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html) using the `ffsim.linear_operator` function. In order for a FermionOperator to conserve particle number and the Z component of spin, it must preserve the number of spin-alpha fermions and the number of spin-beta fermions. So far, the operators we have created do not satisfy these criteria:"
    ]
   },