build: add spelling checker (#248)

Author: oameye

.github/workflows/SpellCheck.yml

@@ -0,0 +1,19 @@
+name: Spell Check
+
+on: 
+  pull_request:
+    types:
+      - opened
+      - reopened
+      - synchronize
+      - ready_for_review
+
+jobs:
+  typos-check:
+    name: Spell Check with Typos
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout Actions Repository
+        uses: actions/checkout@v4
+      - name: Check spelling
+        uses: crate-ci/[email protected]

.typos.toml

@@ -0,0 +1,9 @@
+[default.extend-words]
+ket = "ket"
+Ket = "Ket"
+pn = "pn"
+ba = "ba"
+
+[type.ipynb]
+extend-glob = ["*.ipynb"]
+check-file = false

docs/src/examples/cavity_antiresonance_indexed.md

@@ -1,6 +1,6 @@
 # Cavity Antiresonance
 
-In this example we investigate a system of $N$ closely spaced quantum emitters inside a coherently driven single mode cavity. The model is descriped in [D. Plankensteiner, et. al., Phys. Rev. Lett. 119, 093601 (2017)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.093601).
+In this example we investigate a system of $N$ closely spaced quantum emitters inside a coherently driven single mode cavity. The model is described in [D. Plankensteiner, et. al., Phys. Rev. Lett. 119, 093601 (2017)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.093601).
 The Hamiltonian of this system is composed of three parts $H = H_c + H_a + H_{\mathrm{int}}$, the driven cavity $H_c$, the dipole-dipole interacting atoms $H_a$ and the atom-cavity interaction $H_\mathrm{int}$:
 
 ```math

docs/src/examples/filter-cavity_indexed.md

@@ -25,7 +25,7 @@ We create the parameters of the system including the $\texttt{IndexedVariable}$
 
 
 ```@example filter_cavity_indexed
-# Paramters
+# Parameters
 @cnumbers κ g gf κf R Γ Δ ν N M
 δ(i) = IndexedVariable(:δ, i)
 

docs/src/examples/heterodyne_detection.md

@@ -88,7 +88,7 @@ scaled_eqs = scale(eqs_c)
 ```
 
 # Deterministic time evolution
-Here we define the actual values for the system parameters. We then show that the deterministic time evolution without the noise terms is still accesible by using the constructor ODESystem for the stochastic system of equations and the syntax for the simulation of the time evolution is as usual.
+Here we define the actual values for the system parameters. We then show that the deterministic time evolution without the noise terms is still accessible by using the constructor ODESystem for the stochastic system of equations and the syntax for the simulation of the time evolution is as usual.
 
 
 ```julia
@@ -110,7 +110,7 @@ xlabel("Time (ms)")
 ```
 
 # Stochastic time evolution
-The stochastic time evolution is accesible via the constructor SDESystem, whose syntax is exactly the same as for the ODESystem, but with keyword args as defined in https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/. We then need to provide a noise process for the measurement. If the noise is white the appropriate noise process is a Wiener process. The SDEProblem is then constructed just as the ODEProblem, but with an additional noise argument.
+The stochastic time evolution is accessible via the constructor SDESystem, whose syntax is exactly the same as for the ODESystem, but with keyword args as defined in https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/. We then need to provide a noise process for the measurement. If the noise is white the appropriate noise process is a Wiener process. The SDEProblem is then constructed just as the ODEProblem, but with an additional noise argument.
 
 We can then make use of the EnsembleProblem which automatically runs multiple instances of the stochastic equations of motion. The number of trajectories can then be set in the solve call. See the documentation cited above for more details of the function calls here.
 
@@ -126,7 +126,7 @@ sol = solve(eprob,StochasticDiffEq.EM(), dt = 1e-9, save_noise=true,trajectories
 ```
 
 # Plot the average of the cavity number
-Here we plot the average of the cavity number for the stochastic and determinstic equation of motion with the trajectories in grey in the background. We can see that the dynamics of the system is indeed modified by the measurement backaction.
+Here we plot the average of the cavity number for the stochastic and deterministic equation of motion with the trajectories in grey in the background. We can see that the dynamics of the system is indeed modified by the measurement backaction.
 
 
 ```julia

docs/src/examples/jupyter_notebooks/cavity_antiresonance.ipynb

@@ -6,7 +6,7 @@
    "source": [
     "# Cavity Antiresonance\n",
     "\n",
-    "In this example we investigate a system of $N$ closely spaced quantum emitters inside a coherently driven single mode cavity. The model is descriped in [D. Plankensteiner, et. al., Phys. Rev. Lett. 119, 093601 (2017)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.093601).\n",
+    "In this example we investigate a system of $N$ closely spaced quantum emitters inside a coherently driven single mode cavity. The model is described in [D. Plankensteiner, et. al., Phys. Rev. Lett. 119, 093601 (2017)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.093601).\n",
     "The Hamiltonian of this system is composed of three parts $H = H_c + H_a + H_{\\mathrm{int}}$, the driven cavity $H_c$, the dipole-dipole interacting atoms $H_a$ and the atom-cavity interaction $H_\\mathrm{int}$:\n",
     "\n",
     "```math\n",

docs/src/examples/jupyter_notebooks/cavity_antiresonance_indexed.ipynb

@@ -11,7 +11,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In this example we investigate a system of $N$ closely spaced quantum emitters inside a coherently driven single mode cavity. The model is descriped in [D. Plankensteiner, et. al., Phys. Rev. Lett. 119, 093601 (2017)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.093601).\n",
+    "In this example we investigate a system of $N$ closely spaced quantum emitters inside a coherently driven single mode cavity. The model is described in [D. Plankensteiner, et. al., Phys. Rev. Lett. 119, 093601 (2017)](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.093601).\n",
     "The Hamiltonian of this system is composed of three parts $H = H_c + H_a + H_{\\mathrm{int}}$, the driven cavity $H_c$, the dipole-dipole interacting atoms $H_a$ and the atom-cavity interaction $H_\\mathrm{int}$:"
    ]
   },

docs/src/examples/jupyter_notebooks/filter-cavity_indexed.ipynb

@@ -77,7 +77,7 @@
     }
    ],
    "source": [
-    "# Paramters\n",
+    "# Parameters\n",
     "@cnumbers κ g gf κf R Γ Δ ν N M\n",
     "δ(i) = IndexedVariable(:δ, i)\n",
     "\n",

docs/src/examples/jupyter_notebooks/heterodyne_detection.ipynb

@@ -395,7 +395,7 @@
    "metadata": {},
    "source": [
     "# Deterministic time evolution\n",
-    "Here we define the actual values for the system parameters. We then show that the deterministic time evolution without the noise terms is still accesible by using the constructor ODESystem for the stochastic system of equations and the syntax for the simulation of the time evolution is as usual."
+    "Here we define the actual values for the system parameters. We then show that the deterministic time evolution without the noise terms is still accessible by using the constructor ODESystem for the stochastic system of equations and the syntax for the simulation of the time evolution is as usual."
    ]
   },
   {
@@ -439,7 +439,7 @@
    "metadata": {},
    "source": [
     "# Stochastic time evolution\n",
-    "The stochastic time evolution is accesible via the constructor SDESystem, whose syntax is exactly the same as for the ODESystem, but with keyword args as defined in https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/. We then need to provide a noise process for the measurement. If the noise is white the appropriate noise process is a Wiener process. The SDEProblem is then constructed just as the ODEProblem, but with an additional noise argument.\n",
+    "The stochastic time evolution is accessible via the constructor SDESystem, whose syntax is exactly the same as for the ODESystem, but with keyword args as defined in https://docs.sciml.ai/DiffEqDocs/stable/tutorials/sde_example/. We then need to provide a noise process for the measurement. If the noise is white the appropriate noise process is a Wiener process. The SDEProblem is then constructed just as the ODEProblem, but with an additional noise argument.\n",
     "\n",
     "We can then make use of the EnsembleProblem which automatically runs multiple instances of the stochastic equations of motion. The number of trajectories can then be set in the solve call. See the documentation cited above for more details of the function calls here."
    ]
@@ -474,7 +474,7 @@
    "metadata": {},
    "source": [
     "# Plot the average of the cavity number\n",
-    "Here we plot the average of the cavity number for the stochastic and determinstic equation of motion with the trajectories in grey in the background. We can see that the dynamics of the system is indeed modified by the measurement backaction."
+    "Here we plot the average of the cavity number for the stochastic and deterministic equation of motion with the trajectories in grey in the background. We can see that the dynamics of the system is indeed modified by the measurement backaction."
    ]
   },
   {

docs/src/examples/jupyter_notebooks/unique_squeezing.ipynb

@@ -67,7 +67,7 @@
     "ha = NLevelSpace(Symbol(:spin),2)\n",
     "h = hf ⊗ ha\n",
     "\n",
-    "# Paramter\n",
+    "# Parameter\n",
     "@cnumbers ω Ω ωd η κ g γ N ξ\n",
     "@syms t::Real # time\n",
     "nothing # hide"
@@ -287,7 +287,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "For a suffeciently low excitation we can adiabatically elminate the dynamics of the two-level system(s). This leads to an effective Hamiltonian "
+    "For a suffeciently low excitation we can adiabatically eliminate the dynamics of the two-level system(s). This leads to an effective Hamiltonian "
    ]
   },
   {