A notebook for qutip.distributions

tutorials-v5/visualization/distributions.md

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+---
+jupyter:
+  jupytext:
+    text_representation:
+      extension: .md
+      format_name: markdown
+      format_version: '1.3'
+      jupytext_version: 1.13.8
+  kernelspec:
+    display_name: Python 3 (ipykernel)
+    language: python
+    name: python3
+---
+
+# Using qutip.distributions
+
+Author: Mathis Beaudoin (2025)
+
+### Introduction
+
+This notebook shows how to use probability distributions inside QuTiP. We begin by importing the necessary packages.
+
+```python
+from qutip import fock, about
+from qutip.distributions import HarmonicOscillatorWaveFunction
+from qutip.distributions import HarmonicOscillatorProbabilityFunction
+import matplotlib.pyplot as plt
+```
+
+### Harmonic Oscillator Wave Function
+
+Here, we display the spatial distribution of the wave function for the harmonic oscillator (n=0 to n=7) with the `HarmonicOscillatorWaveFunction()` class.
+
+Optionally, define a range of values for each coordinate with the parameter called `extent`. Also, define a number of data points inside the given range with the optional parameter called `steps`. From this information, the distribution is generated and can be visualized with the `.visualize()` method.
+
+```python
+M = 8
+N = 20
+
+fig, ax = plt.subplots(M, 1, figsize=(10, 12), sharex=True)
+
+for n in range(M):
+    psi = fock(N, n)
+    wf = HarmonicOscillatorWaveFunction(psi, 1.0, extent=[-10, 10])
+    wf.visualize(fig=fig, ax=ax[M-n-1], show_ylabel=False, show_xlabel=(n == 0))
+```
+
+### Harmonic Oscillator Probability Function
+
+The class `HarmonicOscillatorProbabilityFunction()` is the squared magnitude of the data that would normally be in `HarmonicOscillatorWaveFunction()`. We use the same example as before.
+
+```python
+M = 8
+N = 20
+
+fig, ax = plt.subplots(M, 1, figsize=(10, 12), sharex=True)
+
+for n in range(M):
+    psi = fock(N, n)
+    wf = HarmonicOscillatorProbabilityFunction(psi, 1.0, extent=[-10, 10])
+    wf.visualize(fig=fig, ax=ax[M-n-1], show_ylabel=False, show_xlabel=(n == 0))
+```
+
+### About
+
+```python
+about()
+```