[PR-7] feat: add PySCF validation tests and interactive tutorial notebook

[San1357]

Summary

• Added tests/test_pyscf_comparison.py — 15 tests validating both original and improved ERI implementations against PySCF reference values
• Added notebooks/tutorial/Tutorial 3 - Two-Electron Integral Optimizations.ipynb — interactive tutorial covering OS+HGP algorithm, Boys functions, Schwarz screening, high angular momentum, and PySCF validation
• Part of Issue WoC: 2-electron integrals: better performance and more flexibility #221 (Week 8),
• builds on PR [PR-6] feat: implement Schwarz screening for two-electron integral optimization #240

What Changed

File	Lines	What
tests/test_pyscf_comparison.py	+353	15 tests: TestPySCFOriginal (6), TestPySCFImproved (6), TestPySCFPhysicalProperties (3) — H2/STO-3G, chemist/physicist notation, symmetries, physical properties
notebooks/tutorial/Tutorial 3 - Two-Electron Integral Optimizations.ipynb	+546	8-section tutorial: Setup, OS+HGP algorithm, Boys functions (Coulomb/erf/erfc), Schwarz screening, high angular momentum (s/p/d/f), PySCF comparison, summary

How To Test

# PySCF comparison tests (requires pyscf)
pip install pyscf
python3 -m pytest tests/test_pyscf_comparison.py -v

# Run tutorial notebook
jupyter notebook "notebooks/tutorial/Tutorial 3 - Two-Electron Integral Optimizations.ipynb"

Proof That It Works

- All 15 PySCF tests pass when pyscf is installed (pip install pyscf)

First Checklist

• Tests added for PySCF comparison
• All tests pass (or skip if pyscf not installed)
• Tutorial notebook covers all Week 1-8 deliverables
• Docstrings in numpydoc format
• No new dependencies added (pyscf is optional)

Scope Of this PR

• Validates both electron_repulsion_integral and electron_repulsion_integral_improved against PySCF
• Tutorial covers complete OS+HGP pipeline from Boys function to Schwarz screening
• Week 8 deliverable — final validation and documentation
• PySCF is optional dependency — tests skip gracefully if not installed

Second Checklist

• Write a good description of what the PR does.
• Add tests for each unit of code added (e.g. function, class)
• Update documentation (Tutorial 3 notebook added)
• Squash commits that can be grouped together
• Rebase onto master

Type of Changes

Type	Checked
🐛 Bug fix
✨ New feature	✓
🔨 Refactoring
📜 Docs	✓