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Quantum Mechanics

Lecture Notes

Lecture notes are useful when they are focused, current, and clear about conventions. They should usually supplement a textbook or monograph rather than replace one. Cite lecture notes when their exposition, notation, problem set, or maintained online status is the reason they are being used.

When Lecture Notes Are the Right Source

Section titled “When Lecture Notes Are the Right Source”

Use lecture notes for:

  • an alternate explanation of a standard topic,
  • a compact bridge into a specialized field,
  • maintained problem sets or worked calculations,
  • convention comparison across communities,
  • publicly available reading that complements a closed textbook.

Do not use lecture notes as the only authority for subtle theorem statements, historical priority, or active research status unless the author is explicitly writing a review-level resource.

Core Quantum Mechanics

Section titled “Core Quantum Mechanics”

MIT OpenCourseWare 8.04, 8.05, and 8.06.

Best for: a structured three-course route through undergraduate quantum physics, with lectures, assignments, and exams.

Use with: the Undergraduate Physics Roadmap and the Problem Index.

Watch for: OCW materials can be course-specific. Translate notation before using formulas outside their course context.

David Tong, Applications of Quantum Mechanics.

Best for: clear graduate-facing notes on approximation methods, scattering, identical particles, and applications that connect formalism to modern physics.

Use with: the Graduate Quantum Mechanics Roadmap and the QFT Bridge References.

Watch for: the notes assume comfort with theoretical physics notation and move quickly through background material.

Quantum Information

Section titled “Quantum Information”

John Preskill, quantum computation lecture notes.

Best for: graduate quantum information, error correction, entanglement, channels, and the conceptual bridge from quantum mechanics to computation.

Use with: the Quantum Information Roadmap and Quantum Information References.

Watch for: notation is information-theoretic. Check log bases, channel pictures, and tensor-factor ordering.

John Watrous, The Theory of Quantum Information.

Best for: mathematically clean quantum information, semidefinite programming, channels, distance measures, and entanglement theory.

Use with: the Quantum Gates Table and quantum information formulas.

Watch for: the style is theorem-driven; it is not a first introduction to wave mechanics.

Mathematical Quantum Mechanics

Section titled “Mathematical Quantum Mechanics”

Gerald Teschl, Mathematical Methods in Quantum Mechanics.

Best for: rigorous Hilbert-space quantum mechanics, spectral theory, one-dimensional Schrödinger operators, and self-adjointness.

Use with: the Mathematical Quantum Mechanics Roadmap and Rigorous QM References.

Watch for: the emphasis is mathematical structure, so physical interpretation should be cross-checked with standard physics texts.

Brian Hall, lecture-derived mathematical quantum theory material.

Best for: finite-dimensional quantum mechanics, Lie groups, representation theory, and the mathematical structure behind standard examples.

Use with: finite-dimensional Hilbert spaces and angular momentum algebra.

Watch for: different mathematical communities choose the inner product convention differently; check which argument is linear.

How to Cite Lecture Notes

Section titled “How to Cite Lecture Notes”

When citing lecture notes, include the author, title, institution when relevant, URL if stable, and a date or version if supplied. If the notes are a living web resource, use an access date only when the statement depends on the page being live rather than on a stable PDF.

For technical claims, prefer a textbook or review when available. For a distinctive derivation or notation convention, cite the notes directly.

Section titled “Cross-Links”

References

Section titled “References”