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Advanced Quantum Mechanics: Approximation and Scattering

Academic (University) preparation with worked examples, written practice and independent learning assessments.

Independent university-level study of Advanced Quantum Mechanics: Approximation and Scattering. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Hilbert-space review; Symmetries; Unitary transformations; Conservation laws. Stationary perturbation; Degenerate perturbation; Fine structure; Zeeman effects. Variational methods; WKB approximation; Tunneling estimates; Semiclassical quantization. Time-dependent perturbation; Transition probabilities; Golden rule; Adiabatic evolution. Scattering amplitudes; Born approximation; Partial waves; Phase shifts. Identical-particle scattering; Spin coupling; Selection rules; Resonances. Density operators; Entanglement; Open-system evolution; Decoherence. Relativistic wave equations; Spinor structure; Approximation validity; Quantum calculation project. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required. Includes lessons, supplementary YouTube tutorials, practical exercises, quizzes and free/paid practice tests. Erudex is independent, not affiliated with the source institution or awarding body. Its 80% learning checks are not official grades or university credit. Content requires qualified subject review before use as a complete teaching programme.

32h Certificate available
InternationalAcademic (University)Independent preparation

Curriculum

One complete track with its own final exam and certificate.

Independent university-level study of Advanced Quantum Mechanics: Approximation and Scattering. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Hilbert-space review; Symmetries; Unitary transformations; Conservation laws. Stationary perturbation; Degenerate perturbation; Fine structure; Zeeman effects. Variational methods; WKB approximation; Tunneling estimates; Semiclassical quantization. Time-dependent perturbation; Transition probabilities; Golden rule; Adiabatic evolution. Scattering amplitudes; Born approximation; Partial waves; Phase shifts. Identical-particle scattering; Spin coupling; Selection rules; Resonances. Density operators; Entanglement; Open-system evolution; Decoherence. Relativistic wave equations; Spinor structure; Approximation validity; Quantum calculation project. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required.

Hilbert-space review; Symmetries; Unitary transformations; Conservation laws

  • Rigorous Hilbert Space Foundations, Spectral Theory, and Operator Algebras Lab60 min
  • Symmetry Operations, Wigner's Theorem, and Continuous Lie Groups Lab60 min
  • Unitary Transformations, Dynamical Pictures, and Generator Formalism Lab60 min
  • Quantum Conservation Laws, Superselection Rules, and Constants of Motion Lab60 min

Careers this prepares you for

    How you study

    Every lesson pairs an in-depth video with written notes, key takeaways, a hands-on lab, exercises and a quiz. Work at your own pace, then sit the final examination for your Erudex certificate.