Aim

Provide a perspective on why, what, and how to teach quantum physics at A-levels (who + when + where = pre-university Higher 2 Physics students in Singapore)

Background

Shifts in the A-level physics syllabus at Higher 2 level, from 2016 JC1 year of implementation
Question of whether there is anything left to meaningfully teach, and what to actually teach students

Considerations

Disciplinary lens of physics

Profile of students

Nature of science

Assumptions

Approach

  • Emphasis on getting students interested to learn more, by further studies
  • Stick to experimental evidence, limit the theoretical reach. Avoid the stance that borders on "this is what scientists say so it's important".
  • Avoid misconceptions, better to leave it as "you need to learn more to understand it". Can be problematic if misconceptions are introduced and internalised.
  • Early quantum ideas are included: photoelectric effect, photons and atomic spectra, de Broglie wavelength, x-ray production. Blackbody radiation not discussed, but is a candidate for inclusion (links to topic of heat transfer in secondary physics). Rutherford model included, but not Bohr model (possible to include using wave superposition ideas, even if angular momentum not discussed).
  • Options

    1. Schrodinger equation
    2. Heisenberg matrices
    3. Bra-ket state vectors in Hilbert space (linear algebra, matrices a bit foreign in the rest of physics syllabus)
    4. Feynman sum of all paths functional calculus (calculus not quite in the rest of the syllabus)

    Proposed Organising Concepts

    To better align with other parts of the syllabus, and build on what students have already learnt in the rest of physics, the Schrodinger equation seems the most appropriate starting point
    Motivate this equation using concept of mechanical energy
    Interpret solutions as waves, build upon wave concepts
    If can introduce Fourier transform in topic of waves, then some concepts like Heisenberg uncertainty principle can be understood on that basis
    Complication of complex numbers being involved, but not getting students to really grapple with the technicalities of solving
    Can mention Feynman sum of paths formalism, but this might be a bit too much for many students, path integrals, functional integration, and also Lagrangian and Hamiltonian methods (worth a mention in framework of classical mechanics)

    Other thoughts

    Matrices and state vectors are powerful and more modern, simpler... maybe better to reserve it for university courses
    Spin-statistics theorem is great, but maybe too advanced, though would be a good example to highlight the deep interconnections across areas of physics (some idea of angular momentum would be important pre-requisite though)
    Should anyway introduce Maxwell distribution of classical particles before fermion/boson distributions