{"id":77,"date":"2018-01-14T21:01:14","date_gmt":"2018-01-14T21:01:14","guid":{"rendered":"http:\/\/134.169.6.169\/milq\/?page_id=77"},"modified":"2026-10-09T08:51:06","modified_gmt":"2026-10-09T06:51:06","slug":"didaktische-konzepte","status":"publish","type":"page","link":"https:\/\/www.milq.info\/en\/spezialgebiete\/didaktische-konzepte\/","title":{"rendered":"Approaches to teaching Quantum Physics"},"content":{"rendered":"
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In this chapter, we provide an overview of approaches to teaching quantum physics described in the physics education literature other than the milq concept and the basic rules of quantum physics (\u201cWesensz\u00fcge\u201d). Part A (sections 1 to 4) outlines approaches that have emerged since 2010; part B (sections 5 to 9) presents the classic concepts developed between the 1970s and the early 2000s, concentrating on Germany. The focus is on the content structure of the concepts; a didactical or physical discussion of them is beyond the scope of this page. Several of the concepts presented have been tried out and evaluated in the classroom.<\/p>\n

An overview of teaching concepts for quantum physics, including more recent approaches, is given in the chapter \u201cUnterrichtskonzeptionen zur Quantenphysik\u201d<\/a> by R. M\u00fcller and T. Wilhelm in: T. Wilhelm, H. Schecker, M. Hopf (eds.), Unterrichtskonzeptionen f\u00fcr den Physikunterricht<\/em>, Springer Spektrum (2021), pp. 335\u2013368 (in German). How research on quantum physics education has developed since 2000 is shown in a bibliometric analysis by Bitzenbauer (2021): the study documents the enormous growth of the field, accompanied by a shift in research focus from preparing quantum physics content for teaching towards empirical research on teaching and learning processes. A review by Krijtenburg-Lewerissa et al. (2017) summarizes the state of research on teaching and learning quantum physics in upper secondary school and introductory university courses.<\/p>\n

A. Approaches since 2010:<\/strong> 1. The Erlangen teaching concept on quantum optics<\/a> – 2. Two-state systems as an entry point<\/a> – 3. Quantum technologies as a context<\/a> – 4. Interactive simulations<\/a>
\nB. Earlier approaches:<\/strong> 5. The teaching concept of Brachner and Fichtner<\/a> – 6. The Berlin concept<\/a> – 7. The Bremen teaching concept<\/a> – 8.1 The phasor formalism according to K\u00fcblbeck<\/a> – 8.2 The phasor formalism according to Bader<\/a> – 8.3 The proposal by Erb, Sch\u00f6n and Werner<\/a> – 9. Visual Quantum Mechanics<\/a>
\n10. References<\/a><\/p>\n

A. Approaches since 2010<\/h2>\n

A systematic overview of the approaches pursued today has been compiled by the GIREP Thematic Group \u201cTeaching and Learning Quantum Physics\u201d (Michelini et al. 2021; Michelini & Stefanel 2021). It distinguishes five basic approaches: the historical approach, the approach via quantum field theory, two-state systems, the wave function, and Feynman\u2019s sum over paths (phasor formalism). Common core content was identified across all approaches, in particular probability, measurement, superposition, the double-slit experiment and the uncertainty relation. A special issue edited by the group presents current developments (Pospiech, Michelini & Faleti\u010d 2026).<\/p>\n

1. The Erlangen teaching concept on quantum optics<\/h3>\n

The Erlangen concept (Bitzenbauer 2020) deliberately dispenses with the traditional historical approach via the photoelectric effect, the Franck\u2013Hertz experiment and wave\u2013particle dualism. Instead, it leads directly to the characteristic features of quantum physics through real experiments of modern quantum optics with single photons. Its physical foundation is quantum electrodynamics; in particular, it seeks to avoid the notion of the photon as a localizable particle. The experiments are made accessible to students through multimedia representations and an online lab.<\/p>\n

The course comprises four lessons. The first two clarify the technical and methodological foundations of the experiments so that the measurement results can be interpreted in terms of quantum physics in lessons three and four.<\/p>\n

    \n
  1. Detecting nonclassical light:<\/strong> Single-photon detectors (photomultipliers, avalanche photodiodes) produce \u201cclicks\u201d at a rate proportional to the intensity. A click alone is not yet evidence of a single photon: randomly distributed clicks are also compatible with classical light.<\/li>\n
  2. Preparing single-photon states:<\/strong> Photon pairs from parametric down-conversion (BBO crystal). Coincidence method: a click at the gate detector heralds a photon in the other arm (\u201cheralded photons\u201d).<\/li>\n
  3. Anticorrelation at the beam splitter:<\/strong> A heralded photon is never detected at both outputs of a beam splitter at the same time. This contradicts every classical wave model.<\/li>\n
  4. Single-photon interference:<\/strong> Interference with single photons in an interferometer. The wave model remains valid, but the notion of the photon as a localizable particle does not: the property \u201cposition\u201d cannot be permanently ascribed to quantum objects.<\/li>\n<\/ol>\n

    The concept was evaluated in a mixed-methods study (Bitzenbauer 2020, 2021).<\/p>\n

    2. Two-state systems as an entry point<\/h3>\n

    An increasingly common approach does not start with wave functions in position space but with the simplest quantum systems: systems with only two basis states, such as the polarization of photons or the spin of electrons. Such systems are mathematically easy to access, yet they already show the central features of quantum physics (superposition, measurement, entanglement) and allow an early connection to quantum information and quantum technologies.<\/p>\n

    Pioneering work on this approach was done by the group led by Marisa Michelini at the University of Udine. As early as the late 1990s, inspired by Dirac\u2019s presentation of quantum mechanics, the group developed a teaching proposal that introduces the basic concepts of the quantum mechanical formalism using the linear polarization of photons: states, observables as linear operators and probabilistic statements are developed without advanced mathematics from the behavior of photons at polarizing filters and birefringent crystals (Michelini et al. 2000). The learning path was further developed with a simulation environment for thought experiments and tested with several hundred students (Michelini & Stefanel 2021); in Italy it became part of teacher education (IDIFO master\u2019s programs), and it has also been used in other countries (Michelini, Stefanel & T\u00f3th 2022).<\/p>\n

    In the German-speaking countries, D\u00fcr and Heusler (2012) showed what can be learned about quantum physics from a single qubit; for visualization they use, among other things, the Bloch sphere. Empirical comparisons of different two-state contexts are now also available (Bitzenbauer et al. 2024; T\u00f3th et al. 2025). In a field study with 181 upper secondary students, the contexts of photon polarization and the double-well potential led to significantly higher learning gains in understanding the measurement process than a context with single photons and which-path information, which more often led to mixed classical\u2013quantum reasoning.<\/p>\n

    For lower secondary school, a Spin First concept was developed at TU Dresden (Albert 2026; Albert & Pospiech 2023; Albert, F\u00f6rster & Pospiech 2025). It introduces quantum physics in grade 9 qualitatively and without the wave concept: using electron spin as a two-state system, students work out the characteristic features of quantum physics (here: superposition, measurement, the statistical character of measurement results and entanglement); quantum technologies, in particular the quantum computer, serve as the context (Albert 2026).<\/p>\n

    3. Quantum technologies as a context<\/h3>\n

    Approaches that use quantum technologies such as quantum cryptography, quantum computing or quantum sensing as a context for learning quantum physics are becoming increasingly influential. They connect the fundamentals with current applications that receive considerable attention in research and in public, and they are closely linked to the two-state approaches (section 2), since qubits are the basic building blocks of quantum information processing.<\/p>\n

    The competences needed for quantum technologies are described in the European Competence Framework for Quantum Technologies<\/em><\/a> (Greinert & M\u00fcller 2025), developed within the European Quantum Flagship. An example of learning materials in this spirit is the course on this website<\/a> developed in the EU project QTIndu, with modules on the basic principles, on quantum communication and quantum networks, and on quantum myths.<\/p>\n

    4. Interactive simulations<\/h3>\n

    Many recent teaching concepts use interactive simulations. An extensive, freely accessible collection is provided by the QuVis simulations<\/a> of the University of St Andrews (Kohnle et al. 2015). They cover, among other topics, two-level systems, measurement, entanglement and quantum cryptography, as well as potential wells and the time evolution of quantum states. Simulations accompanying the content of this website can be found under Simulation Programs<\/a>.<\/p>\n

    B. Earlier approaches<\/h2>\n

    5. The teaching concept of Brachner and Fichtner<\/h3>\n

    In the late 1970s, Brachner and Fichtner (1977, 1980) developed the first quantum physics course intended for schools, closely modeled on Feynman\u2019s lectures (Feynman 1966).<\/p>\n

    The structure of the course is outlined below:<\/p>\n

    I. Quantum physics<\/em><\/p>\n

      \n
    1. Electrons:<\/strong> Detection of the electron and determination of its mass and charge; observation of the behavior of electrons in the double-slit experiment. Electrons are neither classical particles nor classical waves.<\/li>\n
    2. Photons:<\/strong> Double-slit experiment with attenuated light; photoelectric effect; determination of h; Compton effect. Photons are neither classical particles nor waves.<\/li>\n
    3. Characterization of microobjects:<\/strong> Stochastic behavior; de Broglie relation; angular momentum; spin and polarization. Probabilistic laws in microphysics; quantization of angular momentum; fermions and bosons.<\/li>\n
    4. Energy quantization:<\/strong> Franck\u2013Hertz experiment; energy levels of atoms. The Bohr model of the atom is deliberately avoided.<\/li>\n
    5. Superposition principle:<\/strong> Probability amplitudes and probabilities. As in Feynman, the central role of probability amplitudes is emphasized. The superposition principle applies to them, not to the probabilities.<\/li>\n
    6. Potential wells and the Schr\u00f6dinger equation:<\/strong> Electrons in various one-dimensional potential wells. Time-independent and time-dependent Schr\u00f6dinger equation; infinite potential well; finite potential well; tunneling; chemical bonding.<\/li>\n
    7. Uncertainty relation:<\/strong> Formulation of the uncertainty relation; applications (tunneling, field ion microscope). Loss of the concept of trajectory in microphysics; localization energy.<\/li>\n<\/ol>\n

      II. Atomic physics<\/em><\/p>\n

      The course covers the fundamentals of atomic structure, the ground state of the hydrogen atom, energy levels, and emission and absorption spectra. It also explains the position probability in the orbital model.<\/p>\n

      III. Many-particle systems<\/em><\/p>\n

      The focus is on indistinguishability, the symmetry of the wave function \"\Psi\", the Pauli principle and the structure of atoms, illustrated by scattering experiments between 4<\/sup>He atoms.<\/p>\n

      <\/span><\/p>\n

      The fundamental principle<\/h3>\n

      An important element for Brachner and Fichtner is the so-called fundamental principle of quantum mechanics, which also plays a central role in Feynman (1966). It states:<\/p>\n

      If an event can occur in several different ways (paths) and the experimental arrangement does not determine that one particular way was taken, interference always occurs. If, on the other hand, each event leaves a definite mark on the experimental arrangement by which it can be determined which of the different ways was taken, interference never occurs.<\/strong><\/p>\n

      A paradigmatic application of the fundamental principle is the double slit: if a suitable measuring device makes it possible to determine which slit an electron passed through, no interference occurs. If, however, the experimental arrangement does not allow a particular slit to be assigned to an electron, the electrons form an interference pattern on the screen. Another example is the scattering of 4<\/sup>He atoms mentioned above, where interference effects arise because of indistinguishability. If, on the other hand, 3<\/sup>He is scattered off 4<\/sup>He, no interference occurs.
      \n<\/span><\/p>\n

      6. The Berlin concept<\/h3>\n

      The Berlin concept for introducing quantum mechanics, developed and evaluated by Fischler and Lichtfeldt in collaboration with teachers, was the first teaching proposal to emerge from an analysis of typical learning difficulties and students\u2019 conceptions in quantum physics (Berg et al. 1989).<\/p>\n

      In developing the Berlin concept, the authors sought to take the following difficulties into account:<\/p>\n

      The close association of photons with the particle picture: <\/strong>
      \nA more refined model that may be discussed in class is quickly abandoned in favor of the intuitive particle model.<\/p>\n

      Students\u2019 adherence to the Bohr model of the atom: <\/strong>
      \nIts intuitive nature makes the Bohr model attractive to students. Even when the limitations of the model are discussed, it is not abandoned.<\/p>\n

      The inadequate treatment of the wave\u2013particle problem in most courses:<\/strong>
      \nMisleading formulations about the coexistence of the wave and particle models are often used, steering students\u2019 ideas in the wrong direction.<\/p>\n

      Problems with the concept of matter waves:<\/strong>
      \nStudents likewise fail to interpret this concept in the intended way.<\/p>\n

      Content structure of the concept<\/h3>\n

      The aim was to create a course that \u201con the one hand is compatible with all curricula and on the other hand sets new accents through a modified description of the content and an arrangement of the subtopics that differs from the usual proposals. The central aim of this concept is to make it easier for students to understand the basic principles of quantum physics by viewing the observed quantum phenomena through the lens of modern physics from the very beginning\u201d (Fischler & Lichtfeldt 1994). References to classical physics are to be avoided.<\/p>\n