Educational path proposals on modern physics and in particular quantum mechanics by means of two-states system Marisa Michelini1, Lorenzo Santi1, Alberto Stefanel1, Sergej Feletic2 1Physics Education Research Unit; Department of Mathematics, Computer Science, Physics, University of Udine, Italy 2Faculty of Mathematics and Physics, University of Ljubljana, Slovenja marisa.michelini@uniud.it; lorenzo.santi@uniud.it; alberto.stefanel@uniud.it, sergej.faletic@fmf.uni-lj.si

Educational Dirac approach to QM: PERU - educational proposals for MP: Diffraction as bridge to QP, Optical Spectroscopy, RBS; Cross Section, Electrical Transport Properties of matter, Superconductivity, Mass-Energy, QM. Educational Dirac approach to QM: On the disciplinary level: the concept of state and the superposition principle. On the didactic level: linear polarization as a quantum dynamical property of photons (lab exp and single photon ideal exp with JQM from lab exp on Malus law to ideal single photon exp: preparation of polarized photons; detection Interaction of photons-Polaroids: mutually exclusive & incompatible properties uncertainty principle quantum indeterminism identity of quantum systems Iconographic representation distinguish between the property (eigenvalue) and the state (eigenvector), bringing them towards the vector representation of state. Interaction of photons-birefringent crystals  impossibility of attributing a trajectory. The problem of quantum theory of measurement, of describing macro-objects and non-locality The formal description of the explored processes is in two state vector space. PERU= Physics Education Research Unit of UNIUD. A series of educational proposals for modern physics in secondary school and in introductory courses at university developed in Udine University are relative to Diffraction, Optical Spectroscopy, Rutherford Backscattering Spectroscopy, Cross Section, Electrical Transport Properties of matter, Superconductivity, Mass-Energy, Quantum Mechanics (QM). On the disciplinary level, the course begins with the concept of state and the superposition principle. On the didactic level, the linear polarization was chosen as a quantum dynamical property of photons and it is explored in the lab by means of simple hands-on experiments and of quantitative measurement with on-line sensors. An open environment simulation system (JQM) offers the opportunity to explore ideal experiments and to develop interpretative ideas. Starting from the experimental Malus law obtained in Lab with light beams, students discuss how to prepare polarized light and how to detect it. The polarization as a property of a single photon is confirmed by the validity of Malus law at very low light intensity and suggests to interpret it as the probability of photon transmission. The interaction of photons with Polaroids with different permitted directions identifies mutually exclusive and incompatible properties. The uncertainty principle, the quantum indeterminism, the identity of quantum systems are basic concepts discussed considering photons, which have been prepared using a polaroid-polarizer and interacting with a polaroid-analyser. An iconographic representation is used to help students distinguish between the property (eigenvalue) and the state (eigenvector), bringing them towards the vector representation of state. The interaction of photons with birefringent crystals allows connecting the quantum behaviour with the impossibility of attributing a trajectory to single photons (a quantum system). The problem of quantum theory of measurement, of describing macro-objects and non-locality are treated in the same context, with examples in the phenomenology of particle diffraction and analogies in the macroscopic world. The formal description of the explored processes is in two state vector space. MicheliniSantiStefanel MQUD

Researches on students’ learning Type of activity n activity h N schools N students age grade Apprenticeship° 8 9 192 16-18 13 Curricular* 10 6 208 18-19 Masterclass* 12 369 17-19 12-13 Summer School** 274 285 17-18 Total number of students involved in research studies: 862 * Sites: Udine; Treviso; Trieste; Gorizia; Tolmezzo; Asiago; Crotone; Ancona; Crema; Pordenone Types of schools: Scientific Lyceum 93%; technological institutes 7%. **: Selected high level students from schools from all Italy * & ** activities carried out by researchers ° apprenticeship of prospective teacher MicheliniSantiStefanel MQUD

CQ index based on Pre-Post test (N=126 students) CQ index is defined as Muller Wiesner 2002 suggested: For each of then question of the pre-post test (vedere articolo: I NUCLEI INTERPRETATIVI DEGLI STUDENTI SULLA MECCANICA QUANTISTICA: UNO STUDIO FENOMENOGRAFICO ) was attributed an evaluation from -2 (completely classical vision) to +2 (completely quantum vision); -1 was attributed to Hidden variables typo answers. I dati si riferiscono a un campione di 126 studenti ai quali è stato somministrato lo stesso pre test/post test. Con altri gruppi di studenti sono state effettuati altri tipi di analisi, in particolare guardano a come gli studenti hanno risposto nei tutorial  vedere bibliografia Distribution of CQ values in pre-test (black) and post-test MicheliniSantiStefanel MQUD

Profiles from pre-test and post-test (N=126) Qualitative analysis of tutorial and tests was performed, defining operatively categories of students’ answers by their own sentences. Profiles distinguishing between the classical point of view, the quantum way of thinking and also individuating when students developed ides coherent with a hidden variable approach emerged in the analysis of students’ reasoning. MicheliniSantiStefanel MQUD