ArticlePDF Available

Abstract and Figures

With new quantum technologies and new applications comes a new need for specialists, the new quantum workforce. This brings new challenges for education that the typical quantum mechanics courses for physicists do not address. Requirements for the future quantum workforce need to be collected and training programmes created. In between, there should be a European competence framework on which to build the training programmes. One goal of the European Flagship project QTEdu is to develop this framework for second-generation quantum technologies. The Delphi study presented here serves as a basis for this: The aim is to identify knowledge and competences in the field of quantum information technologies, which are partly already needed in industry today, but especially in the future.
Content may be subject to copyright.
Journal of Physics: Conference Series
PAPER • OPEN ACCESS
Requirements for future quantum workforce – a
Delphi study
To cite this article: F Gerke et al 2022 J. Phys.: Conf. Ser. 2297 012017
View the article online for updates and enhancements.
You may also like
STOCHASTIC SIMULATION TO
PROJECT SUPPLY OF THE
KAZAKHSTAN GENERAL PRACTICE
WORKFORCE TO 2030
Berik Koichubekov, Azamat Kharin, Marina
Sorokina et al.
-
Risk of diseases of the circulatory system
after low-level radiation exposure—an
assessment of evidence from occupational
exposures
Richard Wakeford
-
A review of radiation doses and
associated parameters in Western
Australian mining operations that process
ores containing naturally occurring
radionuclides for 2018–19
Martin I Ralph, Andrew Chaplyn and
Marcus Cattani
-
This content was downloaded from IP address 109.43.48.209 on 26/07/2022 at 18:25
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd
GIREP Malta Webinar 2020
Journal of Physics: Conference Series 2297 (2022) 012017
IOP Publishing
doi:10.1088/1742-6596/2297/1/012017
1
Requirements for future quantum workforce a Delphi study
F Gerke1,a, R Müller1,b, P Bitzenbauer2,c, M Ubben3,d and K-A Weber4,e
1TU Braunschweig, Institut für Fachdidaktik der Naturwissenschaften, Bienroder Weg 82,
38106 Braunschweig, Germany
2 FAU Erlangen, Physikalisches Institut, Staudtstr. 7, 91058 Erlangen, Germany
3WWU Münster, Institut für Didaktik der Physik, Wilhelm-Klemm-Str. 10, Germany
4LU Hannover, Institut für Quantenoptik, Welfengarten 1, 30167 Hannover, Germany
aCorresponding author: F Greinert née Gerke, f.greinert@tu-braunschweig.de
b email: rainer.mueller@tu-bs.de
c email: philipp.bitzenbauer@fau.de
d email: malte.ubben@uni-muenster.de
e email: weber@iqo.uni-hannover.de
Abstract. With new quantum technologies and new applications comes a new need for
specialists, the new quantum workforce. This brings new challenges for education that the typical
quantum mechanics courses for physicists do not address. Requirements for the future quantum
workforce need to be collected and training programmes created. In between, there should be a
European competence framework on which to build the training programmes. One goal of the
European Flagship project QTEdu is to develop this framework for second-generation quantum
technologies. The Delphi study presented here serves as a basis for this: The aim is to identify
knowledge and competences in the field of quantum information technologies, which are partly
already needed in industry today, but especially in the future.
1. Introduction
The increasing relevance of quantum technologies in Europe [1] poses new challenges for the
(university) education of specialists in this field - not only in physics, but also in engineering [2, 3]. One
goal of our research is the development of a competence framework for second-generation quantum
technologies within the European Quantum Flagship [4] project “Coordination and Support Action for
Quantum Technology Education” (QTEdu CSA) [5]. On the basis of this framework, further educational
concepts, (master) courses of study or optional specialisation subjects can be developed. The results of
this study will be used to prepare said competence framework. One additional important aspect is also
the extraction of applications that are deemed crucial for the future of the development of quantum
technologies.
They can then in turn be used to determine requirements for physics teaching in order to lay the
foundation for higher education. It is apparent that not only engineers will have to deal with quantum
technologies in the future - moreover, pupils at school should already be made aware to the social
relevance of quantum physics, which is consequently also a goal of the Quantum Flagship. Teachers of
physics should therefore not only be able to solve the Schrödinger equation, but also acquire more
general skills as they will appear in the competence framework. For this reason, experts with a teaching
background were also included in our study.
Since this field is just forming, there is no work of this kind yet, meaning that we also aim to lay the
foundation in this regard.
GIREP Malta Webinar 2020
Journal of Physics: Conference Series 2297 (2022) 012017
IOP Publishing
doi:10.1088/1742-6596/2297/1/012017
2
2. About the Study
Study design, methods of data analysis and information on the professional background of the
participants are presented in this section.
2.1. Delphi Method
The Delphi method can be used to identify and qualify expert opinions and is characterized by the
iterative process of questioning and feedback, which in turn forms the starting point for the next
survey [6]. As the investigated field of second generation quantum technologies is new and therefore
only a few experts can be interviewed, the study is broadly based and the Delphi method is used as it
was deemed the most suitable way of collecting and structuring relevant empirical data. A strong point
of this approach is that the experts can reflect and comment on other experts’ opinions and statements
without being influenced by group behaviour, paving the way for a potentially more diverse set of data.
In physics education, the Delphi method is well established and several Delphi studies have been carried
out in recent decades [7, 8].
The procedure of this study is shown in figure 1. In the pilot round around March 2020, a smaller
group of experts answered mostly open questions. It gave an overview of this open field for the first
time. The answers of the pilot round were then bundled and opinions collected. In the first main round,
which took place in autumn 2020, these assessments were presented to a larger group of people than in
the pilot for evaluation and completion. A second main round will be used for the final evaluation, so
that on this basis the development of a competence framework will be possible. It will take place around
spring 2020. Note that the Delphi method is exploratory, i.e. we aim to open up the new research field
of QT workforce but we do not want to clarify concrete research questions.
2.2. Data analysis
There were two main types of data resulting from the pilot and the first main round. The first type is
quantitative and comes from close-ended questions. The other type is qualitative data from open-ended
questions. For these, a qualitative content analysis [9] was conducted using MaxQDA [10] version 12
and some exemplary answers were selected. Thereafter, the answers were categorised and for example,
as shown in figure 2, these categories were then visualised by giving exemplary answers in the format
"quote" (answer ID). According to Landis and Koch [11], intercoder reliability was almost perfect for
all categories between 0.82 and 0.89) in the pilot round for 6 (represents 20%) randomly selected
responses.
Figure 1. Study design and timetable.
GIREP Malta Webinar 2020
Journal of Physics: Conference Series 2297 (2022) 012017
IOP Publishing
doi:10.1088/1742-6596/2297/1/012017
3
2.3. Participants
The questions on the professional background showed that in the pilot round, the smaller group of
experts (N=28) mainly assigned themselves to science (almost 90%) or education (about 80%) and about
60% to research/development, while only 10-15% assigned themselves to industry/economy or
computer science/IT.
In the first main round, the group size more than doubled (66 evaluable datasets). Now, 35-40%
assigned themselves to industry/economy or computer science/IT, while the proportion of participants
who assigned themselves to science or education decreased to 50-60%. Slightly more (approx. 65%)
assigned themselves to research/development. Other areas were selected from less than 20%. Details are
shown in table 1.
Table 1. Absolute number of participants who assigned themselves to the professional fields.
Industry/
Economy
Computer
science/ IT
Science
Training/
Instructor
Research/
Development
Application/
Use
Other
N
Pilot
4
3
25
3
17
2
1
28
Main 1
24
22
40
5
41
10
2
65
3. Selected interim results
The future quantum workforce will be made up of people who work with quantum technologies, such
as engineers, computer scientists, chemists, biologists, but who do not have such a strong (quantum)
physics background as physicists. In order to summarise the knowledge and competence areas required
for this group of people, a term is needed, and in the Flagship context the term “Quantum Awareness”
is used. We discuss this term and identify possible alternatives with the help of expert opinions.
In addition, assessments of the relevance of the new quantum technologies, e.g. for industry, were
collected. Some initial results on these relevance assessments of the pilot round have already been
presented in [12] and are not the focus of this article.
3.1. Using the Flagship term “Quantum Awareness”
The term "Quantum Awareness" was introduced to denote a basic, phenomena-oriented understanding
of quantum physics. However, this term is frequently associated with esotericism. Therefore, the use of
this term was criticised in the pilot round.
Thus, in the main round 1, the experts had to answer the question whether this term should be used
or what better terms the participants could think of. 29 participants wanted to stay with “Quantum
Awareness”, while also 29 made other suggestions. Terms such as “Quantum Technology Awareness”
(mentioned 4 times), “Quantum Knowledge” (2 times), “Quantum Readiness” (2) or “Quantum
Literacy” (2) were suggested. In the second main round, these suggestions will now be rated in order to
provide a term which is community-based.
3.2. Competences and contents for the future quantum workforce
In the pilot round, there were open-ended questions about which competences and contents would be
necessary, desirable or less relevant for the future quantum workforce. These answers were subjected to
a qualitative content analysis [9], which led to four areas of possible central competences and contents
for future quantum workforce. Figure 2 shows these areas with exemplary answers in quotation marks
and with the answer ID named, i.e. having the format "answer text" (ID).
The first area covers the basic principles or phenomena such as the measurement effects,
superposition and entanglement or non-locality. But also the "standard" quantum mechanics including
the harmonic oscillator or the Schrödinger equation were mentioned. In the second area, we clustered
mathematics. The answers varied from very general (“Good background”) to more concrete (“Finite-
dimensional complex Hilbert spaces”) or focusing on qubit or state description. The third section collects
answers on the physics background. They include more general answers, concrete physics or
technologies and even address awareness of the conceptual differences between classical and quantum
physics and the fact that (first generation) quantum technologies are already in use. Finally, the last area
includes answers regarding concrete applications or general answers to how they work and what the
GIREP Malta Webinar 2020
Journal of Physics: Conference Series 2297 (2022) 012017
IOP Publishing
doi:10.1088/1742-6596/2297/1/012017
4
novelty is. In the overall picture, we see many answers in the first area on the basics principles, less on
mathematics, a little more on the physical background and again less on concrete applications. This map
was used in the main round 1 questionnaire as a suggestion for the formulation of more concrete
competences.
Figure 2. Competences and contents mentioned in the pilot.
GIREP Malta Webinar 2020
Journal of Physics: Conference Series 2297 (2022) 012017
IOP Publishing
doi:10.1088/1742-6596/2297/1/012017
5
3.3. Using pilot results in the first main round: first results from round 1
For the first main round, participants were shown the map (figure 2) for input/inspiration and asked to
focus on a specific subfield. After naming such a subfield, they were asked to fill in a table to collect
prestructured answers. The structure - inspired by Häußler et al [8] - was a three-step format: addressing
the concrete competence, what this competence would be useful for and what level of expertise would
be needed. For the last item - the level of competence - the participants were asked to distinguish between
“users” (U: ...) and “developers” (D: ...). An exemplary answer for the three aspects in a subfield was
given to the participants and is shown in table 2. It can be read as follows: The “understanding of qubit
operations and quantum gates” would be useful for “composing quantum algorithms and applying them
to specific tasks”, and the needed level of expertise would be for users to have a “deeper basic knowledge
of the qubit concept and the effects of different operators on a formal-logical level. No specific
knowledge of physical implementation of the operators and the qubits themselves is needed.”
Table 2. Example for the prestructured question in the main round 1.
subfield
competence
useful for
needed level of expertise
quantum
software
development
understanding of
qubit operations and
quantum gates
composing quantum
algorithms and applying
them to specific tasks
U: deeper basic knowledge of the qubit
concept and the effects of different operators
on a formal-logical level. No specific
knowledge of physical implementation of the
operators and the qubits themselves is
needed.
This question provided about 180 individual competences for 55 subfields. Three examples of these
mentioned competences together with the chosen subfields are listed in table 3.
Table 3. Selected answers from the main round 1.
subfield
competence
useful for
needed level of expertise
quantum
communication
understanding of
quantum repeaters
determining quantum
communication in
fibre/free space
U: deeper basic knowledge of how quantum
repeaters work. No specific knowledge of
physical implementation of the specific
hardware for quantum repeaters. D: deeper
understanding of specific hardware and
implementation for quantum repeaters
quantum-
algorithm and
quantum-
software
development
knowledge of existing
quantum-algorithm
concepts both for
NISQ and FTQC
understanding and
developing novel
quantum algorithms
D: quantum-developers need to be fluent in
all existing quantum-algorithm concepts so
that they can build on those to develop novel
algorithms or so that they can apply them to
implement quantum solutions
quantum
sensing
programming skills
Data processing
D: good programming skills will help to
create an interface between the sensor and the
PC to see the measurement result
The first evaluation step was to sort the subfields into the four areas “Phenomena/ Basic Principles”,
Mathematics”, “Physical Background” and “Application” (see figure 2). Figure 3 shows in more detail
the sorting of the participants’ statements into these categories. The data shows a similar ratio as in the
pilot round: again, there were many participants who focused on the basics, less on mathematics and a
bit more on the physical background. But there were significantly more in the area of application,
painting a more detailed picture of this topic.
GIREP Malta Webinar 2020
Journal of Physics: Conference Series 2297 (2022) 012017
IOP Publishing
doi:10.1088/1742-6596/2297/1/012017
6
Figure 3. Sorting of the subfields mentioned in the main round 1 to give an impression of
the ratio of answers per area. Some answers are shortened to selected fragments. Each large
sticky note represents one answer, and the answers that fit into more than one area were
divided into smaller sticky notes connected by an arrow.
GIREP Malta Webinar 2020
Journal of Physics: Conference Series 2297 (2022) 012017
IOP Publishing
doi:10.1088/1742-6596/2297/1/012017
7
Next is the analysis and categorisation of the about 180 individual competences. This allows the
development of the concluding questionnaire and finally the creation of the competence framework on
the requirements for the future quantum workforce.
3.4 Discussion
In this article, we present first insights into the qualitative results of a Delphi study. With the help of
experts' opinions from research, industry and teaching, requirements for future quantum professionals
will be extracted. These can act as a basis for further education and training programmes today, and
especially in the future.
The results of the pilot and the first main round led to the identification of four preliminary
competence areas, namely basic principles or phenomena, mathematics, physical background and
applications. In line with the Delphi process, the second main round will be used to validate and refine
these competence areas. The aim is also to tackle existing limitations that are closely interwoven with
the Delphi research method: As is usual in Delphi studies, the researchers not only evaluate the collected
data using recognised empirical methods but they also always intervene in the course of the Delphi
study. For example, when it comes to the question of which results of the previous round are made
available in the next questionnaire and which are not. Furthermore, the sample size has to be mentioned,
and the fact that in the study reported here, mainly subjective assessments of the experts are collected.
For this reason, it is crucial to - in a next Delphi round - increasingly quantify the insights gained so far
so that preliminary results can be validated.
The results of this research may not only be of interest concerning the development of training
programmes for future quantum workforce. Much more, it is in line with physics education research
efforts on quantum physics as different teaching sequences on modern quantum physics in schools and
universities have been developed. For example, teaching sequences using the qubit approach [13, 14] a
quantum optics-approach [15, 16, 17], haptical approaches [18, 19], the double-well approach [20] or
presenting characteristic traits of quantum mechanics [21]. With modern advances in quantum
technologies, new potentials are now emerging for the teaching of modern quantum physics at all levels.
In this respect, the results of our Delphi study could give this debate a further impulse.
4. Conclusion
The pilot round and the first main round of the Delphi study have already produced some interesting
results. For example, the use of the term “Quantum Awareness” was criticized in the pilot round, which
led to a question in the main round 1 to evaluate the use or find alternatives. Therefore, in the main
round 2, selected proposals will be evaluated in competition with the above mentioned term.
In addition to that, the pilot round provided a first impression of possible competences and contents
for the future quantum workforce. These were used as input or inspiration in the main round 1 to collect
more concrete competences. The first analysis of the data of the main round 1 shows a plethora of
competences deemed to be necessary by the experts and also confirms some of the points and
observations extracted from the pilot round: the focus on quantum phenomena / basic principles with
less mathematics and some knowledge in the physical background are needed. This also leads to the
conclusion that in teaching quantum physics, it will be of utmost importance to not solely rely on
mathematics, but also to facilitate the conceptual development regarding topics in quantum physics.
The second main round will now be used for some evaluations and additions so that the competence
framework for the flagship project QTEdu CSA can be created based on broad expert opinion.
5. Acknowledgments
This study is part of a project that has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreement No 951787.
GIREP Malta Webinar 2020
Journal of Physics: Conference Series 2297 (2022) 012017
IOP Publishing
doi:10.1088/1742-6596/2297/1/012017
8
6. Authors’ ORCID iD
Franziska Greinert nee Gerke: 0000-0002-1997-0504
Rainer Müller: 0000-0003-1013-411X
Philipp Bitzenbauer: 0000-0001-5493-291X
Malte Ubben: 0000-0002-8041-5980
Kim-Alessandro Weber: 0000-0003-4509-7654
7. References
[1] Acín A et al. 2018 New J. Phys. 20(8) 080201
[2] Fox M F J, Zwickl B M and Lewandowski H J 2020 Phys. Rev. Phys. Educ. Res. 16(2) 020131
[3] Venegas‐Gomez A 2020 PhotonicsViews 17(6) 348
[4] VDI Technologiezentrum GmbH (Coordinator QFlag) 2021 Quantum Flagship qt.eu
[5] Macchiavello C (Coordinator QTEdu CSA) 2021 QTEdu - Coordination and support action for
Quantum Technology Education qt.eu/about-quantum-flagship/projects/education-coordination-
support-actions/
[6] Häder M 2009 Delphi-Befragungen: Ein Arbeitsbuch. (Wiesbaden: VS Verlag)
[7] Weber K-A. 2018 Quantenoptik in der Lehrerfortbildung (Berlin: Logos Verlag, Studien zum
Physik- und Chemielernen 269)
[8] Häußler P, Frey K., Hoffmann L, Rost J and Spada H 1980 Physikalische Bildung: Eine
curriculare Delphi-Studie Teil II (Kiel: IPN-Arbeitsberichte 42)
[9] Mayring P 2015 Qualitative Inhaltsanalyse (Weinheim: Beltz Verlagsgruppe)
[10] VERBI GmbH 2020 MaxQDA maxqda.com
[11] Landis J and Koch G 1977 Biometrics 33(4) 159-74
[12] Gerke F, Müller R, Bitzenbauer P, Ubben M and Weber K A 2020 Phydid B 437-43
[13] Dür W and Heusler S 2014 Phys. Teach. 52 489
[14] Michelini M, Ragazzon R, Santi L and Stefanel A 2000 Phys. Educ. 35 406
[15] Scholz R, Wessnigk S and Weber K A 2020 Eur. J. Phys. 41 055304
[16] Bitzenbauer P and Meyn J P 2020 Phys. Educ. 55 055031
[17] Bronner P, Strunz A, Silberhorn C and Meyn J P 2009 Eur. J. Phys. 30 345-353
[18] Ubben M and Heusler S 2018 Eur. J. Phy. 39(4)
[19] Heusler S and Ubben M 2019 Symmetry 11(3) 426
[20] Faletič S 2020 Eur. J. Phys. 41 045706
[21] Müller R and Wiesner H 2002 Am. J. Phys. 70 200
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
Quantum sensing, quantum networking and communication, and quantum computing have attracted significant attention recently, as these quantum technologies could offer significant advantages over existing technologies. In order to accelerate the commercialization of these quantum technologies, the workforce must be equipped with the necessary skills. Through a qualitative study of the quantum industry, in a series of interviews with 21 U.S. companies carried out in Fall 2019, we describe the types of activities being carried out in the quantum industry, profile the types of jobs that exist, and describe the skills valued across the quantum industry, as well as in each type of job. The current routes into the quantum industry are detailed, providing a picture of the current role of higher education in training the quantum workforce. Finally, we present the training and hiring challenges the quantum industry is facing and how higher education may optimize the important role it is currently playing.
Article
Full-text available
In this article, an approach to integrate contemporary quantum physics into secondary school teaching is presented. The Erlanger concept on quantum optics provides an experimental-based guideway to aspects of modern quantum physics. We avoid the traditional historical approach in order to overcome the lack of modern concepts of quantum physics. In an acceptance survey, initial empirical evidence for the acceptance of the developed explanatory approaches was evaluated.
Article
Full-text available
This paper presents an educational concept for promoting quantum teaching and learning via an educational structured quantum optical experiment. The experiment is designed to demonstrate the striking differences between classical physics and quantum physics, for example quantum interference of unbreakable photons (the ability of probabilities to interfere due to a phase sensitive superposition of states) and quantum nonlocality (there is no way to locate photonic states without a fundamental loss of information about the characteristics and a complete change of the state). For this proposal, we developed an experimental setup straightforward enough to be used in advanced physics courses even in secondary school student labs. To explain, or in a more quantum-semantic way, to interpret the experimental results quantitatively, we provide an appropriately rigorous quantum optical theory. Our model combines Laplace statistics (to access the statistical behaviour of photon counting) and basic vector calculus to calculate probabilities from the phase sensitivity of probability amplitudes. This article aims to contribute to further discussion and empirical research into novel teaching strategies for a more deeply conceptual approach to quantum theory.
Article
Full-text available
A generalization of the famous Dirac belt trick opens up the way to a haptic model for quantum phases of fermions and bosons in Hilbert space based on knot theory. We introduce a simple paper strip model as an aid for visualization of the quantum phases before and after Hopf-mapping, which can be extended to arbitrary spin states with almost no mathematical formalism. Knot theory arises naturally, leading to the Jones polynomials derived from Artin's braid group for fermionic knots and for bosonic links. The paper strip model explicitly illuminates the relation between these knots and links within the SU(2)-representation of spin-jstates in C 2j+1 before Hopf-mapping and the number p = 2j of nodes in the stellar representation in CP 1 after Hopf mapping.
Article
Full-text available
Within the last two decades, quantum technologies (QT) have made tremendous progress, moving from Nobel Prize award-winning experiments on quantum physics (1997: Chu, Cohen-Tanoudji, Phillips; 2001: Cornell, Ketterle, Wieman; 2005: Hall, Hänsch-, Glauber; 2012: Haroche, Wineland) into a cross-disciplinary field of applied research. Technologies are being developed now that explicitly address individual quantum states and make use of the 'strange' quantum properties, such as superposition and entanglement. The field comprises four domains: quantum communication, where individual or entangled photons are used to transmit data in a provably secure way; quantum simulation, where well-controlled quantum systems are used to reproduce the behaviour of other, less accessible quantum systems; quantum computation, which employs quantum effects to dramatically speed up certain calculations, such as number factoring; and quantum sensing and metrology, where the high sensitivity of coherent quantum systems to external perturbations is exploited to enhance the performance of measurements of physical quantities. In Europe, the QT community has profited from several EC funded coordination projects, which, among other things, have coordinated the creation of a 150-page QT Roadmap (http://qurope.eu/h2020/qtflagship/roadmap2016). This article presents an updated summary of this roadmap.
Article
There is no doubt, we are entering the second quantum revolution. Every week some exciting news about quantum technologies appears in the media. Nowadays, several countries worldwide have initiated a quantum program to develop this emerging market. However, this will require having a highly trained and skilled workforce. How can society be ready when the time comes?
Article
Quantum mechanics is one of the pillars of modern physics, however rather difficult to teach at the introductory level due to the conceptual difficulties and the required advanced mathematics. Nevertheless, attempts to identify relevant features of quantum mechanics and to put forward concepts of how to teach it have been proposed.1–8 Here we present an approach to quantum physics based on the simplest quantum mechanical system—the quantum bit (qubit). 1 Like its classical counterpart—the bit—a qubit corresponds to a two-level system, i.e., some system with a physical property that can admit two possible values. While typically a physical system has more than just one property or the property can admit more than just two values, in many situations most degrees of freedom can be considered to be fixed or frozen. Hence a variety of systems can be effectively described as a qubit. For instance, one may consider the spin of an electron or atom, with spin up and spin down as two possible values, and where other properties of the particle such as its mass or its position are fixed. Further examples include the polarization degree of freedom of a photon (horizontal and vertical polarization), two electronic degrees of freedom (i.e., two energy levels) of an atom, or the position of an atom in a double well potential (atom in left or right well). In all cases, only two states are relevant to describe the system.
Article
Single photons are used for fundamental quantum physics experiments as well as for applications. Originally being a topic of advance courses, such experiments are increasingly a subject of undergraduate courses. We provide interactive screen experiments (ISE) for supporting the work in a real laboratory, and for students who do not have access to a quantum optics laboratory. The main focus of the ISE is on undergraduate education, but some of the experiments are suitable for other levels of higher education as well.
Article
A possible strategy to introduce the basic formalism of the `Dirac formulation' of quantum mechanics without requiring an advanced mathematical or physical background is proposed, generalizing the description of a simple two-state system, namely the linear polarization of photons interacting with polaroids and birefringent crystals. The relation between physical observables and linear operators is discussed on both a conceptual and a formal level. A feasibility study has been performed in the final class of a Liceo.