Heisenberg’s Uncertainty Principle A First Look at Quantum Mechanics and Its Extensions

PDF
Published: Jan 12, 2026
DOI: https://doi.org/10.12681/osj.44027
Keywords:
Heisenberg’s uncertainty principle Wave-particle duality Bohr model
Marina Giannakopoulou
a:1:{s:5:"en_US";s:61:"M. Giannakopoulou, 11th Grade, Athens College, Athens, Greece";}
Abstract

Based on the author’s 2024-2025 Middle Years Program Personal Project, the present work introduces Heisenberg’s uncertainty principle. It is a product of secondary research, which opts to render quantum mechanics accessible to high-school students. Emphasis is primarily given to wave-particle duality, the de Broglie Hypothesis, state vectors, wavefunctions, probability density, and the Bohr model.

Article Details
  • Section
  • Greece
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Authors who publish with this journal agree to the following terms:

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution licence that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g. post it to a repository), with an acknowledgement of its initial publication in this journal.

Authors are permitted and encouraged to post their work online prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

Downloads
Download data is not yet available.
References
References
“Bohr's Atomic Model.” Libre Texts Chemistry, Libre Texts Libraries, n.d., chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/05%3A_Electrons_in_Atoms/5.06%3A_Bohr's_Atomic_Model. Accessed 5 Jan. 2025.
“Conjugate Observables in Quantum Mechanics.” The Quantum Well, Obsidian Publish, n.d., publish.obsidian.md/myquantumwell/Quantum+Mechanics/Quantum+Measurement/Conjugate+observables+in+quantum+mechanics. Accessed 2 Jan. 2025.
Dalal, Mandeep. A Textbook of Physical Chemistry – Volume 1. Dalal Institute, 1 Jan. 2018, pp. 52-54, 24-25, 28, 63-64.
Dwyer, David. Theoretical Physics. 2023, pp. 113-118, 94-95.
Griffiths, David J., and Darrell F Schroeter. Introduction to Quantum Mechanics. Cambridge University Press, 2018, pp. 17-19, 35, 119, 142, 148, 151.
Hilgevoord, Jan, and Jos Uffink. “The Uncertainty Principle.” Stanford Encyclopedia of Philosophy, The Metaphysics Research Lab, 2016, plato.stanford.edu/entries/qt-uncertainty/. Accessed 2 Jan. 2025.
Merzbacher, Eugen. Quantum Mechanics. John Wiley and Sons, Inc, 1998, pp. 2, 4, 8, 15-18, 217-219.
Pultarova, Tereza. “The Bohr model: The famous but flawed depiction of an atom.” Space.com, Future US, 31 Oct. 2022, www.space.com/bohr-model-atom-structure. Accessed 5 Jan. 2025.
“Quantum mechanics.” University of Waterloo, University of Waterloo, 2025, uwaterloo.ca/institute-for-quantum-computing/resources/quantum-101/quantum-mechanics. Accessed 2 Jan. 2025.
Schreiber, Barbara A, et al. “Uncertainty Principle.” Britannica, Encyclopedia Britannica, 2024, www.britannica.com/science/uncertainty-principle. Accessed 2 Jan. 2025.
Susskind, Leonard, and Art Friedman. Quantum Mechanics. Penguin Random House, 2015, pp. xix, xx.
Figure Credits
Arrazola, Juan Miguel. “Anyone can understand quantum mechanics — Part 1.” Qonaom, n.p., 2 May 2016, qonaom.wordpress.com/2016/05/02/anyone-can-understand-quantum-mechanics-part-1/. Accessed 2 Jan. 2025.
Ball, James. “An Experiment Involving Heisenberg’s Uncertainty Principle.” OART Newsletter, Ontario Association of Physics Teachers, 29 Jan. 2016, newsletter.oapt.ca/files/Uncertainty-Experiment.html. Accessed 2 Jan. 2025.
“Bohr Model.” Britannica, Encyclopedia Britannica, 19 Dec. 2024, www.britannica.com/science/Bohr-model. Accessed 5 Jan. 2025.
“3D Complex Wavefunction with Corrected Projections and Probability Density [Graph]” prompt. Google Gemini, Gemini 3 Pro, Google, 28 Dec. 2025, gemini.google.com.
Graham, Michael. “Rafael Nadal opens up on water-bottle obsession, saying: ‘If they aren’t right, I can’t concentrate on the game’.” Tennis Head, Tennishead.net, 7 Feb. 2020, tennishead.net/rafael-nadal-opens-up-on-water-bottle-obsession-saying-if-they-arent-right-i-cant-concentrate-on-the-game/. Accessed 5 Jan. 2025.
OpenStax College. “Young’s Double Slit Experiment.” Physics, n.p., n.d., courses.lumenlearning.com/suny-physics/chapter/27-3-youngs-double-slit-experiment/. Accessed 22 Aug. 2025.
“Research Shows Rituals Have Positive Impact on Mental Performance.” Optimize Mind Performance, Optimize Mind Performance, 18 May 2023, optimizemindperformance.com/study-shows-rituals-have-positive-impact-on-performance/. Accessed 5 Jan. 2025.
“Wavefunction Comparison in the Position and Momentum Space: All Cases [Graph]” prompt. Google Gemini, Gemini 3 Pro, Google, 29 Dec. 2025, gemini.google.com.
“Werner Heisenberg (1901- 76).” A History of Science, n.p., n.d., geoffneilsen.wordpress.com/navigation/twentiethcentury-draft/werner-heisenberg-1901-76/. Accessed 2 Jan. 2025.