Introduction to Quantum Confinement: From Carrots to the Aharonov–Bohm Effect

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Abstract

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This lecture introduces the concept of quantisation and demonstrates how geometry and topology shape quantum phenomena at the nanoscale. Starting from the Schrödinger equation, we will examine how different boundary conditions restrict the allowed wavefunctions. Using the particle-in-a-box model, we will build intuition for nanoscale electronic confinement and energy quantisation. We will use this to explain the colour of carrots and quantum dots. Next, we will extend the discussion to the particle-on-a-ring model, which leads to the quantisation of angular momentum. This sets the stage for the celebrated Aharonov-Bohm effect, in which an enclosed magnetic flux modifies the allowed energy states despite the absence of local fields.

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About the Speaker

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Dr Hariom Jani is a recipient of the Royal Society University Research Fellowship, leading the group on Magnetic Quantum Materials at the University of Oxford. He is also a Visiting Researcher at CNRS-Thales (France). Previously, he held a Marie Curie Fellowship at Oxford and obtained his Ph.D. from NUS (Singapore). His research led to the discovery of antiferromagnetic topology and emergent charges. He has received 9 awards, including Lindau Young Scientist grant (Lindau Nobel Foundation), Emerging Investigator Prize (Institute of Physics Singapore), and Young and Brilliant Lectureship (European Physics of Magnetism). His work has received >1600 citations with key publications recognised as Highly Cited Papers. He is passionate about making science education engaging and has worked with the Ministry of Education to design fun science demonstrations for schools. He also serves on the international user committee at UK’s flagship facility – Diamond Light Source.