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CRC Press eBooks

Applications II

Nandita Rudra

Published Aug 19, 2019• 0 citations
Publisher

Abstract

In this chapter we would consider motion in three dimensions. In § (10.1) we would study Hydrogen Atom . And in the next section we would consider motion of a charged particle in magnetic field, including Landau Levels and Aharonov Bohm Effect .
DOI
10.1201/9780429325762-10

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In two-dimensional space, the topological coupling arising between charged particles with attached magnetic fluxes, via the Aharonov–Bohm effect, causes distinguishable particles to effectively acquire quantum statistics: a nontrivial quantum phase is generated when a particle of one species encircles one of a different species. We discuss a number of exact and numerical results concerning distinguishable particles with fractional statistics. Just like for anyons, the spectrum of such particles confined to the lowest Landau level of a strong magnetic field can be found exactly. Then a system of particles in the presence of static magnetic fluxes (equivalent to particles with infinite mass) is considered, and the low-lying states of one particle in the presence of two fluxes and two particles in the presence of one flux are analyzed.