Abstract
Assuming only a basic knowledge of quantum mechanics, we develop the quantum mechanics of angular momentum, distinguishing between orbital and intrinsic angular momentum or spin. Suitable basis states are introduced, as are the fundamental operators which act upon these. We consider the situation of just two spins interacting via an exchange interaction. This leads us to introduce other spin operators and evaluate their commutators. We discuss what happens when there are large numbers of interacting spins. Finally we introduce the infinite linear (i.e. one-dimensional) chain of spin-1/2 atoms. Some preliminary classical results for this model are given as background for the full quantum treatment which will be studied in detail in the following chapters.
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References
Cohen-Tannoudji, C., Diu, B., Laloë, F.: Quantum Mechanics I. Wiley Interscience, New York, NY (1977)
Kosterlitz, J.M., Thouless, D.J.: J. Phys. C Solid State Phys. 6, 1181 (1973)
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Parkinson, J.B., Farnell, D.J. (2010). Spin Models. In: An Introduction to Quantum Spin Systems. Lecture Notes in Physics, vol 816. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13290-2_2
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DOI: https://doi.org/10.1007/978-3-642-13290-2_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13289-6
Online ISBN: 978-3-642-13290-2
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