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1 - Quantum Many-Body Systems

Published online by Cambridge University Press:  23 July 2021

Tim Byrnes  and
Ebubechukwu O. Ilo-Okeke
Tim Byrnes
Affiliation:
New York University, Shanghai
Ebubechukwu O. Ilo-Okeke
Affiliation:
New York University, Shanghai
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Summary

This chapter introduces the basic theoretical tools for handling many-body quantum systems. Starting from second quantized operators, we discuss how it is possible to describe the composite wavefunction of multi-particle systems, and discuss representations in various bases. The algebra of Fock states is described for single and multi-mode systems, and how they relate to the eigenstates of the Schrodinger equation. Finally, we describe how interactions between particles can be introduced in a general way, and then describe the most common type of interaction in cold atom systems, the s-wave interaction

Keywords

Second quantizationbosonic annihilation and creation operatorsbasis transformationFock statesSchrodinger equationmany-body physicsinteractionss-wave scatteringmulti-particle wavefunction
Type
Chapter
Information
Quantum Atom Optics
Theory and Applications to Quantum Technology
 , pp. 1 - 9
Publisher: Cambridge University Press
Print publication year: 2021

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