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Quantum Mechanics$
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P.J.E. Peebles

Print publication date: 2019

Print ISBN-13: 9780691209821

Published to Princeton Scholarship Online: May 2021

DOI: 10.23943/princeton/9780691209821.001.0001

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Perturbation Theory

Perturbation Theory

(p.259) Chapter 5 Perturbation Theory
Quantum Mechanics

P.J.E. Peebles

Princeton University Press

This chapter examines applications drawn from perturbation theory. The main topic in perturbation theory is the energy and spontaneous decay rate of the 21-cm hyperfine line in atomic hydrogen. Before there were electronic computers, people had quite an accurate theoretical understanding of the energy levels in helium and more complicated systems. The trick was (and is) to find approximation schemes that treat unimportant parts of a physical system in quite crude approximations while reducing the interesting parts to a problem simple enough that it is feasible to compute but yet detailed enough to yield accurate results. The approximation methods in the chapter deal with the effects of small changes in the Hamiltonian, resulting for example from the application of a static or time variable electric or magnetic field. This may cause small changes in energy levels, and it may induce transitions among eigenstates of the original Hamiltonian.

Keywords:   perturbation theory, atomic hydrogen, energy levels, physical system, approximation methods, Hamiltonian, eigenstates

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