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Essential Quantum Mechanics$
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Gary Bowman

Print publication date: 2007

Print ISBN-13: 9780199228928

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780199228928.001.0001

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Why Is the State Complex?

Why Is the State Complex?

(p.128) 10 Why Is the State Complex?
Essential Quantum Mechanics

Gary E. Bowman

Oxford University Press

This chapter begins with basic complex numbers, including their polar form and their representation with Argand diagrams. This leads naturally into a discussion of the phase of a complex number, and the roles of overall and relative phases. All this paves the way for consideration of the complex nature of quantum states. It is shown how, even for spin 1/2 systems, complex coefficients are required to represent adequately states, and the coefficients' phases play a crucial role. Changes in coefficients' phases — which can be brought about by a unitary operator — can alter probabilities, and the conditions under which this occurs are discussed. An example from spin 1/2 illustrates. Finally, the preceding ideas are discussed in the context of wavefunctions.

Keywords:   complex numbers, polar form, Argand diagram, phase, overall phase, relative phase, complex coefficient, unitary operator, wavefunction

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