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Hybrid Phonons in Nanostructures$
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Brian K. Ridley

Print publication date: 2017

Print ISBN-13: 9780198788362

Published to Oxford Scholarship Online: April 2017

DOI: 10.1093/acprof:oso/9780198788362.001.0001

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Scalar and Vector Fields

Scalar and Vector Fields

Chapter:
(p.55) 5 Scalar and Vector Fields
Source:
Hybrid Phonons in Nanostructures
Author(s):

B. K. Ridley

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198788362.003.0007

Those quantum structures describable in terms of Cartesian coordinates (e.g. the quantum well) can be treated with the minimum of formality. Turning to quantum structures describable in terms of curvilinear coordinates, it is convenient to establish a more formal basis in order to describe the LO and TO modes in terms of scalar and vector potentials. This chapter covers: nanostructures described by curvilinear coordinates, the Helmholtz equation, scalar and vector potentials, and results for the cylinder and the sphere.

Keywords:   Helmholtz equation, sphere, scalar fields, vector fields, nanostructures

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