By R. E. Raab

Raab and de Lange, either affiliated with the college of Chemical and actual technological know-how on the college of Natal, South Africa, provide a close advent to classical, quantum-mechanical, and symmetry features of multipole thought in electromagnetism. they give thought to either cost distribution in a vacuum and, through extension, in bulk subject, and supply an account of a few of the successes and screw ups of the direct program of multipole thought to macroscopic media. Required history features a wisdom of introductory electromagnetic idea and introductory non-relativistic quantum mechanics. The booklet is shipped within the US by way of Oxford collage Press

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Y. (1998). Classical electrodynamics, pp. 41-42. Perseus, Reading, MA. D. and Pople, J. A. (1955). Theoretical studies of the Kerr effect I: deviations from a linear polarization law. Proceedings of the Physical Society A, 68, 905-909. [9] Buckingham, A. D. (1979). Polarizability and hyperpolarizability. Philosophical Transactions of the Royal Society London A, 293, 239—248, and references therein. 30 CLASSICAL MULTIPOLE THEORY [10] Buckingham A. D. (1959). Direct method of measuring molecular quadrupole moments.

4) is simplified if we work in the gauge with at each particle. 60). 16). 3). 66) yields where EI and EI are the values at the origin. 68) we have omitted a dc term coming from the lower limit of integration. 60). Consequently this first contribution to the interaction between a harmonic plane wave and a charge distribution is termed the electric dipole approximation. 68) also contains a term in the time derivative of the electric field. 12. 16) wsn = 0 when s = n. 69) as where p\ ' = (pi)nn is the permanent electric dipole moment in the state n^), and Because p is Hermitian, these frequency-dependent polarizabilities possess the intrinsic symmetries Here, and in what follows, we use the same symbol to denote both a frequencydependent polarizability and the corresponding static limit.

Imrie, D. , and Raab, R. E. (1998). Measurement of the electric quadrupole moments of CC>2, CO, N2, Cl2 and BFs. Molecular Physics, 93, 49-56. D. and Stiles, P. J. (1972). Magnetic multipoles and the "pseudo-contact" chemical shift. Molecular Physics, 24, 99-108. [17] See Ref. 6, Sect. 5. D. B. (2001). Historical roots of gauge invariance. Reviews of Modern Physics, 73, 663-680, for the association of this gauge with L. V. Lorenz. , and Raab, R. E. (1992). Multipole moments and Maxwell's equations.