The resurgence of interest in properties of molecules of icosahedral symmetry follows the diswvery of the Cm molecula Because of the high symmehy almost all the electronic and vibrational states are highly degenerate, so m dealing with properties of these systems their Jahn-Teller i n i d o m must almost always be allowed for. In this p a p we explore the gmund states of the G @ (s f 3 h) coupling scheme and those of the WO subsystem,
We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour. (2) We have also shown in part (1) (3) of this paper, that QED with the same transformational behaviour also holds in a second space which we called M-space. Here we use Mspace to show that QED can be reduced to two simple rules for a twobody interaction.
We extend the standard definition of reduction factors (Ham factors) in strongly coupled Jahn-Teller (m) systems. Our aim is to cover linear IT systems in which the vibronic ground state at strong coupling is in close proximity in energy lo low-lying excited states belonging to singlet and non-uivial irreducible representations of the IT cenve. Such a stmcture of low-lying vibronic states is present in Ihe linear IT systems of the icosahedral orbital quartet and quintet, G md H. We calculate all the standard reduction factors as well I extended matrix elements. for the icosahedral Systems G 0 g, G @ h and H 0 fi. We d c u l x e the matrix of Ham factors needed to handle the extra multiplicity of an H operator in an H state A dinct group-theoretic31 approach which explains the origins of various features of our analysis is included.
When students of the physical sciences transition from school to university, they discover that knowledge of calculus is as vital as arithmetic, and that there is precious little useful information written without calculus. However, the lack of calculus in pre-university physics studies persists, especially in its application to the modelling of physical systems. Introductory courses at university in calculus often have a very different style to school-level work, and consequently many students find the step up difficult. This paper hopes to convey some examples of school-level work in numerical methods that can provide useful visualisations to aid comprehension and to incentivise the acquisition of skills in calculus. The modern pre-university student of the physical sciences would also do well to develop the precursors to coding, and learn the basics of modelling using spreadsheets.
We complete our previous (1,2) demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation, (5) including fine structure. We complete our previous derivation (3) of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.
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