The group theory of the harmonic oscillator with applications in physics.
| dc.contributor.author | Haskell, T. G. | |
| dc.date.accessioned | 2017-04-27T20:38:24Z | |
| dc.date.available | 2017-04-27T20:38:24Z | |
| dc.date.issued | 1972 | en |
| dc.description.abstract | The possibility of the group SU₃ being used in the description of the (d+s)N and (d+s)npm many-electron complexes is examined by symmetrization of the Coulomb Hamiltonian. By dividing the Coulomb interaction into symmetry conserving and symmetry violating terms it is found that while the SU₃ scheme tends to give a better description in the (d+s)N case it shows no improvement over the configurational scheme in the (d+s)npm complex. The scheme is, however, very useful for the calculation of matrix elements of operators normally found in atomic spectroscopy and a complete set of symmetrized , scalar, Hermitian spin-independent two particle operators acting within (d+s)npm configurations is constructed. The radial wavefunctions of the harmonic oscillator are found to form a basis for the representations of the group 0(2,1) in the group scheme Sp(6,R) ⊃ S0(3) x 0(2,1). The operators Tkp = r2k are shown to transform simply under the action of the group generators. The matrix elements of Tkq and a selection rule similar to that of Pasternack and Sternheimer are derived. Finally the rich group structure of the harmonic oscillator is investigated and a dynamical group proposed which contains, as subgroups, the groups Sp(6,R), SU(3), H₄ and the direct product 0(2,1) x S0(3). Some remarks are made about contractions of groups, semidirect and direct products, and the generalization of the method to n-dimensions. | en |
| dc.identifier.uri | http://hdl.handle.net/10092/13410 | |
| dc.identifier.uri | http://dx.doi.org/10.26021/8330 | |
| dc.language | English | |
| dc.language.iso | en | |
| dc.publisher | University of Canterbury | en |
| dc.rights | All Rights Reserved | en |
| dc.rights.uri | https://canterbury.libguides.com/rights/theses | en |
| dc.title | The group theory of the harmonic oscillator with applications in physics. | en |
| dc.type | Theses / Dissertations | en |
| thesis.degree.discipline | Physics | en |
| thesis.degree.grantor | University of Canterbury | en |
| thesis.degree.level | Doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |
| uc.bibnumber | 342336 | en |
| uc.college | Faculty of Science | en |