Dimensional continuation in electronic structure and many-body problems
This dissertation concerns the development and application of new techniques for electronic structure calculations motivated by dimensional scaling (analytic continuation in the spatial dimensionality D followed by finitizing scalings). One desirable feature of dimensional scaling as applied to electronic structure problems is that it gives rise to two distinct singular (and hence simplifying) limits, namely D [yields] 1 and D [yields] [infinity]. A scaling procedure which is finitizing and uniform for 1 [le] D [le] [infinity] is presented. Dimensional limit results obtained with this scaling can be used to obtain quite accurate approximations to D = 3 eigenvalues. The procedure is demonstrated for H[sub 2][sup +] and for H[sub 2] in the Hartree approximation. For the latter problem both the D [yields] 1 and D [yields] [infinity] solutions are obtained for the first time. Another advantage of the dimensional scaling approach is its usefulness for studying correlation effects. This is demonstrated for the model many-body problem of N mutually gravitating bosons. The exact and Hartree D [yields] [infinity] solutions are derived (both in closed form), and combined with literature results for the exact and Hartree D [yields] 1 solutions (also both in closed form) to obtain approximate D = 3 solutions. For comparison, the Hartree D = 3 solution is also solved numerically. The dimensionally generalized hamiltonian used for this problem is obtained in a quite general form which should also be useful for other problems. A third benefit of dimensional scaling is that it provides conceptually simple models of electronic structure. The D [yields] [infinity] limit yields classical structures which are useful but by themselves are at best qualitatively correct. A procedure for generating classical representations which incorporates finite-D effects is presented.
- Research Organization:
- Harvard Univ., Cambridge, MA (United States)
- OSTI ID:
- 7262926
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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