Continutation of the Wave Function for Higher Angular Momentum States toDDimensions: II. Elimination of Linear Dependencies
✍ Scribed by M. Dunn; D.K. Watson
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 517 KB
- Volume
- 251
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
In a previous paper the authors have developed a finite expansion for the wave function which allows the methods of dimensional scaling to be applied to higher angular momentum states. The terms in the expansion, though, are not necessarily linearly independent and so the expansion requires a little refining. The sources of linear dependence in the expansion for the wave function are explored and protocols for dealing with them are presented. 1996 Academic Press, Inc. I. INTRODUCTION Consideration of physical systems in spatial dimensions D other than three offers new perspectives on their properties and provides new calculational tools for their study [1, 2]. In the former case, for finite systems, these include otherwise unexplained similarities between states of different angular momenta (interdimensional degeneracies) [3 8], a new model of doubly excited states of two electron atoms (bent rovibrator) [9], a rigorous version of the qualitative electron-dot formulas widely used in chemistry [10], Hunds rules [11], model-independent fewbody properties (Post inequalities) [11 14], properties of circular and near-circular Rydberg states of atomic systems in magnetic fields [15], and near threshold Stark resonances [16]. In the latter category are dimensional perturbation [1, 2, 15, 17 29], dimensional interpolation [1, 10, 30 32], dimensional renormalization [1, 33, 34], and sub-Hamiltonian approaches [35 37].
Although some progress has been made [3 7, 26, 37, 38], extending the above methods to higher angular momentum states of multi-particle systems in a systematic way has proven problematical. The direct approach of expanding the wave function in terms of generalized Wigner rotation matrices in D dimensions achieves the goal of ``factoring out'' the rotational degrees of freedom, that multiply article no.