Introduction and Review of Previous Literature
The purpose of this report is to provide students with a means to calculate the energy levels of impurity ions in solids and analyze experimental results. In order to achieve this goal it is necessary to review material which many readers may have been exposed to elsewhere. This review is rather brief, and the bibliography (sect. 1.4) includes references to specific sections of textbooks, monographs, or papers where the material is discussed in more detail. Unfortunately, as in most fields of science, a number of different notations (in various alphabets) are used in the literature; it is hoped that this review will help overcome some of this difficulty.
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Annotated Bibliography and References
- Condon, E. U., and H. Odabasi (1980), Atomic Structure, Cambridge University Press, Cambridge, U.K. Chapters 3 and 4 give a thorough discussion of the hydrogenic wave function. Pages 190 and 191 tabulate the radial wave functions.Google Scholar
- Judd, B. R. (1963), Operator Techniques in Atomic Spectroscopy, McGraw-Hill, New York, NY. This outstanding textbook is frequently referred to in this report; the book is almost completely free of typographical errors. The problems in general are very difficult and require considerable time. Only the preface and the first two pages are pertinent here.Google Scholar
- Leighton, R. (1959), Principles of Modern Physics, McGraw-Hill, New York, NY, chapter 5, The One Electron Atom.Google Scholar
- Polo, S. R. (1961, June 1), Studies on Crystal Field Theory, Volume I—Text, Volume II—Tables, RCA Laboratories, under contract to Electronics Research Directorate, Air Force Cambridge Research Laboratories, Office of Aerospace Research, contract No. AF 19(604)–5541. [Volume II gives date as June 1, 1961.] The symmetry operations are discussed on pp 1–4ff; Clebsch-Gordon coefficients on pp 8.1ff; and excellent tables of Pℓ(z), Pℓ m(z), and Yℓ m are given in the appendix, all in Vol. I.Google Scholar
- Rainville, E. D. (1960), Special Functions, Macmillan, New York, NY. This is just one of the numerous texts written by this outstanding teacher.Google Scholar
- Rose, M. E. (1957), Elementary Theory of Angular Momentum, Wiley, New York, NY, chapter II.Google Scholar
- Sobelman, I. I. (1979), Atomic Spectra and Radiative Transitions, Springer-Verlag, New York, NY. This is a very excellent monograph and we frequently refer to Sobelman’s derivations. Beware of typographical errors!! Pages 1 through 12 are pertinent.Google Scholar
- Watanabe, H. (1966), Operator Methods in Ligand Field Theory, Prentice-Hall, Englewood Cliffs, NJ. Pages 11 and 12 are applicable here; also, the introduction is interesting. We frequently refer to this monograph. Most of the equations are free of typographical errors. Tables of explicit expressions for Yℓ m for 0 ≤ ℓ ≤ 6 are given in appendix 1.2.Google Scholar