Angular momentum wave functions constructed by projection operators. Technical Note No. 12
The conventional method of constructing wave functions of pure angular momentum for a composite system is based on the idea of coupling the angular momenta of the constituents. Instead of this synthetic method, an analytical approach is here introduced. It is pointed out that an arbitrary trial wave function for the total system in a unique way must be resolvable into orthogonal components of pure angular momentum associated with different quantum numbers. A particular component can be selected by means of certain 'projection operators', which annihilate all components except the one desired. Such a projection operator is simply a product of commuting factors, each one of which annihilates a specific eigenfunction to the angular momentum under consideration. Physically this idea is of importance, since one can now start out from a rough model wave function based essentially on qualitative arguments, for instance of the independent-particle type, and then obtain a mathematically and physically much better trial function by selecting the particular component of the original function which has the correct symmetry type desired. The projection operators are studied in some detail both as products and in expanded form. The case of degenerate subspaces of the same angular momentum quantum numbers is discussed, and the problem of constructing an orthogonal subset of functions is solved by a simple elimination procedure; the connection with the conventional seniority idea is briefly discussed.
- Research Organization:
- Uppsala Univ. (Sweden). Quantum Chemistry Group
- Sponsoring Organization:
- U.S. Air Force, Aeronautical Research Lab., Wright Air Development Center (United States)
- DOE Contract Number:
- AF61(514)-1200
- NSA Number:
- NSA-13-000802
- OSTI ID:
- 4302760
- Report Number(s):
- NP-6982
- Country of Publication:
- Sweden
- Language:
- English
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