By A. L. Goodman
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Extra info for Band Structure and Nuclear Dynamics. Proceedings of the International Conference on Band Structure and Nuclear Dynamics Tulane University, New Orleans
See also ^ ' . In the more recent work, it has been shown how such a variational statement combined with suitable kinematical constraints, arising mainly from commutation relations, provides a complete scheme of quantum mechanics and that in approximate form it leads to the kind of approach to collective motion which has been the writer's stock-in-trade. In fact, the variational approach was also used in a number of model calculations (see 5 2) f o r instance) without, however, the full awareness of its role in the structure of the theory.
We introduce a linear, unitary (ultimately orthogonal) transformation from the original, kinematical, bosons B. 30) l 'λ . , a. 27), which can be handled exactly within the context of the direct product basis constructed from the B. i", becomes a. a. 32) λμ »£ J and can be dealt with in the calculations which follow (which will utilize the direct product basis constructed from the S^) only by partial expansion. [> To illustrate our viewpoint we consider an approximation which has some formal analogy with the real physical problem involving the s and d bosons.
For a single j level, it becomes exact. (ii) If the full complement of bosons is retained, but only single excitations are allowed, and the equations are linearized, we obtain an approximation equivalent to the T. D. approximation. 28 A. KLEIN D. Concluding Observations. We should now be able to understand why the mapping described in subsection B is adequate for the purposes for which it is intended. Thus the bosons bT and b. 2) will play the same role as the kinematical bosons B^ of the pairing discussion.
Band Structure and Nuclear Dynamics. Proceedings of the International Conference on Band Structure and Nuclear Dynamics Tulane University, New Orleans by A. L. Goodman