By Bryce S DeWitt
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Lifshitz, “Quantum Mechanics,” pp. 215–221. Addison-Wesley, Reading, Massachusetts, 1958. ‡ See A. de-Shalit and I. Talmi, “Nuclear Shell Theory,” pp. 268–282. Academic Press, New York, 1963. ‡ H. Goldstein, “Classical Mechanics,” pp. 318–338. Addison-Wesley, Reading, Massachusetts, 1950. ‡ See L. Landau and E. Lifshitz, “Quantum Mechanics,” pp. 64–67. Addison-Wesley, Reading, Massachusetts, 1958. ‡ See L. D. Landau and E. M. Lifshitz, “Quantum Mechanics,” pp. 78–106. Addison-Wesley, Reading, Massachusetts, 1958.
We can interpret the eigenvalues εi as approximate excitation energies of the levels i, and call them the self-consistent energies of the levels. From Eqs. 7) it can be seen that the expectation value of H in the trial ground state is If we evaluate the expectation value of H in the state , which is the configuration in which the particle originally in the level i has been excited to the level k, we find that it is If there are a large number of particles, the last two terms on the right of Eq.
This idea is also of importance in the theory of nuclear structure, and may be applicable to He3. Otherwise, these three chapters are meant to illuminate more fully the ideas introduced in the earlier chapters. The last chapter gives a brief discussion of the properties of many-boson systems. Most of the methods used for many-fermion systems can be applied to the many-boson problem, with slight modifications. The physical significance of the results is rather different, although the formalism is so similar.