Calculation of the Matrix Elements of the Hamiltonian; Orthogonal Spin Functions
In the preceding chapter we have derived the basic formulas for the calculation of the matrix elements of the Hamiltonian and we have discussed the computational aspects of the construction of the representation matrices. The present chapter is devoted to the problem of calculation of the spatial integrals H(P) and I(P) and we shall show how we can combine the use of the spin functions with the given form of the spatial functions. It is convenient to start first with the three methods for the construction of the spin functions: (a) branching-diagram functions, (b) Serber functions, (c) spin-coupled functions. In each case the set of spin functions forms an orthonormal set and the representation matrices are orthogonal matrices. Our treatment will not be comprehensive but we shall present some of the most powerful methods for the calculation of the matrix elements of the Hamiltonian.
KeywordsMatrix Element Spatial Function Representation Matrice Young Tableau Invariant Part
Unable to display preview. Download preview PDF.
- 1.M. Kotani, A. Amemiya, E. Ishiguro and T. Kimura, Tables of Molecular Integrals, Maruzen, Tokyo (1963), Chap. 1.Google Scholar
- 2.T. Yamanouchi, Proc. Phys. Math. Soc. Japan 20, 547 (1938).Google Scholar
- 3.A. Amemiya, Bull. Phys. Math. Soc. Japan 17, 67 (1943).Google Scholar
- 4.M. Kotani, K. Ohno, and K. Kayama, “Quantum Mechanics of Electronic Structure of Simple Molecules,” in Encyclopedia of Physics, Vol. 37/2, Molecules 2, Ed. S. Flügge, Springer-Verlag, Berlin (1961), p. 1.Google Scholar
- 9.R. Pauncz, (unpublished).Google Scholar