Group theory and quantum mechanics

If we have two equivalent nuelei in a moleeule, this always results from a molecular symmetry, i.e. at least one symmetry operation exchanges the positions of these two nuclei. There is no reason at all that electrons should prefer one such nucleus rather than the other. Let us focus on molecular orbitals calculated for a fully symmetric Fock operator. Therefore, 

We know how to apply symmetry operations on molecular orbitals (p. 908) and transform them to other functions. 

Under such a symmetry operation the orbital either remains unchanged (like the bonding mentioned above), or changes sign (like the antibonding)- 

The operator a- of the reflection in the plane x = 0 corresponds to the following unitary transformation matrix of the coordinates I 

In both cases the molecular orbital represents an eigenfunction of the symmetry operator with eigenvalues +1 and —1, respectively. 

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Tinkham M 1964 Group Theory and Quantum Mechanics (New York MoGraw-Hill)... 

Kleinian V, Gordon R J, Park H and Zare R N 1998 Companion to Angular Momentum (New York Wiley) Tinkliam M 1964 Group Theory and Quantum Mechanics York McGraw-Hill)... 

M. Tinkham, Group Theory and Quantum Mechanics McGraw-Hill, New York (1964). R. McWeeny, Symmetry An Introduction to Group Theory and its Applications Pergamon, New York (1963). 

B. L. van der Waerden Group theory and quantum mechanics (Berlin-New York, Springer-Verlag, 1974). 

Puska, M. J., Nieminen, R. M., and Manninen, M. (1981). Physical Review B24,3037. Sutton, A. P. (1993). Electronic structure of materials. Oxford University Press. Tinkham, M. (1964). Group theory and quantum mechanics. McGraw-Hill, New York. Vitek, V. and Srolovitz, D. J. (eds) (1989). Atomistic simulations of materials beyond pair potentials. Plenum, New York. 

Tinkham, M. (1964). Group theory and quantum mechanics. McGraw-Hill, New York. Wood, J. H. (1962). Physical Review 126, 517. 

Tinkham Group theory and quantum mechanics (McGraw-Hill). 

The connection between group theory and quantum mechanics will be established in Section 9.7, where the importance of the representations of a group will become evident. Instead of dealing with the matrices of a representation, for many purposes the information provided by their traces... 

Tinkham, M. (1964) Group Theory and Quantum Mechanics. New York McGraw-Hill. Venkataraman, G., Feldkamp, L. A. and Sahni, V. C. (1975) Dynamics of Perfect Crystals. Cambridge, MA MIT Press. 

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