Quantum Mechanical Treatment of the Two-Spin System

Appendix 3 Quantum Mechanical Treatment of the Two-Spin System 303... 

This simplified treatment does not account for the fine-structure of the hydrogen spectrum. It has been shown by Dirac (22) that the assumption that the system conform to the principles of the quantum mechanics and of the theory of relativity leads to results which are to a first approximation equivalent to attributing to each electron a spin that is, a mechanical moment and a magnetic moment, and to assuming that the spin vector can take either one of two possible orientations in space. The existence of this spin of the electron had been previously deduced by Uhlenbeck and Goudsmit (23) from the empirical study of line spectra. This result is of particular importance for the problems of chemistry. 

This list of postulates is not complete in that two quantum concepts are not covered, spin and identical particles. In Section 1.7 we mentioned in passing that an electron has an intrinsic angular momentum called spin. Other particles also possess spin. The quantum-mechanical treatment of spin is postponed until Chapter 7. Moreover, the state function for a system of two or more identical and therefore indistinguishable particles requires special consideration and is discussed in Chapter 8. 

Detailed accounts of the two-electron two-orbital model are available elsewhere [1-7]. Here, we present a more formalized pedagogical presentation based on the isomorphism of the spin space and the geminal space used in the model, in effect extending the standard "fictitious spin of 1/2" treatment [10] of a two-level one-particle quantum mechanical system to a "fictitious spins of 0 and 1" treatment of a four-level two-particle system. 

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