Second-quantization and the many-body problem

There are many excellent text books on second-quantization techniques to which we refer the interested reader for a more thorough discussion than that given here. We mention, in particular  

In this section, we briefly describe the second quantized formalism giving sufficient details for the application which we describe in this monograph. This also serves to establish our notation. 

We begin by recording something of the historical origins of the second quantization method which should help the reader understand its importance in the study of many-body systems.  

Let us observe that the Schrddinger equation can be easily written down for an atom or, more particularly, a molecule of arbitrary complexity. (We also note that there is no known limit to the complexity of possible molecular species). The difficulty is usually said to lie not in writing down the appropriate eigenvalue problem 

We assume that nearly all the negative-energy states are occupied, with one electron in each state in accordance with the exclusion principle of Pauli. 

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