Second Quantization. Single Nucleon and Two-Body Operators
Igal Talmi
In Section 14 we considered many nucleon states as the antisymmetrized products of single nucleon wave functions. Due to the antisymmetrization, the wave function is completely determined by the single nucleon states which are occupied. This suggests that a direct way to deal with many nucleon states is by using a representation in which occupied single nucleon states, rather than nucleon coordinates, are specified. To do this we have to define a fixed set of single nucleon states. The results ( 14.6 ), ( 14.7 ) indicate that we should provide matrix elements of relevant single nucleon operators, calculated in the basis of these single nucleon wave functions. The results ( 14.11 ), ( 14.12 ) and ( 14.13 ) show that we should also calculate matrix elements of two-body operators in the basis of single nucleon wave functions. These calculations should be performed in the way shown in preceding sections. They are carried out in configuration space by using wave functions of space coordinates as well as spin (and isospin) variables. Equipped with these matrix elements we can introduce the representation in terms of occupied states by using the formalism of second quantization. This formalism will now be briefly described without entering into serious discussions and rigorous proofs.
Routledge eBooks•Oct 6, 2017•0 citations