Читать книгу Quantum Mechanics for Nuclear Structure, Volume 2 - Professor Kris Heyde - Страница 16

The Schwinger representation and its associated basis leads directly to a spinor function basis for SU(2):

where u and are independent functions. We require u and to satisfy (again, ℏ≡1)

Thus, we deduce the realisation

It follows from equations (1.148), (1.149) and (1.147) that

and

It should be noted that are elements of a complex function space which is formally developed in section 1.17 under the title of the Bargmann representation, i.e. this function space is known as Bargmann space. These bases are irreducible (unlike Cartesian tensors).