13 Ladder systems
13.1 Raising and lowering operators
In Section 12.1 we considered a quantum system of arbitrary spin s. For a given value of s, we constructed a “ladder” of Sx eigenstates. These states were linked by “raising” and “lowering” operators S±. The properties of the raising and lowering operators (which followed from the commutation relations between the spin components) completely determined the structure of the Hilbert space s for the spin-s system.
In this chapter, we investigate a similar type of quantum system that we will call ...