A Solutions to Selected Exercises

By comparing the components of (|a〉〈b|) ⊗ (|c〉〈d|) and (|a〉 ⊗ |c〉)(〈b| ⊗ 〈d|), we readily verify the equality of these matrices.

2.2 The time development operator is

U(t) = eiωtσy/2 =

( cosωt/2 sinωt/2

− sinωt/2 cosωt/2

) .