Minimum uncertainty relation for correlated electron state of cooper pair

摘要

We point out that the BCS ground state of correlated electrons makes the uncertainty relation #DELTA#z_1#DELTA#z_2 >= (1/2)|| reach its minimum value, where z_1 = (1/2)(b_k + b_k~(dagger)), z_2 = (i/2)(b_k~(dagger) - b_k), b_k = c_(-k arrow down)c_(k arrow up) and b_k~(dagger) = c_(k arrow up)~ dagger)c_(-k arrow down)~(dagger) denote Cooper pair annihilation and creation operators, z_3 = (1/2)(c_(k arrow up)~(dagger)c_(k arrow up) + c_(-k arrow down)~(dagger)c_(-k arrow down) - 1) centre dot b_k, b_k~(dagger) and z_3 obey a closed pseudospin SU(2) Lie algebra. So, the BCS state is the state most approaching the "classical" situation.