For setting the fermionic state ## |n_1 n_2\rangle## where ##n_i## is the number of particles in the orbital ##i## we can use the following both representations for the state ##|1 1\rangle##: $$ \hat {\mathbf c_1} ^{\dagger} \hat {\mathbf c_2} ^{\dagger} |vac\rangle $$ or $$ \hat {\mathbf c_2}...