- #1
hokhani
- 504
- 8
- TL;DR Summary
- to represent the states without ambiguity in second quantized form
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 $$ \hat {\mathbf c_2} ^{\dagger} \hat {\mathbf c_1} ^{\dagger} |vac\rangle $$ where ##|vac\rangle## is the vaccum state. But these two representations are different in a minus sign, because ##\hat {\mathbf c_1} ^{\dagger} \hat {\mathbf c_2} ^{\dagger} |vac\rangle=-\hat {\mathbf c_2} ^{\dagger} \hat {\mathbf c_1} ^{\dagger} |vac\rangle##, and this issue cause problem in calculations. Which representation is correct?
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