- #1
Einj
- 470
- 59
I have a doubt on the second quantization formalism. Suppose that we have two spin-1/2 fermions which can have just two possible quantum number, 1 and 2. Consider the wave function:
$$
\psi(r_1,r_2)=\frac{1}{\sqrt{2}}\left(\psi_1(r_1)\psi_2(r_2)-\psi_1(r_2)\psi_2(r_1)\right).
$$
The second quantized field is defined as:
$$
\Psi(r)=\sum_{k=1}^2a_k\psi_k(r),
$$
where [itex]a_k[/itex] are the annihilation operators for fermions, i.e. anti-commuting with each other.
What's the action of [itex]\Psi(r)[/itex] on the wave function [itex]\psi(r_1,r_2)[/itex]?
$$
\psi(r_1,r_2)=\frac{1}{\sqrt{2}}\left(\psi_1(r_1)\psi_2(r_2)-\psi_1(r_2)\psi_2(r_1)\right).
$$
The second quantized field is defined as:
$$
\Psi(r)=\sum_{k=1}^2a_k\psi_k(r),
$$
where [itex]a_k[/itex] are the annihilation operators for fermions, i.e. anti-commuting with each other.
What's the action of [itex]\Psi(r)[/itex] on the wave function [itex]\psi(r_1,r_2)[/itex]?