# Quantization of electromagnetic field

• I
Hello everybody,

It is known that electric field operator is shown as

$\hat{E}(r,t)=-i\sum_{k,\lambda}\sqrt{\frac{\hbar\omega_k}{2\epsilon V}}\left(a(t)^\dagger_{k,\lambda} e^{-ik.r} - a(t)_{k,\lambda} e^{ik.r} \right) \hat{e}_{k,\lambda}$

But if I need to represent an electrostatic field in a quantized form, how to proceed?

Thank you everybody.

Apparently you have mixed in your expression above the electric field in the quantized and not quantized forms. AFAIK the electric field operator(electrostatic field is not a meaningful distinction here) is: ##E(r)=i\sum_{k,\lambda}\sqrt{\frac{\hbar\omega}{2\epsilon V}}\left(ξ(\lambda)a^{(\lambda)}(k) e^{ik.r} - ξ(\lambda)a^{\dagger(\lambda)}(k) e^{-ik.r} \right) ##

Last edited:
Apparently you have mixed in your expression above the electric field in the quantized and not quantized forms. AFAIK the electric field operator(electrostatic field is not a meaningful distinction here) is: ##E(r)=i\sum_{k,\lambda}\sqrt{\frac{\hbar\omega}{2\epsilon V}}\left(ξ(\lambda)a^{(\lambda)}(k) e^{ik.r} - ξ(\lambda)a^{\dagger(\lambda)}(k) e^{-ik.r} \right) ##