- #1

naima

Gold Member

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- 54

I start from these formulas(transverse electric and magnetic fields)

## E_\perp(r) = \Sigma_i i \mathscr E_{\omega_i}\epsilon_i [\alpha_i e^{i k_i . r}- \alpha^\dagger_i e^{-i k_i . r}]##

and

##B(r) = \Sigma_i i(1/c) \mathscr E_{\omega_i}(\kappa_i \times \epsilon_i) [\alpha_i e^{i k_i . r}- \alpha^\dagger_i e^{-i k_i . r}]##

where epsilon is a unit vector orthogonal to ##\kappa_i = k_i/|k_i|##.

The authors compute their commutator and write it as

##[E_{x \perp}(r),B_y(r')] = -i (\hbar/\epsilon_0) \partial_z \delta(r - r')##

I do not see where this ##\partial_z## comes from.

Have you an idea?

Is it related to FT(f'(z)) = i k FT(f(k))

## E_\perp(r) = \Sigma_i i \mathscr E_{\omega_i}\epsilon_i [\alpha_i e^{i k_i . r}- \alpha^\dagger_i e^{-i k_i . r}]##

and

##B(r) = \Sigma_i i(1/c) \mathscr E_{\omega_i}(\kappa_i \times \epsilon_i) [\alpha_i e^{i k_i . r}- \alpha^\dagger_i e^{-i k_i . r}]##

where epsilon is a unit vector orthogonal to ##\kappa_i = k_i/|k_i|##.

The authors compute their commutator and write it as

##[E_{x \perp}(r),B_y(r')] = -i (\hbar/\epsilon_0) \partial_z \delta(r - r')##

I do not see where this ##\partial_z## comes from.

Have you an idea?

Is it related to FT(f'(z)) = i k FT(f(k))

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