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## Main Question or Discussion Point

Hi. In second quantization (not QFT or anything advanced like that) we have the particle density [itex]\hat n(x)=\Psi^{\dagger}(x)\Psi(x)[/itex] using the usual field creation/annihilation operators. For a single particle we obtain for the expectation value in the state [itex]|\psi\rangle[/itex]: [itex]\langle \psi | \Psi^{\dagger}(x)\Psi(x) | \psi\rangle=|\psi(x)|^2[/itex]. So does this mean that I should think of [itex]\Psi(x)[/itex] as the second quantized wave function? What is the significance of this formal similarity between the wave function and the creation/annihilation operators?

It seems that whenever you have something in first quantization written in terms of a wave function (i.e. the probability current density), you can replace the wave functions by the creation/annihilation operators and get the second quantized operator...

It seems that whenever you have something in first quantization written in terms of a wave function (i.e. the probability current density), you can replace the wave functions by the creation/annihilation operators and get the second quantized operator...