In coordinate representation in QM probality density is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\rho(\vec{r})=\psi^*(\vec{r})\psi(\vec{r})[/tex]

in RSQ representation operator of density of particles is

[tex]\hat{n}(\vec{r})=\hat{\psi}^{\dagger}(\vec{r})\hat{\psi}(\vec{r})[/tex]

Is this some relation between this operator and density matrix?

Operator of number of particles is

[tex]\hat{N}=\int d^3\vec{r}\hat{\psi}^{\dagger}(\vec{r})\hat{\psi}(\vec{r})[/tex]

Why I can now use

[tex]\hat{\psi}^{\dagger}(\vec{r})=\sum_k\hat{a}_k^{\dagger}\varphi^*_k(\vec{r})\qquad \hat{\psi}(\vec{r})=\sum_k\hat{a}_k\varphi_k(\vec{r})[/tex] ?

where [tex]\{\varphi_k\}[/tex] is complete ortonormal set.

Thanks

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# Representation of second quantization

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