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

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Representation of second quantization

Loading...

Similar Threads - Representation second quantization | Date |
---|---|

I Why the second quantization Hamiltonian works? | Feb 21, 2018 |

A Who wrote "Ch 6 Groups & Representations in QM"? | Jan 11, 2018 |

B Gravity and spin 2 representation | Jan 6, 2018 |

A Transformation of position operator under rotations | Nov 27, 2017 |

I Dirac equation solved in Weyl representation | Nov 15, 2017 |

**Physics Forums - The Fusion of Science and Community**